The effect of oxygen storage capacity on the dynamic characteristics of an automotive catalytic converter

Energy Conversion and Management 49 (2008) 3292–3300

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Energy Conversion and Management journal homepage: www.elsevier.com/locate/enconman

The effect of oxygen storage capacity on the dynamic characteristics of an automotive catalytic converter Tariq Shamim * Department of Mechanical Engineering, The University of Michigan-Dearborn, Dearborn, MI 48128-2406, United States

a r t i c l e

i n f o

Article history: Available online 3 July 2008 Keywords: Engine emissions Engine exhaust after-treatment Dynamic behavior Numerical simulations

a b s t r a c t Automotive catalytic converters, which are employed to reduce engine exhaust emissions, are subjected to highly transient conditions during a typical driving cycle. These transient conditions arise from changes in driving mode, the hysteresis and flow lags of the feedback control system, and result in fluctuations of air–fuel ratio, exhaust gas flow rates and temperatures. The catalyst performance is also strongly influenced by the oxygen storage capacity. This paper presents a computational investigation of the effect of oxygen storage capacity on the dynamic behavior of an automotive catalytic converter subjected to modulations in exhaust gases. The modulations are generated by forcing the temporal variations in exhaust gases air–fuel ratio, gas flow rates and temperatures. The study employs a single-channel based, one-dimensional, non-adiabatic model. The results show that the imposed modulations cause a significant departure in the catalyst behavior from its steady behavior, and the oxygen storage capacity plays an important role in determining the catalyst’s response to the imposed modulations. Modulations and oxygen storage capacity are found to have relatively greater influence on the catalyst’s performance near stoichiometric conditions. Ó 2008 Elsevier Ltd. All rights reserved.

1. Introduction To meet the progressively stringent emission regulations, the oxygen storage capacity (OSC) has been established to be a key parameter for the appropriate catalytic performance of commercial three-way catalytic converters [1–3]. The OSC allows the storage of the extra oxygen in the catalyst substrate under fuel lean conditions and the release of it under rich conditions [4]. The released oxygen may participate in the reactions with the reducing agents, thereby increasing the conversion of CO and HC in a rich exhaustgas environment [4]. Such a capacity is developed in the modern catalyst by coating its substrate with a wash-coat material containing ceria. The OSC is recognized as an important mechanism affecting catalyst behavior during vehicle’s acceleration and deceleration. It also affects the catalyst performance during other transient conditions, which mainly arise from the hysteresis and flow lags of the feedback control system. The transients result in fluctuations of gas flow rates, compositions and temperatures. These transients make the catalyst behavior differ significantly from that under steady state conditions [5–12]. Due to its practical significance, the investigation of the catalyst dynamic behavior has been a subject of active research for more than two decades. Particularly, the effects of air–fuel ratio (A/F) * Tel.: +1 313 593 0913; fax: +1 313 593 3851. E-mail address: [email protected] 0196-8904/$ - see front matter Ó 2008 Elsevier Ltd. All rights reserved. doi:10.1016/j.enconman.2007.11.015

and composition modulations have been studied by many researchers [8–12]. These studies determined that modulations have both beneficial and harmful effects on pollutant conversion depending upon the catalyst type, driving mode, exhaust conditions, and pollutants to be removed [8]. The coupled effect of the OSC and imposed modulation is important since it is well known that the limitations of the OSC restricts the duration and amplitudes of the rich or lean excursions that a catalyst can be subjected without reducing its effectiveness [13,14]. A number of researchers investigated the effect of the OSC on the catalyst performance under A/F modulations [5–7,10]. Shamim and Medisetty [10] found that the catalyst is more sensitive and its conversion response to the imposed A/F modulations is relatively larger in the absence of the OSC. Silveston reported that the OSC increases the CO conversion rate when the catalyst is subjected to composition modulation [5]. Kocˇ´ı et al. [12] investigated the effects of the OSC during the forced modulation of oxygen concentration on the light-off characteristics of the catalyst. They found that the modulation result in lowering of the light-off temperature depending upon the level of the OSC. With the decreasing OSC, higher modulation amplitudes are necessary to reach the light-off. In summary, the past studies indicate a strong impact of the OSC on the catalyst performance under oscillatory conditions. However, a clear understanding of the effect of the OSC on the catalyst response to various kinds of imposed modulations is still

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Nomenclature C jg

gas phase concentration of species j, mol/m3

C js

3

surface concentration of species j, mol/m specific heat of gas, J/(kg K) specific heat of substrate, J/(kg K) geometric surface area, m2/m3 heat of reaction of species k, J/mol heat transfer coefficient between flow and substrate, J/ (m2 s K) heat transfer coefficient between substrate and atmosphere, J/(m2 s K) mass transfer coefficient for species j, m/s reaction rate of kth reaction, mol/(m2 s) external surface to volume area ratio, m2/m3

C pg C ps Ga DHk hg h1 kmj Rk Sext

lacking. Hence the objective of the present study is to conduct a systematic investigation of the influence of OSC on the catalyst performance during oscillatory conditions. The oscillatory conditions are simulated by considering the catalyst subjected to temporal modulation in A/F, exhaust gas composition and exhaust gas temperature. In the simulations, the effects of various imposed modulations are isolated and decoupled from each other. 2. Mathematical formulation The governing equations were developed by considering the conservation of mass, energy and chemical species. Using the assumptions and notations listed elsewhere [15], the governing conservation equations for a typical single channel may be written as follows: The gas phase energy equation:



qg C pg e

oT g oT g þ vg ot oz



¼ hg Ga ðT g  T s Þ

ð1Þ

The gas phase species equations (for 7 species):

e

oC jg oC jg þ vg ot oz

! j

¼ km Ga ðC jg  C js Þ

ð2Þ

The surface energy equation:

ð1  eÞqs C ps þ Ga

nreaction X

oT s o2 T s ¼ ð1  eÞks 2 þ hg Ga ðT g  T s Þ  h1 Sext ðT s  T 1 Þ ot oz n

Rk ðT s ; C 1s ; . . . ; C s species Þ  DHk

ð3Þ

k¼1

The surface species equations (for 7 species):

ð1  eÞ

oC js ot

j

N

¼ km Ga ðC jg  C js Þ  Ga Rj ðT s ; C 1s ; . . . ; C s species Þ

ð4Þ

The superscript j in species equations varies from 1 to 7, representing the following species: CO, NO, NH3, O2, C3H6, H2 and C3H8. In addition to these species, the kinetic expressions also include CO2, H2O and N2. A 13-step chemical mechanism was used to model the heterogeneous surface chemistry [15]. The conservation equation for the surface oxygen storage mechanism is represented by Eq. (4) excluding the convective mass transport term. The catalyst’s oxygen storage capacity was modeled by using a 9-step mechanism of Otto [16], which is listed below:

1 hSi þ O2 ! hOSi Site oxidation 2 hOSi þ CO ! hSi þ CO2 Site reduction by CO H2 O þ CO ! H2 þ CO2 Water—gas shift

ðR-1Þ ðR-2Þ ðR-3Þ

t T1 Tg Ts vg z

time, s ambient temperature, K gas temperature, K substrate temperature, K gas flow velocity, m/s coordinate along catalyst axis, m

Greek symbols e void volume fraction thermal conductivity of substrate, J/(m s K) ks qg gas density, kg/m3 qs substrate density, kg/m3

hOSi þ H2 ! hSi þ H2 O Site reduction byH2 ðR-4Þ  a CHa þ H2 O ! CO þ 1 þ ðR- 5Þ  H2 Steam reforming 2   3 1 3 CHa þ hOSi ! hSi þ C þ CO þ a H2 Reduction by HC 2 2 4 ðR- 6Þ C þ O2 ! CO2

Coke burn-off 1 hSi þ NO ! hOSi þ N2 NO storage 2 2 2 3 hOSi þ NH3 ! hSi þ NO þ H2 ONH3 5 5 5

ðR- 7Þ ðR- 8Þ Site reduction

ðR-9Þ

where a is hydrogen-to-carbon ratio of the hydrocarbon. The details of the chemical mechanisms and the corresponding kinetic data are given elsewhere [15]. The heat and mass transfer coefficients in the above equations are calculated from the conventional correlations of Nusselt and Sherwood numbers [17]. The governing equations were discretized by using a non-uniform grid and employing the control volume approach with the central implicit difference scheme in the spatial direction. A standard tridiagonal matrix algorithm with an iterative successive line under relaxation method was used to solve the finite difference equations. The spatial node size ranging from 0.1693 mm to 19.32 mm and the time step of 0.001 second were employed. The grid insensitivity of results was ensured by performing a sensitivity study. Details of the solution procedure are described elsewhere [15]. 3. Results and discussion The numerical model was validated by comparing with the experimental measurements as reported in our previous paper [15]. The validation results showed the suitability of the model in simulating the transient performance of catalyst. The catalyst used for the present study was palladium-based and had a length of 3 cm, cross-sectional area of 86.0254 cm2, cell density of 62 cells/cm2, and wall thickness of 0.1905 mm. The catalyst aging conditions were similar to those of Ref. [17]. The gas mass flow rate was 1.417  102 kg/s with 9.9205  106 kg/s CO, 2.0834  106 kg/s total HC, and 8.0280  106 kg/s NO, and the stoichiometric value of A/F was 14.51. The feed gas temperature was 327 °C (600 K). The influence of exhaust gas modulation on the catalyst dynamic behavior was investigated by considering a steady operating catalyst suddenly subjected to transient effects. The transient effects were simulated by sinusoidal and independent variations of A/F, composition and temperature of the exhaust gas entering the catalyst. The A/F was varied by changing the oxygen concentration and keeping the exhaust composition of CO, HC and NO

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concentrations unchanged. The exhaust composition was modulated by individually varying the concentrations of CO, HC and NO, while keeping the A/F constant through corresponding variations in oxygen concentration. During these oscillations, other inlet conditions remained unchanged. The effect of OSC on the catalyst performance during imposed modulation was investigated by considering the catalyst’s response with and without OSC effect.

a

Near Stoichiometric (A/F= 14.7) Lean (A/F= 17.5) Rich (A/F= 12.5) 100 80 60 40

CO

20

3.1. Effect of sinusoidal modulation in air–fuel ratio Conversion Efficiency(%)

80 60 40 20

HC

0 100 80 60 40 20

NO

0

Air/Fuel Ratio

18 16 14 12 0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

4.0

3.5

4.0

Time Period

b

Near Stoichiometric (A/F= 14.7) Lean (A/F= 17.5) Rich (A/F= 12.5) 100 80 60 40

CO

20

Conversion Efficiency (%)

0 100 80 60 40 20

HC

0 100 80 60 40 20

NO

0 18

Air/FuelRatio

Fig. 1 shows the results of the imposed sinusoidal modulation in A/F near stoichiometric conditions for both OSC and non-OSC cases. During the simulations, the A/F, initially set at 14.7, is varied sinusoidally with a frequency of 1 Hz and amplitude of 5%. The A/F ranges between 13.97 and 15.43, and the catalyst undergoes a transition between rich and lean operating conditions during each modulation time period. The results of the non-OSC case, plotted in Fig. 1a, show that the catalyst conversion performance of all three species responds to the imposed A/F modulation. The response amplitude is the largest for the CO conversion. The response exhibits a square wave pattern rather than that of a sinusoidal. The CO conversion efficiency fluctuates between 0% and 99.9%. The modulation results in a significant decrease in the CO conversion. The time-average conversion efficiency, which is obtained by considering the cumulative pollutant species in and out of the catalyst during the first four cycles, is decreased by 38.2% below its steady state value of 93.3% (see Table 1). For these operating conditions and the CO/HC ratio, the HC conversion is relatively low during the initial steady state conditions. It is, however, improved by the imposed modulation. The result, listed in Table 1, shows that the HC time-average conversion efficiency exhibits an increase of 49% from its steady state value. The catalyst’s response is unsmooth and is asymmetric with respect to its initial steady state value. The catalyst response amplitude (defined as the difference of peak and trough values of conversion efficiency) is approximately 65.6%, which indicates the strong sensitivity of the HC conversion to the imposed modulations. The effect of imposed modulation on NO emission conversion is also significant but it is relatively lower (response amplitude is 36.2%). The NO conversion response is relatively smoother with sinusoidal profile during the lean zone. The NO conversion efficiency reaches the peak value of 100% during the rich zone and remains insensitive to the A/F variations in that zone. Overall, the imposed modulation has a positive influence on NO conversion. The NO time-average conversion efficiency increases by 9% from its steady state value. The results of the corresponding OSC case, plotted in Fig. 1b, show that the effects of imposed A/F modulation on the catalyst performance with the OSC are generally similar to that of the non-OSC case. The inclusion of OSC mainly results in a slight decrease of the response amplitudes and makes the catalyst relatively less sensitive to the imposed modulation. With a 10% reduction in the response amplitude, the effect of the OSC is greater on the HC conversion response. The effect is the lowest on the CO conversion, which exhibits similar response and response amplitude as that of the non-OSC case. The catalyst’s conversion performance depends greatly on the mean A/F. Hence, the catalyst’s responses to A/F modulation in rich and lean zones are also investigated. The lean zone results were obtained by initially setting the A/F at 17.5. The catalyst is subjected to sinusoidal modulations in the A/F with a 1 Hz frequency and 5% amplitude. The resulting A/F ranges between 16.63 and 18.38, which keeps the A/F in the lean zone during the imposed modulation. Under these conditions, there is a significant differ-

0 100

16 14 12 0.0

0.5

1.0

1.5

2.0

2.5

3.0

Time Period Fig. 1. Catalyst response to sinusoidal modulations in A/F: (a) without OSC; (b) with OSC. (Mean exhaust temperature = 600 K, frequency = 1 Hz, amplitude = 5%.)

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T. Shamim / Energy Conversion and Management 49 (2008) 3292–3300 Table 1 Comparison of time-average conversion efficiencies for exhaust gas modulations (mean exhaust gas temperature = 600 K) Mean conversion efficiency (%)

Air/fuel modulation (amp = 5%, freq = 1 Hz)

Temperature modulation (amp = 10%, freq = 0.01 Hz)

CO modulation (amp = 50%, freq = 1 Hz)

HC modulation (amp = 50%, freq = 1 Hz)

NO modulation (amp = 50%, freq = 1 Hz)

Steady state

CO

Near Lean Rich Near Lean Rich Near Lean Rich Near Lean Rich Near Lean Rich Near Lean Rich

stoichiometric

stoichiometric

stoichiometric

stoichiometric

stoichiometric

stoichiometric

ence between the steady state values of NO conversion efficiency for OSC and non-OSC cases. The difference between these values is mainly due to inaccuracies of kinetic parameters which were obtained from the experimental measurements of the OSC cases. Hence, the NO conversion efficiency value for the non-OSC case may not be quantitatively accurate and should only be used for qualitative trends. The imposed A/F modulation affects NO conversion efficiency, which responds with a significant increase for the OSC case. The increase is owing to the enhancement of the reaction rates of (R-2) and (R-8) of the OSC mechanism. For the non-OSC case, there is no significant effect on the NO conversion efficiency from its steady state value, which is already high. The A/F modulation reduces the difference between the catalyst NO conversion performance for the OSC and non-OSC cases which was large during the steady state conditions. Under these conditions, the CO and HC conversions are very high and remain insensitive to the imposed A/F modulation for both OSC and non-OSC cases. The rich zone results were obtained by initially setting the A/F at 12.5. The catalyst is subjected to sinusoidal modulations in the A/F with a 1 Hz frequency and 5% amplitude. The resulting A/F ranges between 11.88 and 13.13. Under rich conditions, the catalyst conversion performance is not sensitive to the imposed A/F modulation. Particularly, the CO and NO conversions are very insensitive and remain at their steady state values. The HC conversion shows a slight response to the imposed modulation (response amplitude is 2%). The OSC has no effect on the catalyst’s response to the imposed modulation. Such a response was expected since the catalyst, under rich operating conditions, does not have any stored O2, which can be released to improve the conversion performance. 3.2. Effect of modulation in exhaust composition The catalyst’s response to composition modulation was investigated by considering a steady state catalyst subjected to sinusoidal modulation in exhaust composition. 3.2.1. Modulation in CO concentration Fig. 2 shows the results of the imposed modulation in CO concentration at the catalyst inlet. The CO concentration is varied sinusoidally with a frequency of 1 Hz and amplitude of 50% with the inlet CO mass flow rate ranging between 4.9603  106 kg/s and 1.4881  105 kg/s.

HC

NO

Non-OSC

OSC

Non-OSC

OSC

Non-OSC

OSC

55.14 100 0 90.21 99.94 0 93.29 99.94 3.77 92.02 100 29.57 91.90 100 15.47 93.30 99.90 0

56.64 99.92 0 91.18 99.92 0 94.34 99.93 3.77 94.34 99.93 29.12 94.48 100 15.97 94.50 99.90 0

77.00 93.48 78.59 31.37 93.30 78.59 27.74 93.51 73.17 28.24 93.50 63.48 25.24 93.51 66.61 27.72 93.51 78.61

81.22 93.45 78.59 42.17 93.37 78.59 39.35 93.50 73.17 37.37 93.49 63.63 39.77 93.61 66.55 39.84 93.61 78.61

86.72 39.56 99.52 80.63 30.05 99.52 78.57 37.58 99.41 89.19 38.72 99.74 80.43 38.37 99.67 77.70 38.70 99.50

85.09 38.80 99.52 84.71 28.26 99.52 87.81 31.39 99.41 79.41 28.79 99.73 80.95 0.70 99.67 81.60 0.80 99.50

Fig. 2a shows the results of the non-OSC case. The results near stoichiometric conditions show that the CO and HC conversion efficiencies respond to the imposed modulation with small amplitudes. The modulation has no appreciable effect on the catalyst’s CO and HC conversion performances. However, the modulation affects NO conversion (response amplitude is 7%) since the NO reduction by CO (CO + NO ? CO2 + 1/2N2) is the significant contributor to the total NO conversion. Overall, the time-average value of the NO conversion efficiency is slightly improved by the CO. Similar to the non-OSC case, the imposed CO modulation has no effect on the catalyst CO and HC conversions for the OSC case as well (see Fig. 2b). The modulation improves the NO conversion from its steady state value. The inclusion of the OSC effect makes the catalyst relatively more sensitive to the imposed modulation (particularly the NO conversion, which has 3.7% higher response amplitude for the OSC case). The increase in time-average conversion efficiency and sensitivity for the OSC case is caused by an increase of reaction between N2 and the site hSi (reaction R-8), which is effected by an increase of reaction (R-2) and the corresponding higher availability of site hSi. Under lean conditions, as mentioned earlier, there is a significant difference between the steady state values of NO conversion efficiency for OSC and non-OSC cases. The imposed CO modulation affects only NO conversion, which responds with amplitudes of 25.7% and 24% for non-OSC and OSC cases respectively. The catalyst response to the imposed modulation depicts a delay for the OSC case, which is not present for the non-OSC case. The response delay is owing to the oxidation of CO through OSC mechanism. After the initial delay, the NO conversion responds to the imposed CO modulation. Overall, the modulation results in a significant increase of NO conversion efficiency for the OSC case, which is owing to the increase in the reaction rates of the NO reduction by CO (CO + NO ? CO2 + 1/2N2), and reactions (R-2) and (R-8) of the OSC mechanism. For the non-OSC case, there is no significant effect on the NO conversion efficiency from its steady state value, which is already high. Similar to the A/F modulation, the CO modulation also reduces the difference between the catalyst NO conversion performance for the OSC and non-OSC cases which was large during the steady state conditions. Under rich conditions, there is no appreciable effect of OSC on the catalyst’s performance during steady state and the CO modulating cases. As mentioned earlier, such a response was expected since the catalyst, under rich operating conditions, does not have

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T. Shamim / Energy Conversion and Management 49 (2008) 3292–3300

a

any stored O2, which can be released to improve the conversion performance. For both OSC and non-OSC cases, the imposed CO modulation has a positive effect on CO conversion (an increase of time-average conversion efficiency by 3.8%), a negative effect on HC conversion (a decrease of time-average conversion efficiency by 5%), and no effect on NO conversion.

Near Stoichiometric (A/F= 14.7) Lean (A/F= 17.5) Rich (A/F= 12.5) 100 80 60 40

CO

20

Conversion Efficiency (%)

0 100 80 60 40 20

HC

0 100 80 60 40 20

NO

0

Inlet CO (%)

0.12 0.09 0.06 0.03 0.00 0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

4.0

3.5

4.0

Time Period

b

Near Stoichiometric (A/F= 14.7) Lean (A/F= 17.5) Rich (A/F= 12.5) 100 80 60 40

CO

20

Conversion Efficiency (%)

0 100 80 60 40 20

HC

0 100 80 60 40 20

NO

0

Inlet CO (%)

0.12 0.09 0.06 0.03 0.00 0.0

0.5

1.0

1.5

2.0

2.5

3.0

Time Period Fig. 2. Catalyst response to sinusoidal modulations in inlet CO concentration: (a) without OSC; (b) with OSC. (Mean exhaust temperature = 600 K, frequency = 1 Hz, amplitude = 50%.)

3.2.2. Modulation in HC concentration Fig. 3 presents the results for the catalyst subjected to modulations of HC concentration at the catalyst inlet. The HC concentration is varied sinusoidally with a frequency of 1 Hz and amplitude of 50% with the inlet HC mass flow rate ranging between 1.0417  106 kg/s and 3.1251  106 kg/s. Fig. 3a shows the results of the non-OSC case. Near stoichiometric conditions, all three conversion efficiencies are sensitive to the imposed modulation, with the HC conversion being the most sensitive (response amplitude 38.4%) and the CO conversion being the least sensitive (response amplitude 8.5%). The response is cyclic but not sinusoidal. The HC conversion efficiency shows some discontinuity near the trough values. This discontinuity is not visible in the outlet HC concentration and is highlighted in the HC conversion efficiency owing to the phase difference between the inlet and outlet HC concentrations. The discontinuity is also exhibited by the NO conversion response, which responds sinusoidally with the amplitude of 17.4% during a part of the modulating cycle, and then jumps to a higher value and stays there for the remaining part of the modulating cycle. This discontinuity in the response occurs near the peak inlet HC and is effected by the reactions involving NO reduction by the HC. The NO conversion efficiency jumps back to the lower value and starts fluctuating again at the beginning of the next modulating cycle. Overall, the modulation results in small reduction of CO conversion (1.3%) and a very small increase of HC conversion (0.5%). The modulation has a stronger and positive effect on the NO conversion (an increase of 11.5% from the steady state value). The sensitivity of the NO conversion on HC concentration indicates the significance of NO reduction by HC, which is included in the reaction mechanism of the present study. The inclusion of OSC makes the catalyst response smoother and more sinusoidal. The discontinuity in the non-OSC case disappears (see Fig. 3b). The catalyst’s CO and HC conversion performances become relatively less sensitive and the NO conversion becomes more sensitive to the imposed modulation. Compared to the nonOSC case, the response amplitudes are 3.7% and 2% lower for the CO and HC conversions respectively. The response amplitude is 8.2% higher for the NO conversion. The higher sensitivity of NO conversion is owing to the indirect effect of the HC modulation on reaction (R-8) through other reactions (mainly (R-2), (R-3), (R4), (R-5), and (R-6)) of the OSC mechanism. The effect of modulation on the time-average conversion efficiencies is different from that of the non-OSC case since the OSC mechanism also contributes to the conversion performance. The modulation results in a decrease of 0.2%, 2.5% and 2.2% for CO, HC and NO conversions respectively. Similar to the CO modulation, the major effect of the OSC during the imposed HC modulation is on the NO conversion, which is effected by reaction (R-8) of the OSC mechanism. Under lean conditions, only NO conversion is sensitive to the imposed HC concentration modulation. There is no significant influence on CO and HC conversions for both OSC and non-OSC cases. Similar to the CO modulation, the catalyst response to the imposed modulation depicts a delay for the OSC case, which is not present for the non-OSC case. The response delay is owing to the oxidation of HC through OSC mechanism. After the initial delay, the NO conversion responds to the imposed HC modulation. The modulation improves the NO conversion significantly for the OSC case, which is owing to the increase in the reaction rates of the NO reduction by HC, and reactions (R-2), (R-3), (R-4), (R-5), (R-6),

T. Shamim / Energy Conversion and Management 49 (2008) 3292–3300

a

and (R-8) of the OSC mechanism. For the non-OSC case, there is no significant effect on the NO conversion efficiency from its steady state value, which is already high. The HC modulation also reduces the difference between the catalyst NO conversion performance for the OSC and non-OSC cases which is large during the steady state conditions. Under rich conditions, the catalyst’s CO and HC conversions are very responsive to the imposed HC modulation for both non-OSC and OSC cases. The NO conversion remains high and is not much responsive to the imposed modulation. The modulation results in a 29.6% increase for the CO conversion and a 15% decrease for the HC conversion. With the exception of small changes in the response amplitudes, there is no appreciable effect of the OSC on the catalyst’s performance during the HC modulation under rich conditions.

Near Stoichiometric (A/F= 14.7) Lean (A/F= 17.5) Rich (A/F= 12.5) 100 80 60 40

CO

20

Conversion Efficiency (%)

0 100 80 60 40 20

HC

0 100 80 60 40 20

NO

0

Inlet hC (PPM)

500 400 300 200 100 0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

4.0

3.5

4.

Time Period

Near Stoichiometric (A/F= 14.7)

b

Lean (A/F= 17.5) Rich (A/F= 12.5) 100 80 60 40

CO

20

Conversion Efficiency (%)

0 100 80 60 40 20

HC

0 100 80 60 40 20

NO

0

Inlet HC (PPM)

500 400 300 200 100 0.0

3297

0.5

1.0

1.5

2.0

2.5

3.0

Time Period Fig. 3. Catalyst response to sinusoidal modulations in inlet HC concentration: (a) without OSC; (b) with OSC. (Mean exhaust temperature = 600 K, frequency = 1 Hz, amplitude = 50%.)

3.2.3. Modulation in NO concentration Fig. 4 presents the results for the catalyst subjected to modulations of NO concentration at the catalyst inlet. The NO concentration is varied sinusoidally with a frequency of 1 Hz and amplitude of 50% with the inlet NO mass flow rate ranging between 4.0140  106 kg/s and 1.2042  105 kg/s. Near stoichiometric conditions, all three conversion efficiencies are relatively less sensitive to the imposed modulation. For the non-OSC case, the response is cyclic and sinusoidal during a part of the modulation cycle followed by discontinuous non-sinusoidal behavior near the trough values of inlet NO. During this discontinuity, the conversion performance experiences a jump and shifts to a different value and stays there without modulating. Overall, the modulation results in small reduction of CO and HC conversions (1.4% and 2.5%, respectively) and a small increase of NO conversion (2.7%). Similar to other cases, the inclusion of the OSC makes the catalyst response smoother and more sinusoidal (see Fig. 4b). The discontinuity in the non-OSC case disappears and the catalyst becomes relatively more sensitive to the imposed modulation. The effect of modulation on the time-average conversion efficiencies is very small. Only the NO conversion exhibits a minor decrease (0.7%) caused by the imposed modulation, which indicates a negative effect of the imposed NO modulation on reaction (R-8) of the OSC mechanism. Under lean conditions, the imposed NO modulations do not have any influence on CO and HC conversions. There is also no net effect on the NO conversion efficiency (no appreciable changes in time-average conversion efficiencies). However, the imposed modulation affects the instantaneous NO conversion, which responds sinusoidally with amplitudes of 13.7% and 11.1% for nonOSC and OSC cases respectively. In contrast to other modulation cases, the large difference between the catalyst NO conversion performance for the OSC and non-OSC cases during the steady state conditions remain present during the NO modulating conditions. Under rich conditions, the catalyst’s CO and HC conversions are responsive to the imposed NO modulation for both non-OSC and OSC cases. The NO conversion remains high and is not much responsive to the imposed modulation. The HC conversion efficiency shows discontinuity in its response. During a part of the modulating cycle, the HC conversion responds sinusoidally with the amplitude of 36%. At some point, the HC conversion jumps to a higher value and stays there for a certain part of the modulating cycle. Beyond which it jumps back the lower value and starts fluctuating again. This discontinuity in the response occurs near the peak inlet NO. The modulation results in 15.5% increase for the CO conversion and a 12% decrease for the HC conversion. With the exception of small changes in the response amplitudes, there is no appreciable effect of the OSC on the catalyst’s performance during the NO modulation under rich conditions.

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T. Shamim / Energy Conversion and Management 49 (2008) 3292–3300

a

3.3. Effect of sinusoidal modulation in exhaust gas temperature

Near Stoichiometric (A/F= 14.7) Lean (A/F= 17.5) Rich (A/F= 12.5) 100 80 60 40 20

CO

Conversion Efficiency (%)

0 100 80 60 40 20

HC

0 100 80 60 40 20

NO

Inlet NO (PPM)

0 800 600 400 200 0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

4.0

3.5

4.0

Time Period

b

Near Stoichiometric (A/F= 14.7) Lean (A/F= 17.5) Rich (A/F= 12.5) 100 80 60 40 20

CO

Conversion Efficiency (%)

0 100 80 60 40 20

HC

0 100 80 60 40

NO

20

Inlet NO (PPM)

0 800 600 400 200 0.0

0.5

1.0

1.5

2.0

2.5

3.0

Time Period Fig. 4. Catalyst response to sinusoidal modulations in inlet NO concentration: (a) without OSC; (b) with OSC. (Mean exhaust temperature = 600 K, frequency = 1 Hz, amplitude = 50%.)

Fig. 5 shows the results of the imposed exhaust gas temperature modulation near stoichiometric conditions. During the simulations, the exhaust gas temperature, initially set at 600 K, is varied sinusoidally with a frequency of 0.01 Hz and amplitude of 10%. The low value of modulation frequency is selected in order to emphasize the effect of imposed modulation even though it is lower than that of the typical realistic modulations. The effect of other frequencies, which include more realistic values (such as 0.1– 5 Hz), is found to be similar but with different response amplitude [18]. With the exhaust gas temperature ranging between 540 K and 660 K, the selected value of amplitude (i.e. 10%) represents a modest level of modulation. Higher modulation amplitudes generally result in higher response amplitudes [18]. Fig. 5a shows the results of the non-OSC case. The results show that CO and HC conversion efficiencies respond smoothly to the imposed sinusoidal temperature modulations. The CO conversion efficiency fluctuates between 75.5% and 98.6% (response amplitude is 23.1%). The modulation results in a small decrease in the CO conversion. The time-average conversion efficiency is decreased by approximately 3% below its steady state value of 93.3% (see Table 1). The HC conversion response is perfectly sinusoidal with the conversion efficiency fluctuating from 5.8% to 62.1%. Under these conditions, the HC conversion response amplitude is the largest (56.3%). The NO conversion response is relatively low with the amplitude of 4.5%. The response is cyclic but unsmooth. The imposed modulation has a positive influence on the HC and NO conversions, which improve by approximately 4% and 3% from their respective steady state conversion performance values. Fig. 5b shows the results of the OSC case. The results show that the effects of imposed exhaust gas temperature modulation on the catalyst performance with the OSC are generally similar to that of the non-OSC case for HC and NO conversions. The imposed temperature modulation’s negative effect on the heterogeneous reactions involving CO oxidation, as shown by the non-OSC case, is compensated by its positive effect on reactions (R-2) and (R-3) of the OSC mechanism. Hence, for the OSC case, the catalyst’s CO conversion performance during the imposed modulation remains close to its steady state value. Another major effect of the OSC is that the response amplitudes are different from the non-OSC case. The response amplitudes are 1.2% lower, and 8.4% and 13.2% higher from the non-OSC case for the CO, HC and NO conversions, respectively. Table 1 shows that the time-average conversion efficiencies are higher for the OSC case. In contrast to the A/F modulation, the inclusion of the OSC effect makes the catalyst more sensitive to the imposed modulation. The effects of temperature modulation in rich and lean regimes are presented next. The lean regime results indicate that the CO and HC conversions are high (100% and 93%, respectively) and are not strongly influenced by the imposed modulations. The NO conversion responds sinusoidally to the imposed modulation during a part of the imposed modulation cycle, and drops to a low value and stays there for the remaining part of the cycle. The efficiency jumps back to the higher value and starts fluctuating again during the next modulating cycle. This discontinuity in response occurs near the peak temperatures. Overall, the modulation results in the reduction of the NO conversion efficiency since the time-average conversion efficiency drops by 9% below its initial steady state value. Similar to the non-OSC case, the imposed temperature modulation has no appreciable effect on the catalyst CO and HC conversions for the OSC case as well. The modulation, however, has strong effect on reaction (R-8) of the OSC mechanism and improves the NO conversion from its steady state value by approximately 27.5%. Similar to other modulation cases, the large difference

T. Shamim / Energy Conversion and Management 49 (2008) 3292–3300

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between the catalyst performance for the OSC and non-OSC cases during the steady state conditions is reduced by the imposed temperature modulation. The discontinuity exhibited by the NO conversion near the peak temperature is also present for the OSC case. The rich regime results depict that the catalyst is less sensitive to the imposed temperature modulations. The conversion performance responds to the modulations with very small amplitudes. Overall, there is no appreciable influence of modulation on the catalyst conversion performance for both OSC and non-OSC cases.

Near Stoichiometric (A/F= 14.7) Lean (A/F= 17.5) Rich (A/F= 12.5) 100 80 60 40 20

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4. Conclusions

80 60

In this work, the influence of oxygen storage capacity on the catalyst dynamic behavior was examined. The transient conditions were simulated by considering the catalyst subjected to temporal modulation in air–fuel ratio, exhaust gas composition and temperature. The scope of the present study was limited to the identification of global effects of the OSC on the catalyst performance during transient modulating conditions. The isolation and quantification of the role of individual OSC reactions on the catalyst dynamic behavior will be done in a future study, which will include systematic investigation of the sensitivity of various OSC reactions to the imposed modulation parameters. The results of the present study led to the following conclusions:

40 20

HC

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Temperature (K)

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HC

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Temperature (K)

680

 The presence of the OSC affects the catalyst’s sensitivity and influences its response to the imposed modulation. The specific effect depends on the operating conditions and the type of the imposed modulations.  The catalyst is most sensitive to the imposed modulations and the coupled effect of OSC near stoichiometric conditions. The catalyst’s response to the imposed A/F and exhaust gas temperature modulations are generally similar for the OSC and nonOSC cases. The inclusion of OSC mainly affects the response amplitude and the average conversion performance. The inclusion of the OSC effect makes the catalyst less sensitive to the imposed A/F modulation and more sensitive to the imposed exhaust gas temperature modulation. The effect of the OSC on the catalyst’s response to the imposed exhaust gas composition modulation depends upon the modulating species. For most cases, the inclusion of OSC makes the catalyst response smoother and more sinusoidal.  There are no appreciable effects under lean conditions, and the catalyst generally remains insensitive to the imposed modulations for both OSC and non-OSC cases. In some cases, the difference between the catalyst performance with and without OSC may be reduced by subjecting the catalyst to the imposed modulation.  Under rich conditions, the effect of OSC is mainly limited to variations in response amplitudes when the catalyst is subjected to HC and NO modulations. For other types of imposed modulations, the catalyst remains insensitive to modulations for both OSC and non-OSC cases.

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Acknowledgements

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2.0

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Time Period Fig. 5. Catalyst response to sinusoidal modulations in exhaust gas temperature: (a) without OSC; (b) with OSC. (Mean exhaust temperature = 600 K, frequency = 0.01 Hz, amplitude = 10%.)

The financial support from the Ford Motor Company and the Henry W. Patton Center for Engineering Education and Practice (HPCEEP) of the University of Michigan-Dearborn is greatly appreciated. References [1] Duprez D, Descorme C, Birchem T, Rohart E. Oxygen storage and mobility on model three-way catalysts. Top Catal 2001;16–17(1-4):49–56.

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