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Journal of Combustion
VolumeΒ 2012Β (2012), Article IDΒ 927081, 8 pages
http://dx.doi.org/10.1155/2012/927081
Research Article

Extending Lean Operating Limit and Reducing Emissions of Methane Spark-Ignited Engines Using a Microwave-Assisted Spark Plug

1Department of Mechanical Engineering, University of California, Berkeley, 50B Hesse Hall, Berkeley, CA 94720-1740, USA
2Imagineering Inc., Room 351, Welv Rokko 2nd Building, 4-1-1 Fukada, Nada, Kobe 657-0038, Japan

Received 10 May 2012; Accepted 4 July 2012

Academic Editor: ShiYongΒ Liao

Copyright Β© 2012 Vi H. Rapp et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

A microwave-assisted spark plug was used to extend the lean operating limit (lean limit) and reduce emissions of an engine burning methane-air. In-cylinder pressure data were collected at normalized air-fuel ratios of πœ†=1.46, πœ†=1.51, πœ†=1.57, πœ†=1.68, and πœ†=1.75. For each πœ†, microwave energy (power supplied to the magnetron per engine cycle) was varied from 0 mJ (spark discharge alone) to 1600 mJ. At lean conditions, the results showed adding microwave energy to a standard spark plug discharge increased the number of complete combustion cycles, improving engine stability as compared to spark-only operation. Addition of microwave energy also increased the indicated thermal efficiency by 4% at πœ†=1.68. At πœ†=1.75, the spark discharge alone was unable to consistently ignite the air-fuel mixture, resulting in frequent misfires. Although microwave energy produced more consistent ignition than spark discharge alone at πœ†=1.75, 59% of the cycles only partially burned. Overall, the microwave-assisted spark plug increased engine performance under lean operating conditions (πœ†=1.68) but did not affect operation at conditions closer to stoichiometric.

1. Introduction

Concerns with greenhouse gases, air quality, and shortage of fossil fuels have encouraged the development of new technology and alternative fuels that reduce emissions of combustion engines. Natural gas (containing mostly methane) offers lower greenhouse gas emissions than other hydrocarbon fuels because of its high hydrogen-to-carbon ratio. Natural gas can also be combusted at high compression ratios without the risk of producing engine knock. Burning natural gas (containing mostly methane) with air-fuel ratios larger than stoichiometric (lean conditions) in spark-ignited engines has the potential to produce lower emissions and higher thermal efficiencies than petroleum-burning engines [1, 2]. However, if the air-fuel mixture is too lean, the high amount of air dilution destabilizes combustion, decreasing flame speeds and making the air-fuel mixture more difficult to ignite [3, 4]. When combustion becomes unstable due to increased air dilution, engine performance and efficiency deteriorate, limiting the full potential of lean combustion. This unstable combustion point is well known as the β€œlean limit.”

One method of increasing burn rates of lean natural gas mixtures and extending the lean limit is to increase turbulent mixing inside the combustion chamber. Das and Watson [1] modified an engine to increase turbulent mixing by swirling the charge during induction and using a squish motion during the compression stroke, which broke up the intake-generated turbulence into small-scale turbulence inside the combustion chamber. Using this technique and changing the compression ratio, Das and Watson were able to operate the engine at normalized air-fuel ratio (πœ†) of 1.88. However, the peak thermal efficiency occurred at πœ†=1.20. The engine also produced less carbon dioxide (CO2), hydrocarbon, and nitrogen oxide (NOπ‘₯) emissions than equivalent petroleum engines. Evans [5] achieved similar results using a β€œsquish-jet” combustion chamber but also investigated the effects of a partially stratified-charge mixture near the spark plug to enhance ignition of lean mixtures. Evans’ results showed that the partially stratified-charge combustion system extended the lean limit of operation and reduced NOπ‘₯ emissions. Cho and He [6] found that delaying fuel injection reduced CO and HC emissions at 25% throttle and 100% throttle.

Another method for stabilizing lean operation and reducing emissions is addition of hydrogen to natural gas-fueled engines. Several researchers have shown that addition of hydrogen increases flame propagation of the air-fuel mixture, extending the lean operating limit and reducing emissions [7–14]. Smutzer [8] developed a hydrogen-assisted lean operation (HALO) engine that achieved operation at ultralean conditions (πœ†=2.0), eliminating NOπ‘₯ production and reduced spark ignition energy by 22%. However, nonuniformities in fueling lead to high cylinder-to-cylinder variation in the engine. Wang et al. [10] investigated the cycle-to-cycle variations in natural gas-hydrogen blends and found that addition of hydrogen is strongly correlated with peak in-cylinder pressure, pressure rise rate, and crank angle degree of peak in-cylinder pressure. They also found that addition of hydrogen decreased cycle-to-cycle variation under stoichiometric conditions and lean conditions. Kornbluth et al. [11] found that adding hydrogen (30%–50% by volume) to landfill gas (containing mostly methane and CO2) while operating under lean conditions increased engine stability and power, while decreasing emissions, especially NOπ‘₯. Their results also show that increasing the concentration of hydrogen extended the lean limit [11].

High-energy ignition devices have also been used to extend lean limits beyond the capabilities of a traditional spark discharge ignition systems [15, 16]. One such high-energy ignition technology of current research interest is the microwave-assisted spark plug, under development by Imagineering Inc., which delivers microwaves into the combustion chamber in addition to the standard spark discharge [17, 18]. A capacitive discharge spark initiates plasma in the combustion chamber, and microwaves expand the plasma. As compared to arc discharges, which traditionally ignite internal combustion engines, microwave plasma discharges are characterized by higher spatial uniformity, lower plasma potential, higher electron energy, and increased excitation of vibrationally and electronically excited states of molecules [19]. High-energy electrons, having received energy from microwaves, can enhance mixture reactivity through electron impact reactions which generate radicals and metastable electronically excited chemical species [19]. Past studies have shown that a microwave-assisted spark plug can extend the lean limit of gasoline-fueled engines [17, 20, 21] and that microwaves can enhance flame speed in wall-stagnated methane flames [22].

Although the microwave-assisted spark plug has proven effective for gasoline-fueled engines operating under lean conditions [17, 20, 21], its effectiveness has not previously been demonstrated for use on engines burning methane-based fuels (such as natural gas). For this study, a single-cylinder engine burning methane-air was modified to operate using a microwave-assisted spark plug system. The performance of the microwave-assisted spark discharge was compared to the spark-only discharge over a range of air-fuel ratios and microwave energy levels.

Following this section, the instrumentation, experimental design, and variables used to measure engine stability and performance are described. Next, results and discussions are presented. Last, conclusions are made, and future work is suggested.

2. Material and Methods

2.1. Engine Specifications

Experiments were conducted using a single cylinder Waukesha ASTM-Cooperative Fuel Research (CFR) engine. Engine specifications can be found in Table 1. A schematic of the CFR engine with the microwave-assisted spark plug system is shown in Figure 1. A compressed gas cylinder supplied methane to the CFR gaseous fuel injector. The CFR engine was fitted with the Imagineering, Inc. microwave-assisted spark plug system, which transmits 2.45 GHz microwaves into the combustion chamber through the spark plug insulator. The microwaves interact with plasma initiated by a 30 mJ capacitive spark discharge [17].

tab1
Table 1: Engine specifications.
927081.fig.001
Figure 1: Schematic of Cooperative Fuel Research (CFR) engine with microwave-assisted spark plug system. Sensors are marked with dashed lines.

2.2. Measurement Instrumentation

In-cylinder pressure was measured using a 6052B Kistler piezoelectric pressure transducer in conjunction with a 5044A Kistler charge amplifier and was recorded every 0.1 crank angle (CA) degree. The cylinder pressure transducer was mounted in the cylinder head. Intake pressure was measured using a 4045A5 Kistler piezoresistive pressure transducer in conjunction with a 4643 Kistler amplifier module. Intake temperature and exhaust temperature were measured using K-type thermocouples. Crank angle position was determined using an optical encoder, while an electric motor, controlled by an ABB variable speed frequency drive, controlled the engine speed. A Motec M4 ECU (Engine Control Unit) controlled injection timing, injection pulse width, and injection duty cycle. A Horiba analyzer measured emissions and equivalence ratio. A wideband lambda sensor was used to establish stoichiometric conditions and compared with emissions results. Figure 1 shows a schematic of the engine with the location of each sensor.

2.3. Experimental Design

Microwave-assisted spark plug performance was explored over a range of microwave energy inputs, normalized air-fuel ratios (πœ†), and spark timings. Compression ratio and engine speed were held constant, and the engine was operated naturally aspirated at wide-open throttle. Engine operating conditions are outlined in Table 2. At each operating condition, spark timing was adjusted to achieve Maximum Brake Torque (MBT), at which point 300 thermodynamic cycles of in-cylinder pressure data were recorded (each cycle consisting of 720 CAD). The parameter space of normalized air-fuel ratio included πœ†=1.46,πœ†=1.51,πœ†=1.57, and πœ†=1.75. The parameter space of total energy supplied to the magnetron per engine cycle included 0 mJ (spark only), 130 mJ, 900 mJ, and 1600 mJ. The 130 mJ energy input condition was achieved by supplying the magnetron with peak power of 2.6 kW at a 12.5% duty cycle over a 0.36 ms duration. The 900 mJ and 1600 mJ conditions also operated with peak input power of 2.6 kW, but with 25% duty cycle and durations of 1.32 ms and 2.65 ms, respectively. The power supplied to the magnetron falls off with increasing duration, explaining why total energy input does not scale linearly with energy input duration. The total microwave energy delivered to the combustion chamber is estimated to be approximately 17% of the energy supplied to the magnetron after accounting for reflection and transmission losses.

tab2
Table 2: Engine operating conditions.

2.4. Data Analysis

The performance of the microwave-assisted spark plug is characterized by using the indicated mean effective pressure (IMEP) and the indicated thermal efficiency [23]. Engine stability is characterized by two parameters. The first parameter is the coefficient of variation of the IMEP (COVIMEP): COVIMEP=𝜎IMEPπ‘₯IMEPΓ—100,(1) where 𝜎IMEP is the standard deviation in IMEP and π‘₯IMEP is the mean IMEP [23]. COVIMEP increases when engine operation becomes unstable, leading to partial burn cycles and misfires [23].

The second parameter is the modified pressure ratio (MPR): 𝑝MPR=max𝑝motoring-maxβˆ’1,(2) where 𝑝max is the maximum pressure with ignition and 𝑝motoring-max is the maximum pressure while motoring (no ignition) [24]. The MPR determines if a cycle has completely combusted, partially burned, or misfired (no combustion) [24]. For methane, at πœ†=1.68, the limits of complete combustion, partial burn, and misfire were identified as complete 1.8<MPR≀3.5, partial burn 0.5<MPR≀1.8, misfire 0≀MPR≀0.5.

Under lean conditions, the normalized air-fuel ratio, πœ†, was calculated using π‘šπœ†=𝑓,stoichπ‘šπ‘“,(3) where π‘šπ‘“,stoich is the stoichiometric mass of the fuel injected per cycle and π‘šπ‘“ is the actual mass of the fuel injected per cycle [23, 25].

The change in emissions is determined by ξ‚΅%changeinemissions=ppmMWppmSpkξ‚Άβˆ’1Γ—100,(4) where ppmMW is the measured emission in ppm when microwave energy is added and ppmSpk is the measured emissions in ppm when no microwave energy is added (spark only).

Uncertainty in measured data is reported as mean Β± uncertainty with a confidence level of 95%. Uncertainty in calculated parameters is reported from an uncertainty analysis, and the details can be found in the Appendix.

3. Results and Discussion

The performance of the microwave-assisted spark plug is gauged by the following: engine stability, engine power, and emissions output. Engine stability is expressed by COVIMEP and the percentage of complete combustion cycles. Engine power and performance are given by IMEP and the indicated thermal efficiency. Emissions output for each experiment is provided and compared with stability and performance variables.

3.1. Engine Stability

Engine operation was considered to be stable when COVIMEP was no more than 10%, and the percentage of complete combustion cycles was at least 95%. Shown in Figure 2 is the dependence of COVIMEP on πœ† for all operating conditions. At the leanest operating condition (πœ†=1.75), stable combustion could not be achieved, and multiple misfires occurred using a standard spark discharge. Supplying 1600 mJ per engine cycle to the magnetron consistently ignites the mixture, shown in Figure 2; however, the COVIMEP is 41%, and the percentage of complete combustion cycles is 37% (59% partial burn and 4% misfire), indicating unstable operation.

927081.fig.002
Figure 2: Engine stability increases with the addition of microwave energy as πœ† increases. Increasing microwave energy from 900 mJ to 1600 mJ did not further increase engine stability.

Decreasing πœ† to 1.68 continued to result in unstable operation when using a standard spark discharge. Figure 2 shows the COVIMEP is 35% and the percentage of complete combustion cycles is 77%, while 17% of the cycles partially burn and 6% of the cycles misfire as seen in Figure 3. Adding 130 mJ of energy to the microwave system decreases COVIMEP to 25% and increases the number of complete combustion cycles to 89% (7% partial burn cycles and 4% misfire). Further addition of microwave energy (900 mJ) decreases COVIMEP to 8% and increases the complete combustion cycles to 98% (2% partial burn cycles), resulting in stable operation. Figure 2 shows that addition of 1600 mJ of microwave energy decreases engine stability; however, the difference in partial burn cycles and thermal efficiency from the 900 mJ case was less than 2% for both. The observed small difference implies that adding 1600 mJ of energy neither decreases nor further improves engine stability. These results also suggest that the microwave input may be most effective during the earliest stage of ignition since the 1600 mJ and the 900 mJ energy inputs have the same power, but the 1600 mJ setting is operated for a longer duration, as stated in the methods. Addition of microwave energy did not affect COVIMEP at operating conditions closer to stoichiometric (πœ†<1.52) because almost all the cycles (>99%) completely burned.

927081.fig.003
Figure 3: At πœ†=1.68, adding microwave energy to the spark discharge per cycle decreases occurrence of misfire and partial-burn cycles, thus increasing the total number of complete combustion cycles.
3.2. Engine Power and Performance

Engine power and performance are given by IMEP and the indicated thermal efficiency. Figure 4 shows IMEP decreases with increasing πœ† for all operating conditions. For πœ†>1.55, the microwave-assisted spark plug increases engine performance by enhancing burning, leading to better engine stability. At πœ†=1.68, addition of microwave energy slightly increases IMEP. For πœ†<1.55, the microwave appears to have almost no effect on IMEP.

927081.fig.004
Figure 4: Addition of microwave energy slightly increased IMEP at larger πœ†. Increasing microwave energy did not further increase IMEP. Error bars are Β± the uncertainty calculated using propagation of error (see Appendix  A).

For the standard spark discharge, Figure 5 shows an increase in indicated thermal efficiency as air-fuel ratio increases from πœ†=1 to πœ†=1.46. Beyond πœ†=1.46, the indicated thermal efficiency decreases due to incomplete combustion. Addition of microwave energy at πœ†=1.68 increases indicated thermal efficiency by up to 4% but shows minimal improvement between πœ†=1.46 and πœ†=1.57. The peak indicated thermal efficiency occurred at πœ†=1.46, which are slightly leaner conditions than previous studies burning only natural gas [1, 6].

927081.fig.005
Figure 5: Addition of microwave energy increases thermal efficiency at πœ†=1.68. Error bars are Β± the uncertainty calculated using propagation of error (see Appendix  A).
3.3. Engine Emissions

The effects of the microwave spark-plug system on emissions were explored by normalizing the microwave operating condition emissions with the standard spark discharge emissions and finding the percent difference (see (4)). Figure 6 shows NOπ‘₯ production increases when the engine is run with 1600 mJ of microwave energy. At πœ†=1.46, when stable combustion is unaffected by microwaves, microwave-enhanced ignition increases NOπ‘₯ production by 13% (about 100 ppm), indicating a small direct contribution of the added microwave energy towards NOπ‘₯ formation. As operating conditions become leaner (πœ†=1.57 and πœ†=1.68,) the difference in NOπ‘₯ production between spark-only and microwave-enhanced operation widens. This increase is due to an increase in complete combustion cycles when the engine is operating with microwave energy in addition to the direct contribution of NOπ‘₯ when adding microwave energy. The minimum NOπ‘₯ measurement for all operating conditions was 3.75 g/kWh.

927081.fig.006
Figure 6: The percent change in NOπ‘₯ emissions with 1600 mJ microwave-enhanced ignition from NOπ‘₯ emissions with spark-only ignition. Under stable operating conditions (πœ†=1.46), addition of microwave energy increases NOπ‘₯ production by 13% (~100 ppm). Increasing πœ† further increases NOπ‘₯.

Figure 7 shows that addition of 1600 mJ of microwave energy decreases carbon monoxide (CO) and total unburned hydrocarbons (THC) as operating conditions become leaner. This trend agrees with previous results [11] and is due to an increase in complete combustion cycles with the addition of microwave energy under leaner operating conditions (πœ†>1.51).

927081.fig.007
Figure 7: The percent change in carbon-monoxide (CO) emissions and total unburned hydrocarbon (THC) emissions with 1600 mJ of microwave-enhanced ignition from emissions with spark-only ignition. Addition of microwave energy decreases the amount of CO and THC at leaner conditions. A decrease in THC is expected under lean operation with the microwave because more cycles are complete combustion.

4. Conclusions and Recommendations

In this study, we found that a microwave-assisted spark plug extends the lean stable operating limit of an engine burning methane-air. The addition of microwave energy improved engine stability and as a result also increased engine performance. At the leanest operating condition (πœ†=1.75), a standard spark discharge did not consistently ignite the air-fuel mixture and resulted in multiple misfires. However, with the addition of microwave energy, the mixture ignited, resulting in mostly partial burn cycles (59%) and few misfire cycles (4%). Decreasing the normalized air-fuel ratio from πœ†=1.75 to πœ†=1.68 allowed for engine performance comparisons between the spark discharge alone and the spark discharge with microwave energy assistance. Addition of microwave energy at πœ†=1.68 increased the number of complete combustion cycles, the indicated mean effective pressure, and the indicated thermal efficiency.

Increasing the total microwave energy input to the magnetron per cycle from 130 mJ to 900 mJ improved engine stability. Further increasing input energy to the microwave system from 900 mJ to 1600 mJ by increasing the duration of energy input showed no additional improvements. These results suggest that microwave input may be effective only during the earliest stage of ignition, when a small flame kernel is still present near the spark plug electrode. For richer mixtures (πœ†<1.52), microwave energy did not improve engine stability because almost all the cycles completely burned.

Addition of microwave energy decreased CO and total unburned hydrocarbon emissions but increased NOπ‘₯ emissions. The increase in NOπ‘₯ is due to an increase in complete combustion cycles when microwave energy is added to the ignition. Also, under leaner operating conditions (πœ†=1.57), combustion advances slightly, allowing more time for NOπ‘₯ formation.

The present microwave-assisted spark plug fully eliminated misfires under lean conditions (πœ†=1.68) and could likely allow for steady, lean operation when burning other alternative fuels. However, performance of the microwave-assisted spark plug should be further tested using alternative fuels. Using a higher-turbulence engine with the microwave spark-plug system may also increase power output and further extend the lean limit. Additionally, investigating flame occurrence and propagation using optical techniques may also provide further insight on the effectiveness of a microwave-assisted spark plug.

Appendix

A. Uncertainty Analysis

An uncertainty analysis was performed on all engine measurements and calculations, except emissions. For the measured values, the random uncertainty was calculated using 95% confidence intervals (approximately 2 times the standard error, 𝜎π‘₯ for normally distributed errors) [26]: 𝑅π‘₯=2Γ—πœŽπ‘₯=2𝜎π‘₯βˆšπ‘,(A.1) where π‘₯ is the measured value, 𝑁 is the number of cycles, 𝜎π‘₯ is the standard deviation, defined as 𝜎π‘₯=1π‘βˆ’1𝑁𝑖=1ξ€·π‘₯π‘–βˆ’π‘₯ξ€Έ2ξƒͺ1/2,(A.2) and π‘₯ is the mean of the measured values.

The general formula for error propagation in an equation with multiple variables was calculated using [26, 27] π‘ˆπ‘Ÿ=ξƒŽξ‚΅πœ•π‘Ÿπœ•π‘₯1π‘ˆπ‘₯1ξ‚Ά2+ξ‚΅πœ•π‘Ÿπœ•π‘₯2π‘ˆπ‘₯2ξ‚Ά2ξ‚΅+β‹―+πœ•π‘Ÿπœ•π‘₯π‘›π‘ˆπ‘₯𝑛2,(A.3) where uncertainty is being measured in π‘Ÿ and π‘₯𝑛 are independent variables with measured uncertainties. This error propagation formula was used to determine the uncertainty in calculated variables.

A.1. In-Cylinder Pressure

As mentioned previously, the in-cylinder pressure was measured using a 6052B Kistler piezoelectric pressure transducer in conjunction with a 5044A Kistler charge amplifier. The systematic error for the transducer, 𝐡𝑃, is listed as 0.2 bar. Random uncertainty in the pressure data was calculated using (A.1) and a minimum of 300 cycles.

Using the random uncertainty and the systematic error in the pressure, the total uncertainty in pressure can be calculated using [26, 27] π‘ˆπ‘=𝑅2𝑝+𝐡2𝑝.(A.4)

A.2. Volume

The volume at each crank angle degree can be calculated by [27] 𝑉=𝑉𝑐+πœ‹π΅24𝑙𝑙+π‘Žβˆ’π‘Žcosπœƒβˆ’2βˆ’π‘Ž2sin2πœƒξ€Έ1/2,(A.5) where 𝑉𝐢 is the clearance volume, 𝐡 is the bore, 𝑙 is the connecting rod length, and π‘Ž is crank radius [23]. Top Dead Center (TDC) of the motoring traces was calculated using the method outlined by Tunestal [28]. The uncertainty in crank angle degree, using Tunestal’s method to find TDC, is 0.05Β°. The uncertainty in volume can be determined using π‘ˆπ‘‰=π‘‘π‘‰π‘ˆπ‘‘πœƒπœƒ,(A.6) where 𝑑𝑉=1π‘‘πœƒ4πœ‹π΅2ξƒ©π‘Žπ‘Žsinπœƒ+2sinπœƒcosπœƒβˆšπ‘™2βˆ’π‘Ž2sin2πœƒξƒͺ.(A.7)

A.3. Indicated Work

The indicated work is calculated using the trapezoidal method of integration: π‘Š=π‘›βˆ’1𝑖Δ𝑉𝑖𝑝𝑖+1+𝑝𝑖2,(A.8) where 𝑛 is the number of divisions and 𝑝 is the pressure [23]. Using (A.3), the uncertainty in the work can be determined by π‘ˆ2π‘Š=ξ‚΅πœ•π‘Šπœ•Ξ”π‘‰1π‘ˆΞ”π‘‰1ξ‚Ά2+ξ‚΅πœ•π‘Šπœ•π‘1π‘ˆπ‘1ξ‚Ά2+ξ‚΅πœ•π‘Šπœ•π‘2π‘ˆπ‘2ξ‚Ά2ξ‚΅+β‹―+πœ•π‘Šπœ•Ξ”π‘‰π‘›βˆ’1π‘ˆΞ”π‘‰π‘›βˆ’1ξ‚Ά2+ξ‚΅πœ•π‘Šπœ•π‘π‘›βˆ’1π‘ˆπ‘π‘›βˆ’1ξ‚Ά2+ξ‚΅πœ•π‘Šπœ•π‘π‘›π‘ˆπ‘π‘›ξ‚Ά2.(A.9)

A.4. Indicated Power, IMEP, and Indicated Thermal Efficiency

Knowing the uncertainty in the work, the uncertainty in the indicated power indicated mean effective pressure (IMEP), and the indicated thermal efficiency (πœ‚th) can be determined using the equation for uncertainty in products and quotients: ξ‚΅π‘ˆπ‘Ÿξ‚Ά|π‘Ÿ|2=ξ‚΅π‘ˆπ‘₯1||π‘₯1||ξ‚Ά2+ξ‚΅π‘ˆπ‘₯2||π‘₯2||ξ‚Ά2ξ‚΅π‘ˆ+β‹―π‘₯𝑛||π‘₯𝑛||ξ‚Ά2,(A.10) where uncertainty is being measured in π‘Ÿ and π‘₯𝑛 are independent variables with measured uncertainties [27].

Using (A.10), the uncertainty in indicated power (𝑃𝑖), IMEP, and πœ‚th can be determined by the following: π‘ˆπ‘ƒπ‘–=π‘ƒπ‘–ξ‚΅π‘ˆπ‘Šπ‘Šξ‚Ά,π‘ˆIMEPξ‚΅π‘ˆ=IMEPπ‘Šπ‘Šξ‚Ά,π‘ˆπœ‚th=πœ‚thξ‚΅π‘ˆπ‘Šπ‘Šξ‚Ά.(A.11)

Acknowledgments

This research was partially supported by the University of Michigan, Award no. 3001397038, through a cooperative agreement with the US Department of Energy entitled β€œA University Consortium on High Pressure Lean Combustion (HPLC) for Efficient and Clean ICE.” The authors wish to acknowledge the assistance of T. Dillstrom, N. Killingsworth, and M. Wissink in conducting experimental measurements.

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