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Energy & Fuels 1998, 12, 78-82
Chemical Kinetic Modeling of Hydrogen under Conditions Found in Internal Combustion Engines N. M. Marinov, H. J. Curran, W. J. Pitz,* and C. K. Westbrook Lawrence Livermore National Laboratory, P.O. Box 808, L-14, Livermore, California 94551 Received July 2, 1997. Revised Manuscript Received September 25, 1997X
A chemical kinetic model is used to study the combustion characteristics of hydrogen under conditions found in internal combustion engines. Laminar flame speeds are predicted under the high-pressure and high-temperature conditions found in a spark-ignition engine. The variation of laminar flame speed with temperature, pressure, and equivalence ratio is examined. The autoignition of hydrogen and hydrogen-natural gas mixtures is also studied under conditions found in a free-piston compression-ignition engine. This engine is expected to exhibit high efficiencies operating on hydrogen. The results suggest that adding small amounts of natural gas to hydrogen will reduce NOx emissions from a free-piston compression-ignition engine. Calculations showed that the predicted NO concentrations correlated well with the maximum temperature in the cycle and that the NO was mostly produced by N2 + O ) NO + N.
Introduction Public concern for improved urban air quality, finite fossil fuel resources, and global warming trends supports the need for a clean-burning alternative fuel. Hydrogen is an attractive alternative fuel because it does not produce CO2 greenhouse gas and offers the potential of reduced NOx and hydrocarbon pollutant emissions. The combustion characteristics of hydrogen make it an attractive fuel for internal combustion (IC) engines. Hydrogen allows operation of the IC engine at ultralow equivalence ratios where NOx emissions are low. Hydrogen has much higher flame speeds than hydrocarbon fuels, which gives it an acceptable burn rate even at ultralow equivalence ratios. Hydrogen is also attractive for use in compression-ignition engines because of its high octane quality. By use of hydrogen, compressionignition engines can operate at very high compression ratios, which gives correspondingly high efficiencies. In this study, we examine the chemical kinetics of hydrogen under conditions found in spark-ignition engines and compression-ignition engines. In the first part of the paper, laminar flame speeds for hydrogenair mixtures under conditions found in spark ignition engines are predicted. These laminar flame speeds are needed for use in turbulent flame submodels, which are used in multidimensional models of combustion in hydrogen engines.1 In addition, there is very little information in the literature on laminar flame speeds under the extreme conditions of pressure and temperature found in an internal combustion engine. In the * Corresponding author. E-mail:
[email protected]. Fax: (510) 422-2644. X Abstract published in Advance ACS Abstracts, November 1, 1997. (1) Amsden, A. A.; Ramshaw, J. D.; O’Rourke, P. J.; Dukowicz, J. K. KIVA: A computer program for two and three-dimensional fluid flows with chemical reactions and fuel sprays. Los Alamos National Laboratory Report LA-10245-MS; Los Alamos National Laboratory: Los Alamos, NM, 1985.
second part of the paper, autoignition of fuel-lean hydrogen-natural gas mixtures under conditions found in a compression-ignition engine is predicted. The investigation focuses on the free-piston engine,2 which is a compression-ignition engine being developed to utilize hydrogen and hydrogen-blended fuels. The computed results give the trends in NOx emissions as increasing amounts of hydrogen are added to natural gas. Since the free-piston engine achieves very high pressures at top dead center, we also examine real gas effects and their influence on computed pressures and temperatures. Chemical Kinetic Mechanism The chemical kinetic model for hydrogen was previously developed and is documented in ref 3. In ref 3, the chemical kinetic model was validated by comparing computed results to experimental data on laminar flame speeds, species composition profiles across a burnerstabilized flame, and ignition delay in a shock tube. Careful attention was given to obtaining rate constant expressions that were valid over wide ranges of pressure and temperature. The C5 mechanism used to treat natural gas-hydrogen mixtures is a submechanism of a larger C7 mechanism documented in ref 4. The NOx submechanism from GRI Mech has been added to the C5 mechanism.5 This submechanism consists of 21 (2) Van Blarigan, P. Advanced Hydrogen Fueled Internal Combustion Engines. Energy Fuels, in press. (3) Marinov, N. M; Westbrook, C. K.; Pitz, W. J. Detailed and Global Chemical Kinetics Model for Hydrogen. In Transport Phenomena in Combustion; Chan, S. H., Ed.; Talyor and Francis: Washington, DC, 1996; Vol. 1, pp 118-141. (4) Curran, H. J.; Gaffuri, P.; Pitz, W. J.; Westbrook, C. K. A Comprehensive Modeling Study of n-Heptane Oxidation. Combust. Flame, in press. (5) Bowman, C. T.; Hanson, R. K.; Davidson, D. F.;. Gardiner, W. C., Jr.; Lissianski, V.; Smith, G. P.; Golden, D. M.; Frenklach, M.; Goldenberg, M. http://www.me.berkeley.edu/gri_mech/, 1997.
S0887-0624(97)00104-7 CCC: $15.00 © 1998 American Chemical Society Published on Web 01/12/1998
Modeling of Hydrogen
Figure 1. Laminar flame speed and nitrogen oxides variation with H2-air equivalence ratio at a fixed pressure of 40 atm and an unburned gas temperature of 900 K.
speciesand 123 reactions and allows treatment of reactions involving the formation and consumption of oxides of nitrogen. The combined mechanism consists of 351 species and 1784 reactions. The Premix code6 was used to calculate laminar flame speeds of hydrogen mixtures. The HCT code7 was used to calculate the autoignition of H2-natural gas mixtures in a free-piston compression-expansion machine. Results and Discussion Laminar Flame Speeds under Spark-Ignition Engine Conditions. In a spark-ignition engine, a spark-ignited flame propagates into unburned gases that are at elevated pressures and temperatures. Information on the laminar flame speed of hydrogen-air mixtures burning at these elevated pressures and temperatures is needed to refine the turbulent flame speed model used in multidimensional, computational fluid dynamics codes such as KIVA.1 Most of the experimental data available from the literature on laminar flame speeds of hydrogen are reported at unburned gas conditions of 1 atm and room temperature. A computational investigation of the effects of unburned gas temperature, pressure, and hydrogen-air equivalence ratio upon the laminar flame speeds and NOx production rates was carried out. This parametric investigation was performed at conditions typical of the unburned gas at top dead center in a hydrogen-fueled, spark-ignition engine: temperature of 900 K, pressure of 40 atm, and equivalence ratio of 0.4. The ultralow equivalence ratio of 0.4 was addressed because that is the approximate operating condition that a spark ignition engine fueled by hydrogen would be expected to operate to achieve low NOx emissions.8 The results of the computational investigation are shown in Figures 1-3. Figure 1 shows calculations performed for the effect of variation in the hydrogen-air equivalence ratio (φ) (6) Kee, R. J.; Grcar, J. F.; Smooke, M. D.; Miller, J. A. A Fortran Program for Modeling Steady Laminar One-Dimensional Premixed Flames. Sandia Report SAND85-8240; Sandia National Laboratories: Albuquerque, NM, 1985. (7) Lund, C. M. HCT - A General Computer Program for Calculating Time-Dependent Phenomena Involving One-Dimensional Hydrodynamics, Transport, and Detailed Chemical Kinetics. Lawrence Livermore National Laboratory Report UCRL-52504; Lawrence Livermore National Laboratory: Livermore, CA, 1978. (8) Van Blarigan, P. Development of a hydrogen fueled internal combustion engine designed for single speed/power operation. SAE Future Transportation Conference, Vancouver, Canada; Society of Automotive Engineers, 1996; Paper 961690.
Energy & Fuels, Vol. 12, No. 1, 1998 79
Figure 2. Laminar flame speed and nitrogen oxides variation with unburned gas temperature at 40 atm and φ ) 0.4.
on laminar flame speed and nitrogen oxides production at an unburned gas temperature of 900 K and 40 atm. The computed laminar flame speeds exhibited a range 7.4-837 cm/s for equivalence ratios of 0.2-0.7, respectively. The computed NOx concentrations in the burnt gas are also shown to indicate the expected trends in NOx emissions. In a spark-ignition engine, NOx emissions depend on the residence time of the burnt gases at the high temperatures near top dead center (TDC). Here, we are reporting the NOx levels in the burnt gases near the hot boundary of the laminar flame calculation. The computed thermal NOx exhibited an interesting elbow around the hydrogen-air equivalence ratio of 0.5. Equivalence ratios greater than φ ) 0.5 show a dramatic increase in NOx production. This is due to the contribution of
N2 + O ) NO + N
(1)
which is the main contributor to NO production at high temperatures. For the φ ) 0.4, 0.5, and 0.6 flames, the burned gas temperatures are 1930, 2150, and 2330 K, respectively. Between φ ) 0.5 and 0.6, the flame reaches a temperature threshold where NO production from reaction 1 becomes important. As the equivalence ratio in the flame is raised further, the burnt gas temperature rises and the NO levels increase rapidly because of the high activation energy of reaction 1. Calculations were also performed to examine the sensitivity of laminar flame speed and NOx production due to the variation of the unburned gas temperature while maintaining the pressure and equivalence ratio constant at 40 atm and φ ) 0.4, respectively. Figure 2 shows the results of this parametric variation. The flame speed and nitrogen oxides tend to increase exponentially with unburned gas temperature in the 700-1200 K range. The behavior of the laminar flame speed with unburned gas temperature is very similar to that computed by Warnatz9 for 1 atm pressure and stoichiometric H2-air. Figure 3 shows the effect of variation in pressure on laminar flame speeds at 900 K unburned gas temperature and a hydrogen-air equivalence ratio of 0.4. The laminar flame speeds (Su) decreased as the pressure was increased from 1 to 70 atm by the relation Su ≈ P-0.2, under fuel-lean conditions. This result is noted by the curve-fitted expression as shown in Figure 3. This pressure dependence compares to P+0.2 computed by (9) Warnatz, J. Combust. Sci. Technol. 1981, 26, 203-213.
80 Energy & Fuels, Vol. 12, No. 1, 1998
Marinov et al. Table 1. Summary of Simulation Results for Sandia Free-Piston Compression-Expansion Machine mixture composition
Figure 3. Laminar flame speed variation with pressure at a hydrogen-air equivalence ratio of 0.4 and unburned gas temperature of 900 K.
Warnatz9 for stoichiometric hydrogen-air mixtures with an unburned gas temperature of 298 K. The pressure dependence of the flame speed is a result of the combined effect of chemical kinetics and transport processes. However, we expect that the difference in pressure exponent between the ultralow equivalence ratio flame and the stoichiometric flame is primarily due to the influence of chemical kinetics. The chemical kinetic behavior can be explained by the competition between the H-atom reactions:
H + O2 ) OH + O
(2)
H + O2 (+M) ) HO2 (+M)
(3)
Reaction 2 leads to chain branching, which accelerates the flame, and reaction 3 leads to chain termination, which deaccelerates the flame. The ratio of the rates of these two reactions is given by
R ) k3[M]/k2 where k2 and k3 are the forward rate constant for reactions 2 and 3, respectively, and [M] is the total concentration. Under the present conditions of the ultralow equivalence ratio flame, reaction 3 competes effectively for H atoms, leading to the unreactive HO2 radical. As the pressure is increased, the ratio R increases; chain termination is increased at the expense of chain branching and contributes to a decrease in the flame speed as seen in Figure 3. However, for the stoichiometric flame studied by Warnatz, reaction 3 does not compete effectively for H atoms with reaction 2. With its higher burnt gas temperatures (about 2400 versus 1900 K in the ultralow equivalence ratio flame), the rate of reaction 2 with its high activation energy (about 17 kcal/mol) is much higher than the rate of reaction 3. An increase in pressure does increase the rate of reaction 3 but not enough to compete with reaction 2. The pressure dependence of the flame speed is influenced by the chain-branching of reaction 2 whose reaction rate increases with pressure for two reasons. First, reaction 2 is bimolecular and its reaction rate increases with pressure through the increase in concentrations of H and O2. Second, the rate constant with its high activation energy increases because of a slight increase in burnt gas temperature. As the pressure is raised from 1 to 2 atm in the stoichiometric flame, the burnt gas temperature goes up from 2380 to 2400 K. These chemical kinetic effects lead to a greater pressure
natural gas [%]
H2 [%]
CCR
NO [ppm]
NO2 [ppm]
N2O [ppm]
TMAX [K]
TTDC [K]
100 75 50 25 20 10 5 0
0 25 50 75 80 90 95 100
58.0 54.5 50.5 45.8 44.5 42.0 40.8 39.0
70.6 65.2 67.5 84.4 88.2 114.0 148.0 186.0
6.6 6.1 6.2 7.1 7.3 8.7 10.5 12.2
1.9 1.8 1.7 1.6 1.5 1.4 1.3 1.3
2146 2142 2144 2161 2167 2187 2205 2226
1212 1196 1177 1156 1151 1141 1138 1131
exponent for the stoichiometric flame versus the ultralow equivalence ratio flame. Free Piston Engine. The free-piston engine (FPE) is a novel engine concept with a freely moving piston and a combustion chamber on each end of the piston.2 In one combustion chamber, the piston compresses the fuel-air mixture until autoignition occurs near TDC while the burnt gases in the combustion chamber at the opposite end are being expanded. With high octane quality fuel, the FPE can operate at very high compression ratios to give high thermodynamic efficiencies. Hydrogen and hydrogen-hydrocarbon mixtures offer the high octane quality needed for the FPE. Experiments have been performed in a free-piston compression-expansion machine2 to simulate combustion in a FPE. The chemical kinetic model was used to predict autoignition and NOx emissions in this machine. In the free-piston compression-expansion machine, hydrogenair mixtures are compressed with a free piston until autoignition occurs. Then the gases expand as the free piston moves backward. This compression and expansion was simulated using the HCT code.7 The fuel-air mixture was assumed to be homogeneous, and global heat loss was taken into account using the Woshni correlation.10 The HCT calculation follows the chemical evolution of the fuel-air mixture as it is compressed and expanded. The volume history of the gas being compressed and expanded was specified using a typical experimental record.2 A series of simulations was carried out with fuel-air mixtures at φ ) 0.332, varying from 100% natural gas and 0% H2 to 0% natural gas and 100% H2. The initial conditions for the calculations were 1 atm and 298 K at bottom dead center. The natural gas composition was based on the average composition as determined by a Gas Research Institute survey.11 The average composition is 93.9% methane, 3.0% ethane, 0.7% propane, 0.2% n-butane, 0.2% isobutane, 1.0% nitrogen, and 1.0% carbon dioxide. Each simulation followed the experimental volume history in the compression-expansion machine, while the compression ratio was varied until the critical compression ratio (CCR) was reached (defined as the minimum compression ratio at which autoignition occurs when the piston reaches top dead center (TDC)). A summary of the simulations performed and their results are given in Table 1 and Figure 4. (10) Heywood, J. B. Internal Combustion Engines; McGraw-Hill Publishing Company: New York, 1988; pp 679-680. (11) Liss, W. E.; Thrasher, W. H.; Steinmetz, G. F.; Chowdiah, P.; Attari, A. Variability of Natural Gas Composition in Select Major Metropolitan Areas of the United States. Gas Research Institute Report GRI-92/0123; Gas Research Institute: Chicago, IL, 1992.
Modeling of Hydrogen
Figure 4. Predicted NO, NO2, and N2O emissions and maximum temperature from combustion of natural gashydrogen-air mixtures with φ ) 0.332 in a free-piston compression-expansion machine.
A much higher compression ratio was required to achieve autoignition at TDC for natural gas (CCR ) 58.0) compared to hydrogen (CCR ) 39.0) (Table 1). It is interesting to compare the temperature and pressures of the two cases at TDC without chemical reaction because the peak temperature and pressures are important parameters that drive the chemistry of the mixture. The temperature (TTDC) in Table 1 gives the temperature at TDC computed with the chemical reaction rates set to zero. The TTDC of the natural gas (1212 K) is only 7% higher than that of hydrogen (TTDC ) 1131 K) even though the compression ratio for natural gas was much higher. This result is due to the higher ratio of specific heats (γ ) Cp/Cv) for hydrogen versus natural gas. For the series of runs in Table 1, the temperature histories computed without reaction are fairly similar even though the compression ratios are quite different. However, the pressure histories without chemical reaction are much different, with pure natural gas attaining 240 atm and pure hydrogen attaining a maximum pressure of 151 atm. As the mixture composition is changed from pure hydrogen to pure natural gas, the difference in temperature is 7% versus a 59% difference in pressure. Note that chemical kinetics are much more sensitive to temperature than pressure. One of the key results of these calculations is that the concentration of NOx emissions increases with H2 concentration; the higher the H2 content the higher the NOx emissions. These results suggest that adding small amounts of natural gas to hydrogen will significantly reduce NOx emissions from a free-piston compressionignition engine. These computed results are consistent with experimental results obtained by Van Blarigan et al.12 in the free-piston machine where propane-air mixtures gave NOx levels much less than H2-air mixtures for the same ultralow equivalence ratio. To investigate our computed results, the maximum temperature (TMAX) in the compression-expansion cycle was examined and is recorded in Table 1 and plotted in Figure 4 along with the previously calculated oxides of nitrogen. As seen in Figure 4, the NO concentration correlates closely with the maximum temperature (TMAX) that occurs during the piston cycle. As natural gas is added to the hydrogen, TMAX decreases, which causes a (12) Van Blarigan, P. Private communication.
Energy & Fuels, Vol. 12, No. 1, 1998 81
decrease in NO concentration as explained later. TMAX is determined by the temperature rise due to compression by the piston (TTDC - 300 K) and the temperature rise due to the nearly constant volume combustion at TDC. The temperature rise due to compression increases with added natural gas and does not explain the observed trends in NO concentration. The temperature rise due to constant volume combustion (∆TCVC ) TMAX - TTDC) decreases with added natural gas and is consistent with the NO trends. ∆TCVC is only dependent on thermodynamic quantities (the internal energy of the fuel-air mixture at TDC and the equilibrium composition of the products of combustion) and not chemical kinetics. Therefore, the decrease in NO with addition of natural gas is due to the change in thermodynamic quantities of the mixture at TDC. The good correlation between TMAX and NO concentration is consistent with the NO being primarily formed by a thermal (or Zeldovich) mechanism. The extended Zeldovich mechanism is
N2 + O ) NO + N
(1)
O2 + N ) NO + O
(4)
OH + N ) NO + H
(5)
NO formation is initiated by reaction 1, which has a high activation energy (about 76 kcal/mol13 ) and which becomes important at high temperatures. Reaction 1 produces a NO plus a N atom that can react via reactions 4 and 5 to produce another NO. A series of calculations were performed where selected reactions forming NO were “turned off” by setting the reaction rate constant to zero. In this way we could examine the role of each reaction in NO production. First, a calculation was performed with reaction 1 “turned off” and the NO concentration dropped from 186 to 58 ppm for the pure H2 case. “Turning off” reaction 1 not only prevents production of a NO from reaction 1 but also prevents the production of a second NO from reactions 4 and 5. Thus, “turning off” reactions 1, 4, and 5 gave the same result as “turning off” reaction 1. These calculations show that the extended Zeldovich NO steps are the primary formation steps for NO under the present conditions. A calculation was performed in which the NNH reactions
H + N2 T NNH NNH + O f NH + NO were “turned off”. These reactions comprise a newly discovered route to NOx.13 With the NNH reactions “turned off” the NO level dropped from 186 to 182 ppm, indicating a minor role for these reactions. Calculations were performed where the NO-producing reactions were “turned off” individually and in combinations. It was found that “turning off” the following series of reactions would reduce the NO and NO2 to below 0.01 ppm and the N2O below 2 ppm for the pure (13) Dean, A. M.; Bozzelli, J. W. In Combustion Chemistry II; Gardiner, W. J., Ed.; Springer-Verlag: New York, 1997.
82 Energy & Fuels, Vol. 12, No. 1, 1998
Marinov et al.
hydrogen and pure natural gas cases:
N2 + O ) NO + N
(1)
N2O + O ) NO + NO
(6)
N2O + H ) NH + NO
(7)
N2 + OH ) NH + NO
(8)
NNH + O ) NH + NO
(9)
These calculations indicate that NO and NO2 formation is nearly eliminated by “turning off” the production of NO from N2 (reactions 1 and 8), from N2O (reactions 6 and 7), and from NNH (reaction 9). We examined whether the hydrocarbon chemistry was affecting the NO production as natural gas was added to hydrogen. The most important effect would be hydrocarbon reactions producing or consuming O atoms and influencing the O atom concentration. Any change in O atom concentration would affect NO production through reactions 1, 6, and 9 above. The calculations showed that the O atom levels were controlled entirely by reactions contained in the hydrogen-oxygennitrogen reaction submechanism. Hydrocarbon reactions producing or consuming O atoms had a negligible influence on the O atom concentration. Real Gas Effects in the Free-Piston Compression-Expansion Machine. At top dead center with a fuel-air equivalence ratio of 0.31 and a compression ratio of 34:1, the pressures reach 120 atm before the hydrogen-air mixture autoignites. These pressures are high enough to raise concerns about real gas effects. The current model developed to simulate these experiments uses the HCT code that assumes an ideal gas equation of state. If real gas effects are important, the temperatures and pressures being calculated by HCT for the free-piston experiments could be in error. To assess real gas effects, the Chemkin Real Gas code was obtained from Professor Barry Butler at University of Iowa.14 A series of calculations were performed assuming constant volume combustion at top dead center after isentropic compression by the free piston. A number of different compression ratios were considered to give the pressures 3, 10, 30, 100, and 300 atm and associated temperatures at top dead center. These temperatures and pressures were calculated by the isentropic relation assuming a constant γ of 1.34 for a hydrogen-air mixture. A fuelair equivalence ratio of 0.31 was used based on the freepiston experiments. Constant volume equilibrium calculations were carried out using both real gas and ideal gas equations of state. The Peng-Robinson equation of state was used for the real gas case.14 The final pressures and temperatures attained after combustion at top dead center for the real gas and ideal gas cases were compared. Calculations showed that the real gas pressure after combustion is higher than the ideal gas pressure by as much as 5% at the initial pressure of 300 atm at top dead center. At the experimentally measured pressure of 120 atm at top dead center before (14) Schmitt, R. G.; Butler, P. B.; French, N. B. Chemkin Real Gas: A fortran package for analysis of thermodynamic properties and chemical kinetics in nonideal systems. Report UIME PBB 93-006; The University of Iowa: Iowa City, 1994.
autoignition, the computed real gas pressure is about 3% higher than the ideal gas pressure. Calculations showed that the difference between the real gas and ideal gas temperature after autoignition is very small and only about 0.1% at a 300 atm initial pressure. The temperature based on the ideal gas equation of state was slightly higher than that based on the real gas equation of state. However, the chemical kinetic calculations of autoignition are much more sensitive to temperature than to pressure. We do not expect the small difference in temperature (about 10 K at TDC after combustion) or pressure to have much effect on the computed results. Conclusions A chemical kinetics model for hydrogen-air combined with NOx kinetics was used in a parametric investigation of laminar flame speeds and NOx concentration levels for conditions applicable to lean hydrogen-fueled internal combustion engines. These results can be used for the development of a turbulent flame speed submodel for CFD codes such as KIVA, which simulate combustion and fluid dynamics in engines. The results also provide laminar flame speeds for extreme conditions of pressure and temperature found in internal combustion engines. Very little information on laminar flame speed under these conditions is available in the literature. The detailed chemical kinetic model was used to predict NO, NO2, and N2O emissions for a series of natural gas-hydrogen in air mixtures in the freepiston compression-expansion machine. It was seen that addition of natural gas to hydrogen fuel reduces the computed levels of nitrogen oxides. Calculations showed that the predicted NO concentrations correlated well with the maximum temperature in the compression-expansion cycle and that the NO was mostly produced by
N2 + O f NO + O The effect of real gas behavior on combustion of hydrogen-air mixtures has been assessed at high-pressure conditions attained in the free-piston engine experiments. The computed real gas pressures were as much as 3% higher than the ideal gas pressures. The computed temperature at top dead center showed very little dependence on the choice of ideal or real gas equation of state. We expect that these real gas effects will have a small effect on the computed results, which assumed an ideal gas equation of state. Acknowledgment. The authors greatly appreciate the assistance of Peter Van Blarigan at Sandia National Laboratories who gave us experimental volume histories from the machine, Scott Goldsborough at Sandia National Laboratories who modified HCT to simulate the free-piston compression-expansion machine, and Professor Barry Butler at the University of Iowa who sent us a copy of Real Gas Chemkin. This work was supported by the U.S. Department of Energy, Office of Solar Thermal, Biomass Power, and Hydrogen Technologies and carried out under the auspices of the U.S. Department of Energy by the Lawrence Livermore National Laboratory under Contract W-7405-ENG-48. EF9701044
