Reduced Kinetics Schemes for Oxides of Nitrogen Emissions from a

Feb 14, 2003 - The model is developed for use in a machinery space simulator for training marine engineers and in a predictive emissions monitoring sy...
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Energy & Fuels 2003, 17, 450-456

Reduced Kinetics Schemes for Oxides of Nitrogen Emissions from a Slow-Speed Marine Diesel Engine Laurie Goldsworthy† Australian Maritime College, P.O. Box 986, Launceston 7250, Tasmania, Australia Received August 5, 2002

A number of reduced chemical kinetics schemes are compared for prediction of NOx emissions from a slow-speed marine diesel engine, using a zero-dimensional model. The kinetic evolution of NO is tracked in 10 representative parcels of burnt gas, formed sequentially during combustion. Dilution of the burnt gas by unburnt air is accounted for. The model is developed for use in a machinery space simulator for training marine engineers and in a predictive emissions monitoring system. It runs in real time on a standard PC and requires experimental data for calibration. Kinetics schemes modeled include the extended Zeldovich mechanism and five schemes involving nitrous oxide. The addition of nitrous oxide reactions to the extended Zeldovich mechanism increases predicted NOx by up to 15%. The N2O reactions which give the most significant contribution to NOx in the context of a large marine diesel engine have been identified. NO from fuel bound nitrogen is likely to be significant for engines operating on residual fuel oil.

Introduction Worldwide, ship oxides of nitrogen (NOx) emissions have been estimated at about 10 million tonnes per annum, equivalent to about 50% of the land-based NOx emissions from the USA or 14% of total NOx emissions from fossil fuels.1 NOx emissions participate in the formation of photochemical smog and acid rain, and contribute to greenhouse warming.2 Marine sourced emissions can have significant impact on air quality on land, especially near busy coastal waterways. Control measures include engine tuning, modified fuel injectors, water injection, fuel-water emulsions, and after-treatment using selective catalytic reactors. Essential features of NOx formation in slow-speed engines include formation primarily on the lean side of the flame and mixing of burnt gas with oxygen rich unburnt gases.3-5 The NOx model attempts to incorporate these features into a real time model in a meaningful way. The NOx model is developed for use in a machinery space simulator for training marine engineers6 and in a predictive emissions monitoring system for use onboard. Inclusion of an intelligent NOx model in the simulator mathematical model allows engineers to develop an awareness of the ways in which engine operating conditions and NOx control measures affect NOx output and fuel consumption. The model has to run in real time on a standard PC. † Phone: +61 3 63354774. Fax: +61 3 63354720. E-mail: [email protected]. (1) Corbett, J. J.; Fischbeck, P. Science 1997, 298, 823-824. (2) IPCC Intergovernmental Panel on Climate Change, Climate Change 2001: The Scientific Basis, Technical Summary. UNEP, WMO, 2001. (3) Dec, J. E.; Canaan, R. E. SAE 980147 1998. (4) Easley, W. E.; Mellor, A. M.; Plee, S. L. SAE 2001, 0582. (5) Zabetta, E. C.; Kilpinen, P. Energy Fuels 2001, 15, 1425-1433. (6) Goldsworthy, L.; Jung Byung-Gun.; Niekamp, P.; Earl, S. MARTECH 2002 Conference Proceedings, Singapore, 2002.

The Australian Maritime College Marine Diesel Simulator mathematical model predicts power output, cylinder pressure, heat release rate, exhaust temperature, and thermal efficiency using a simple single zone combustion model.7 A zero-dimensional 10-zone model for NOx emissions is superimposed onto this combustion model.8 NOx Model The kinetic evolution of NO is tracked in 10 representative parcels of burnt gas (NO zones). Each zone represents the burnt gas from a single combustion calculation step. The first zone represents the burnt gas from the start of combustion. The final zone represents the burnt gas from the combustion calculation step at the end of combustion. Eight more zones are formed during the combustion process. Each zone represents the gases burned at a particular time. The zones are not necessarily spatially coherent. The temperature history of each NO zone is followed by a simplified energy analysis which accounts for compression/expansion, heat transfer and mixing of the gas with unburnt air. The starting temperature for each NO zone is the constant pressure adiabatic flame temperature at the time the zone is formed. The constant pressure adiabatic flame temperature is known to be representative of diffusion flame temperatures.9 The initial fuel/air equivalence ratio for the flame temperature calculations for all zones is set at a single value less than 1 (fuel lean). The rate of dilution of the NO rich gas by unburnt air is controlled by the burn (7) Goldsworthy, L. C. Sea Australia 2000 Conference Proceedings, Sydney, 2000. (8) Goldsworthy, L. IMarEST Journal of Marine Engineering and Technology 2002. Revised paper submitted for publication. (9) Strehlow, R. A. Combustion Fundamentals; McGraw-Hill: New York, 1984.

10.1021/ef020172c CCC: $25.00 © 2003 American Chemical Society Published on Web 02/14/2003

NOx Emissions from Slow-Speed Marine Diesel Engine

rate. A constant dilution rate factor is applied to the burn rate at each load point, to set the dilution rate. Dilution increases the oxygen content and decreases the temperature. Depending on conditions, dilution can increase or reduce NO production. In a slow-speed engine, the turbulence levels during combustion will be determined by the rate of injection/combustion as well as the swirl velocity.10 The major part of the combustion process will be mixing rate controlled. Thus, the burn rate is controlled by the turbulence levels, which control the mixing of fuel and air as well as the mixing of the burnt gas with unburnt charge. In the present model, the rate of mixing is controlled by the burn rate. The burn rate is determined by setting the combustion model parameters to give the measured cylinder pressure development. The rate of mixing of unburnt charge with an NO zone is defined as the fractional zone mass change per second. For example, a dilution rate of 25 s-1 signifies a change of mass of 2.5% of the original zone mass, per millisecond, due to mixing of unburnt air into the zone. As the unburnt air mixes with the burnt gas, the equivalent fuel/air mixture strength is calculated. This is then used in the calculation of equilibrium composition, which is in turn used in the NO kinetics calculations. The temperature of the air mixing into the NO zones is found by assuming adiabatic compression/ expansion from the cylinder conditions just prior to ignition. This same temperature is used as the reactants temperature for the initial flame temperature calculations. The chosen initial equivalence ratio affects both the NO zone temperature and composition. This allows for the formation of NO in fuel lean areas ahead of the flame and in diluted postcombustion gases. Even if the combustion occurs more near to stoichiometric conditions, the gases well ahead of the flame will be subject to lower temperatures than the stoichiometric flame temperature. Combustion will occur, and NO will form, over a range of temperatures and compositions. Combustion products will be transported into the unburnt gas ahead of the flame, and oxygen will be transported from the unburnt air to the flame. The model simulates these complex processes with NO zones which follow representative temperature and composition histories. The final NO concentration is found by summing the average value of subsequent zones, weighted according to the mass of fuel burnt between. NO Kinetics A common approach in engine modeling is to use reduced NOx kinetics schemes to save computer resources. For fuel lean, high-pressure combustion, the extended Zeldovich mechanism and nitrous oxide reactions are the primary source of NO.11-15 Zabetta and (10) Rodatz, P.; Weisser, G.; Tanner, F. X. SAE 2000-01-0948 2000. (11) Lavoie, G. A.; Heywood, J. B.; Keck, J. C. Combust. Sci. Technol. 1970, 1, 313-326. (12) Miller, J. A.; Bowman, C. T. Prog. Energy Combust. Sci. 1989, 15, 287-338. (13) Malte, P. C.; Pratt, D. T. Combust. Sci. Technol. 1974, 9, 221232. (14) Easley, W. E.; Mellor, A. M.; Plee, S. L. SAE 2000-01-0582 2000. (15) Drake, M. C.; Blint, R. J. Combust. Sci. Technol. 1991, 75, 261285.

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Kilpinen5 demonstrate that reactions involving NO2 are unimportant for NO formation in large diesel engines. NO2 is more important for NO formation in fuel rich areas. Kinetics schemes which may give significant NO production in fuel lean areas are included. Five different reaction schemes are evaluated and compared. For all schemes, the concentration of N2, O2 and the radicals O, H and OH are taken as partial equilibrium values. N and N2O are assumed to remain at steady state. A number of different rate constants are compared. First NO Scheme. The first is the commonly used extended Zeldovich mechanism.11 This is also called the thermal mechanism and accounts for most of the NO formed.5,11,16

N2 + O T NO + N

(R1)

N + O2 T NO + O

(R2)

N + OH T NO + H

(R3)

By assuming that the concentrations of O2 and the radicals O, H and OH remain at equilibrium and that the concentration of N remains at steady state, the rate of formation (and decomposition) of NO can be calculated. The concentration of the O and OH radicals will depend on the concentration of oxygen as well as temperature. The concentration of oxygen will increase as the zone is diluted, but the temperature will decrease. Second NO Scheme. The second mechanism evaluated is the extended Zeldovich mechanism with an N2O Intermediate mechanism added.5 This is the same mechanism as used by Easley et al.4 in high-speed diesel engine studies. Mellor et al.17 showed that at pressures and temperatures representative of diesel engines, the Zeldovich mechanism dominates and the N2O mechanism contributes significantly. Their study also demonstrated the increased importance of reaction R4 at high pressures. The N2O reactions for this scheme are

N2O + M T N2 + O + M

(R4)

N2O + O T NO + NO

(R5)

where M is a third body. Third NO Scheme. The third reaction scheme is the reduced scheme developed by Zabetta and Kilpinen.5 It involves the previous five reactions plus five additional reactions. The five additional reactions are called the N2O Extension path. They involve oxidation of N2O to NO via NH and HNO intermediates. Thus,

N2O + H f NH + NO

(R6)

N2O + OH f HNO + NO

(R7)

NH + OH f HNO + H

(R8)

NH + O2 f HNO + O

(R9)

HNO + M f H + NO + M

(R10)

Zabetta and Kilpinen5 derived a solution to this 10 (16) Heywood, J. B. Internal Combustion Engine Fundamentals; McGraw-Hill: New York, 1988. (17) Mellor, A. M.; Mello, J. P.; Duffy, K. P.; Easley, W. L.; Faulkner, J. C. SAE 981450 1998.

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reaction mechanism which does not require explicit computation of the concentration of the NH and HNO intermediate concentrations. They found that these five reactions are essentially irreversible at engine conditions. Only the first two need to be considered. Reactions R8, R9, and R10 are fast compared to reactions R6 and R7. Thus reactions R6 and R7 control the rate of NO formation. Essentially, every mole of NH or HNO produced by R6 and R7 is rapidly converted to NO by reactions R8-R10. Thus, every mole N2O consumed by reactions R6 or R7 produces 2 mol of NO. The formation of NO by reactions 6 and 7 requires only the concentrations of O, OH, and N2O. The quasi-steady-state assumption for N and N2O and partial equilibrium assumption for O, H, and OH are employed. This is chosen as the reference scheme. This scheme was derived by reduction of a detailed scheme, “Kilpinen 97”, which includes 353 elementary gas-phase reactions between 57 chemical species. Zabetta et al.18 report that the detailed scheme was based on the mechanism of Glarborg et al.19,20 and Miller and Glarborg,21 with some modifications for high-pressure conditions.22 Zabetta and Kilpinen5 identified the important reactions using detailed kinetic modeling under isobaric, isothermal, plug flow conditions, for pressures up to 150 bar and temperatures up to 2500 °C. Conditions were chosen to match those found in large bore marine diesel engines. They compared the reduced and detailed schemes at representative engine pressures. The reduced scheme tended to overpredict NO in the lower range of temperature expected in the post flame gases of a large diesel engine (2000 °C, decreasing), by about 15%. In the higher range of expected temperature (2500 °C, decreasing), the reduced scheme underpredicted NO relative to the detailed scheme. The degree of underprediction was unclear. The deviations were attributed to the partial equilibrium approximation for O, H, and OH. Fourth NO Scheme. The fourth scheme evaluated is a reduced form of the third, involving only reactions R1-R6. Miller and Bowman12 report that the sequence involving reactions R4-R6 is an important source of NO for equivalence ratio less than 0.8. As with the third scheme, it is assumed that reaction R6 is irreversible at the conditions studied. Fifth NO Scheme. The fifth scheme evaluated is the same as the third (extended Zeldovich and N2O intermediate) with three additional reactions involving N2O, but not the ones used by Zabetta and Kilpinen.5 The additional reactions are

H + N2O T N2 + OH

(R11)

O + N2O T N2 + O2

(R12)

N2O + OH f N2 + HO2

(R13)

Reaction R13 is assumed to be irreversible, to avoid modeling HO2. This gives an upper estimate of the (18) Zabetta, E. C.; Kilpinen, P.; Hupa, M.; Stahl, K.; Leppalahati, J.; Nieminen, J. Energy Fuels 2000, 14, 751-761. (19) Glarborg, P.; Kubel, D.; Kristenssen, P.; Hansen, J.; DamJohansen, K. Combust. Sci. Technol. 1995, 461, 110-111. (20) Glarborg, P.; Kubel, D.; Kristenssen, P.; Hansen, J.; DamJohansen, K. Final Report, Gas Research Institute, 5091-260-2126. Nordic Gas Technology Center, 1993.

impact of reaction R13 on N2O depletion. The effect of excluding reaction R13 was assessed, to set a lower limit. If reaction R13 is neglected, this is the scheme of Horlock and Winterbone,23 which is that of Lavoie, Heywood, and Keck11 with reaction R4 added. Reactions R11-R13 were applied by Tanner et al.24 in a recent CFD study of large bore marine diesels. They used the extended Zeldovich mechanism, the N2O Intermediate reactions (R4 and R5) and reactions R11R13. Two additional reactions involving NO2 were applied, but none of the N2O Extension reactions. Partial equilibrium values were used for H, O, OH, and HO2. The scheme used by Tanner et al.24 came from the work of Weisser,25 who applied the full N/H/O scheme of Miller and Bowman12 along with four CO/CO2 reactions. Weisser25 progressively reduced the full scheme in the context of a zero dimensional model of a mediumspeed diesel engine, which employed multiple burnt gas zones and mixing of unburnt air with the burnt gas. He used atom-flow analysis to detect insignificant reaction paths and intermediate species and found that NOx predicted with the extended Zeldovich mechanism alone was around 10 to 20% lower than the full mechanism. Adding the two NO2 reactions (NO2 + OH T NO + HO2; NO2 + H T NO + OH) to the extended Zeldovich mechanism alone made negligible difference to predicted NOx. The extended Zeldovich mechanism plus the five N2O reactions R4, R5, and R11-R13 gave predicted NOx about 5% lower than the full mechanism. Adding the two NO2 reactions gave a slight improvement in prediction accuracy. For these evaluations, Weisser used 20 reactions to represent the H/O system. Wolfrum26 and Malte and Pratt13 proposed a nitrous oxide pathway involving reactions R4-6, R11, and R12. Drake and Blint15 proposed that additional reactions such as reaction R13 may be needed. Tanner et al.24 applied reactions R4, R5, and R11-R13 but not R6 in their reduced scheme. Sixth NO Scheme. The sixth scheme evaluated includes all 13 reactions, with reactions R8-R10 handled as in the third scheme. The six schemes are compared in the present engine model. While these comparisons do not necessarily indicate which mechanism is most correct, they do indicate the relative importance of the key reactions under realistic conditions, and the relative behavior of the various combinations. This is with the given assumptions of partial equilibrium O, H, and OH, as well as steady-state N2O and N. The rate constants used are detailed in the Appendix. Superequilbrium O, H, and OH. Miller and Bowman12 showed that superequilibrium concentrations of O in the vicinity of the flame can lead to substantial (21) Miller, J. A.; Glarborg, P. In Springer Series in Chemical Physics; Springer-Verlag: Berlin, Germany, 1996. (22) Kilpinen, P.; Hupa, M.; Abo, M. Proceedings of the 7th International Workshop on Nitrous Oxide Emissions, Cologne, Germany, 1997. (23) Horlock, J. H.; Winterbone, D. R. The Thermodynamics and Gas Dynamics of Internal Combustion Engines Volume II; Oxford University Press: New York, 1986. (24) Tanner, F. X.; Brunner, M.; Weisser, G. SAE 2001-01-1069 2001. (25) Weisser, G. Swiss Federal Institute of Technology: Zurich, 2001. (26) Wolfrum, J. Chemie Ingenieur Technik 1972, 44, 656.

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Table 1. Reference Engine Operating Conditions: Indicative Data Supplied by MAN B&W for a 7L70MC mk6 IMO NOx Compliant Engine with VIT

diffusion flames found in diesel engines. Mellor et al.17 contend that any premixed flames in diesel engines tend to be fuel lean and thus prompt NO is likely to be negligible. Dec and Canaan3 measured NO formation in a high-speed diesel engine operating on low nitrogen content fuel, using PLIF. They found negligible NO formation in the flame. Fuel NO. A small proportion of engine NOx is derived from fuel-bound nitrogen, up to 10%, for engines operating on residual fuel oil.27 The data used in the present study are for an engine operating on test bed gas oil, so this source of NOx will be negligible. For operation on residual fuel oil, a simplified model of NO formation from fuel nitrogen will be necessary. Precise modeling of this source of NO requires a considerable degree of detail in modeling of the combustion chemistry. Bazari28 assumed that all fuel bound nitrogen is converted to NO. This simplified approach would give some measure of the impact of changes in fuel nitrogen on NOx, if the nitrogen content of the fuel was known. Miller and Bowman12 suggest that fuel nitrogen is rapidly converted to HCN and NH3, with aromatics yielding mainly HCN and amines yielding mainly NH3. It may be possible to assume complete conversion of fuel nitrogen to HCN and NH3, in proportion according to fuel composition, then follow the oxidation of these with a reduced scheme, such as that proposed by De Soete.29

load speed (rev/min) scavenge pressure (MPa absolute) exhaust pressure (MPa absolute) fuel/cylinder/s (kg/s) air/cylinder/s (kg/s) scavenge temperature (°C) power (MW) compression pressure (MPa abs) maximum pressure (MPa abs) cylinder cooling load (kW) injection angle (degrees after BDC) measured NOx (g/kWh)

100% 108 0.360 0.327 0.1368 7.3095 41 19.810 13.1 14.1 3000 179.0 13.6

75% 98.1 0.280 0.253 0.1009 5.885 34 14.858 10.1 12.6 2400 178.5 17.6

50% 85.7 0.200 0.181 0.0684 4.190 29 9.905 7.5 9.9 1890 179.5 19.1

25% 68.0 0.138 0.125 0.0360 2.164 34 4.953 5.1 7.0 1335 179.5 16.5

Table 2. Engine Combustion Model Outputs at the Reference Conditions load maximum pressure (MPa) power output (MW) compression pressure (MPa) air temperature at injection (°C) maximum pressure rise rate (MPa/deg) exhaust temperature before turbine (°C) cylinder cooling load (kW) crank angle at peak pressure (deg after BDC)

100% 14.1 19.81 13.1 559 0.31

75% 12.6 14.86 10.3 544 0.49

50% 9.9 9.91 7.4 535 0.52

25% 7.0 4.95 5.1 545 0.38

333

284

257

259

3006 188.8

2391 189.9

1869 190.9

1325 189.9

Model Conditions The engine simulated is a MAN B&W 7L70MC mk6, direct injection, turbocharged, aftercooled, uniflow scavenged, slowspeed marine diesel, with the specifications:

number of cylinders ) 7 bore ) 0.70m stroke ) 2.268m effective compression ratio ) 12.60 fuel calorific value ) 42700kJ/kg fuel carbon-to-hydrogen ratio (mass) ) 7 Figure 1. Dilution Rate Factor vs Load, initial equivalence ratio ) 0.96, third scheme.

specific humidity of charge air ) 0.01071kg/kg dry air (ISO reference humidity)

increase in the NO formation rate due to the extended Zeldovich mechanism. However, they found that the accelerated rates were sufficiently low that very little NO is actually formed. In their studies of laminar premixed methane/air flames, Drake and Blint15 showed the importance of superequilibrium concentrations of O on NO formation by the extended Zeldovich mechanism decreases as pressure increases. Zabetta and Kilpinenl5 contend that the equilibrium assumption for radical concentrations can lead to significant errors. Weisser25 pointed out that superequilibrium concentrations of O would also lead to increased NO formation rates by the nitrous oxide pathway. However, the partial equilibrium assumption for O, H and OH is likely to be used in engine combustion models where computational time is an important factor. CFD modeling of large bore engines is particularly challenging because of the large number of cells required.10 Prompt NO. Weisser25 considers the contribution from prompt NO is likely to be of minor importance because of the very short residence times in the thin

fuel: test bed gas oil power output: 19.81MW at 100% load (108 rpm) speed-load relationship: propeller law The measured data were supplied by MAN B&W for the modeled engine. Table 1 details the supplied data. The engine has variable injection timing (VIT). The single zone combustion model is calibrated to give accurate modeling of measured compression pressure, maximum pressure and engine power. The outputs are given in Table 2. Scavenging efficiency is set to vary linearly from 100% at full load to 97.5% at 25% load. Matching the Measured NOx Values. The available parameters for adjustment are flame temperature, dilution rate, and initial equivalence ratio of the NO zones. (27) Holtbecker, R.; Geist, M. Emissions Technology, Sulzer RTA Series, Exhaust Emissions Reduction Technology for Sulzer Marine Diesel Engines. Wartsila NSD, 1998. (28) Bazari, Z. SAE 920462 1992. (29) De Soete, G. G. In Proceedings of the 15th Symposium (International) on Combustion; The Combustion Institute: Pittsburgh, PA, 1975.

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Figure 2. Zonewise temperature history, 75% load.

Figure 3. Zonewise NO history, 75% load, third scheme. The adiabatic flame temperature is an upper estimate of the combustion temperature. Factors such as flame radiation and nonequilibrium chemistry may result in a lower actual temperature than the adiabatic flame temperature. Current CFD models tend to underpredict combustion temperature and thus NOx, especially for slow-speed engines, where the grid size is a limitation. NOx may be underpredicted by a factor of 2 to 5.10,24 In the present study, predicted NOx is in the range of measured NOx when using adiabatic flame temperature as the starting temperature for the NO zones. The NOx model is set up for the reference kinetic scheme (Scheme 3). A constant initial equivalence ratio of 0.96 is chosen. It is the equivalence ratio for maximum NOx at intermediate dilution factor. Dilution rate factor is adjusted, as shown in Figure 1, to match predicted and measured NOx, within about 0.5%. Final NO concentration is converted to NOx output in g/kWh, assuming all NO is converted to NO2.30

Results Range of Equivalence Ratio. As the NO zones are diluted with unburnt air, the effective equivalence ratio (30) IMO 1998.

is reduced. For the first burned gas, equivalence ratio by the end of burn is between 0.56 and 0.70, for the four load points, in inverse proportion to the dilution rate factor. Subsequent zones are subject to less overall dilution. Predicted NOx History. NO zone temperature and NO development through the engine cycle are plotted in Figures 2 and 3, for the 75% load point. A definite peak in the NO concentration occurs for the early burned gases. Calculations for the early burned gas show that at the crank angle corresponding to the maximum value of NO concentration, NO is still being produced by the kinetics mechanism, but the rate of decrease of NO concentration due to dilution begins to outstrip the rate of production. Decomposition of NO by the kinetics mechanism begins at a later crank angle, but never reaches a significant value compared with the early formation rates, due to the rapid temperature falloff. Similarly, NO decomposition is not significant in the later burned gases. The NO peak is absent for the later burned gases, because dilution is not as significant due to the lower combustion rate. Thus, final

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Table 3. Comparison of NOx Predicted by 5 Kinetics Schemes, at 75% Load scheme number 1 2 3 4 5 6

NO scheme extended Zeldovich extended Zeldovich with N2O intermediate extended Zeldovich with N2O intermediate and R6 extended Zeldovich with N2O intermediate and N2O extension extended Zeldovich with N2O intermediate and R11-R13 all 13 reactions

NOx (g/kWh) 15.4 15.7 16.5 17.6 15.7 17.5

NO concentration is generally formation rate limited in the present context. This is apparent for all load points. Six Kinetics Schemes Compared. Predicted NOx for six different kinetics configurations are compared, for the reference settings of the initial equivalence ratio and dilution rate factor. Adding N2O Intermediate and N2O Extension to the extended Zeldovich mechanism results in 15% more NOx at full load, reducing to 12% more NOx at 25% load. The results for 75% load are presented in Table 3. The 75% load point is emphasized as it has the heaviest weighting in the ISO E3 cycle, which applies to marine propulsion diesels.30 Reactions R11-R13 have negligible impact on predicted NOx when added to the N2O Intermediate set. Adding reactions R11-R13 to the N2O Extension set reduces predicted NOx by less than 1%. Reaction R6 adds significantly to the value predicted using extended Zeldovich with N2O Intermediate. The N2O Extension reactions give significantly more NOx than reaction R6 alone. This is expected as the contribution from reaction R6 is doubled and reaction R7 also contributes. However, the contribution from reaction R7 is small compared with reaction R6. Removing reaction R7 from the N2O Extension set reduces predicted NOx at 75% load from 17.6 to 17.4 g/kWh, while removing both reactions R6 and R7 reduces predicted NOx to 15.7 g/kWh. Relative Contributions of Thermal Mechanism, N2O Intermediate, and N2O Extension. Zabetta and Kilpinen5 detail the relative contributions from the thermal (extended Zeldovich), N2O intermediate, and N2O extension mechanisms as 70%, 20%, and 10% respectively. The results in Table 3 show different relative contributions of 88%, 2%, and 10%. The Zabetta and Kilpinen5 tests were conducted for very fuel lean conditions (equivalence ratio ) 0.5), a constant temperature of 2173 K and constant pressure. The results in Table 3 are for initial temperature of the NO zones around 2600 K and pressure varying as in a real engine. The initial equivalence ratio of the NO zones is 0.96. The effect of temperature and oxygen content on the relative contribution of the three mechanisms, at 75% load, is illustrated in Figure 4. The NOx model was manipulated to yield a number of combinations of initial NO zone temperature and equivalence ratio. It can be seen that decreasing temperature and increasing oxygen content each increase the contribution from the N2O Intermediate mechanism. For high temperature, low oxygen content, the N2O Extension mechanism produces more NO than the N2O Intermediate mechanism, and

Figure 4. Effect of burnt gas conditions on relative contributions to NOx from the thermal, N2O intermediate, and N2O extension mechanisms.

vice versa for low-temperature, high oxygen content. The trends at initial temperature 2100K and initial equivalence ratio 0.5 agree with the findings of Zabetta and Kilpinen5 at similar conditions. Conclusions A number of reduced kinetics schemes, for NO formation in the burnt gas, were tested in the context of a zero-dimensional, multizone NOx model for a slow-speed marine diesel. The addition of nitrous oxide reactions to the extended Zeldovich mechanism increases predicted NOx significantly. The N2O pathway involving the following reactions is a significant source of NO in the present context:

N2O + M T N2 + O + M

(R4)

N2O + O T NO + NO

(R5)

N2O + H f NH + NO

(R6)

N2O + OH f HNO + NO

(R7)

NH + OH f HNO + H

(R8)

NH + O2 f HNO + O

(R9)

HNO + M f H + NO + M

(R10)

This pathway adds an extra 15% to the NOx predicted by the extended Zeldovich mechanism at 100% load, reducing to 12% additional NOx at 25% load. The following reactions do not play a significant role:

H + N2O T N2 + OH

(R11)

O + N2O T N2 + O2

(R12)

N2O + OH f N2 + HO2

(R13)

Relative contribution to NO production from the N2O Intermediate reactions (R4 and R5) increases as temperature decreases and oxygen content increases, while

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Goldsworthy Table A.1. Rate Constantsa literature values rate constant: s-1, cm3 g mol s, m6/g mol2 s

a F

1

N2+O ) NO+N NO+N ) N2+O

2

N+O2 ) NO+O

3

NO+O ) N+O2 N+OH ) NO+H

4

NO+H ) N+OH N2O(+M) ) N2+O(+M)

5

N2+O(+M) ) N2O(+M) N2O+O ) NO+NO

6

NO+NO ) N2O+O N2O+H ) NH+NO NO+NH ) N2O+H

7

N2O+OH ) NO+HNO

11

NO+HNO ) N2O+OH N2O+H ) N2+OH

12

N2O+O ) N2+O2

13

N2O+OH ) N2+HO2

present study rate constant: s-1, m3/kmol s

66 -17.694 b k1 /1.00 × 10 T 2.7 × 1013 exp[-178.7/T] c 3.3 × 1012T0.3 b,d 9.0 × 109T exp[-3271.3/T] c 6.4 × 109T exp[-3160.5/T] b,d 29 -7.520 b k+ 2 /1.00 × 10 T 3.36 × 1013 exp[-193.8/T] c 3.8 × 1013 b,d 14 -11.200 b k+ 3 /6.00 × 10 T k∞ 7.91 × 1010 exp[-28193.3/T] c k0 6.37 × 1014 exp[-28505.3/T] c 4.00 × 1014 exp[-28233.5/T] b,d -31T8.358 b k+ 4 /9 × 10 2.9 × 1013 exp[-11650.7/T] c,b 6.6 × 1013 exp[-13402.1/T] d 36 -9.259 b k+ 5 /2.00 × 10 T 25T-7.343 b /3.00 × 10 k6 3.65 × 1014T-0.5 c 2.90 × 1014T-0.4 b,d 1.2 × 10-4T4.33 exp[-12622.5/T] d 2.0xT3.45 exp[-13085.1/T] b 2.00 × 1012 exp[-13085.1/T] b 3.87 × 1014 exp[-95017.6/T] c 4.4 × 1014 exp[-9689.98/T] b,d 1.4 × 1012 exp[-5440.4/T] c 1.0 × 1014 exp[-14091.6/T] d 1.4 × 1012 exp[-5435.33/T] b 2.0 × 1012 exp[-10599.9/T]c 1.3 × 10-2 T4.72 exp[-18400.1/T]d 2.0 × 1012 exp[-20130.85/T]b

is mixture molar density. xie is equilibrium mole fraction of species i.

the contributions from the extended Zeldovich mechanism and the N2O extension (R7-R10) reduce. Final NO is generally formation rate limited in the present context. Prompt NO is probably not significant in the context of a slow-speed marine diesel engine. NO from fuel nitrogen will be significant when operating on residual fuel oil. Appendix Rate Constants. Equilibrium composition is used to relate forward and backward rate constants for all schemes. Equilibrium concentrations are calculated using the method of Olikara and Borman,31 modified to include N2O. Rate constants are drawn from Zabetta and Kilpinen18 (Kilpinen97), Glarborg et al.,32 and GRI Mech 3.0.33 They are summarized and compared in Table A.1. Kilpinen9718 rate constants for reactions R1-R4, R6b, and R11 are identical to those of Glarborg et al.32 Tanner et al.24 used the same backward rate constant as Kilpinen9718 for reaction R1 and the same forward rate constant for reactions R2 and R3. (31) Olikara, C.; Borman, G. L. SAE0468 1975. (32) Glarborg, P.; Alzueta, M. U.; Dam-Johanssen, K.; Miller, J. A. Combust. Flame 1998, 115, 1-27. (33) Smith, G. P.; Golden, D. M.; Frenklach, M.; Moriarty, N. W.; Eiteneer, B.; Goldenberg, M.; Bowman, C. T.; Hanson, R. K.; Song, S.; Gardiner, W. C., Jr.; Lissianski, V. V.; Qin, Z. www.me.berkeley.edu/ gri_mech/ 2002.

b

Kilpinen 97.18

k1 xNOexNe/(xOexN2e) 3.3 × 109T0.3 6.4 × 106T exp[-3160.5/T] k+ 2 xNexO2e/(xNOexOe) 3.8 × 1010 k+ 3 xNexOHe/(xNOexHe) k∞/(1 + k∞/(k0[M])) k+ 4 xN2Oe/(FxN2exOe) 2.9 × 1010exp[-11650.7/T] k+ 5 xN2OexOe/(xNOexNOe) 9.667 × 10-15T6.943 2.00 × 10-3T3.45 exp[-13085.1/T] 4.4 × 1011 exp[-9689.98/T] 1.4 × 109 exp[-5435.33/T] 1.3 × 10-5 T4.72 exp[-18400.1/T]

c

GRI Mech 3.0.33

d

Glarborg et al.32

Reactions R1b-R3, R6b, and R11 served as optimization variables in GRI Mech 3.0.33 High- and low-pressure rate constants for reaction R4 are combined using the Lindemann falloff form, as given in GRI Mech 3.033 and Glassman.34 This gives about 1.5% less NOx from the reference scheme over the load range, compared with using the rate constant of Glarborg et al.32 or Kilpinen97.18 The GRI Mech 3.033 highpressure constant, when used alone, results in negligible difference in predicted NOx compared with the combined form, indicating that pressure dependence of the rate constants could be neglected in diesel engines if the high-pressure values are used. This is because gas temperatures in a diesel engine fall rapidly as pressure decreases, so the reaction rates become negligible before low pressure correction is indicated.5 Reactions R11-R13 make only a small difference to predicted NOx in the present context. The rate constant from Glarborg et al.32 for reaction R13 is used. It gives only 0.2% less NOx than the rate constant from GRI Mech 3.0,33 at 75% load. The Kilpinen9718 rate constant gives 1.3% more NOx than the rate constant from GRI Mech 3.0.33 The Kilpinen9718 and Glarborg et al.32 rate constants for reaction R12 yield the same predicted NOx at 75% load. EF020172C (34) Glassman, I. Combustion, 3rd ed.; Academic Press: San Diego, 1996.