n-heptane mixtures at low and elevated pressures

Energy 197 (2020) 117242

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Shock tube and kinetic study on ignition characteristics of lean methane/n-heptane mixtures at low and elevated pressures Zhen Gong, Liyan Feng*, Lai Wei, Wenjing Qu, Lincheng Li Institute of Internal Combustion Engine, Dalian University of Technology, No.2 Linggong Road, Dalian, China

a r t i c l e i n f o

a b s t r a c t

Article history: Received 9 August 2019 Received in revised form 12 February 2020 Accepted 23 February 2020 Available online 26 February 2020

To acquire ignition control methods for dual-fuel marine engine and HCCI engine, ignition characteristics of lean n-heptane/methane mixture under pressure of 2.0 bar and temperature range from 1241 to 1825 K were studied by shock tube and CHEMKIN with LLNL3.1 mechanism. And ignition processes under temperature range from 700 to 1200 K and pressure range from 40 to 140 bar were investigated by CHEMKIN with NUI mechanism. The results illuminate that at low-pressure high-temperature condition, n-heptane’s replacement and the increase of n-heptane content obviously reduced ignition delay times (IDT). The reduction degree of IDT decreased when n-heptane content was high. N-heptane’s addition also reduced IDT. But this reduction magnitude was less than that of n-heptane’s replacement. Methane’s addition slightly inhibited n-heptane’s auto-ignition. The reaction time of n-heptane was obviously earlier than that of methane. N-heptane decomposition induced radical formation firstly, which triggered subsequent n-heptane’s H-abstraction and the advance of methane’s oxidation. At ultra-high-pressure low-temperature condition, increasing n-heptane’s content enhanced negative temperature coefficient (NTC) behavior. The end time point of complete consumption of two fuels was the same. Lowtemperature condition inhibited n-heptane decomposition, with n-heptane’s H-abstraction dominating ignition process. © 2020 Elsevier Ltd. All rights reserved.

Keywords: Methane N-heptane Ignition delay time Shock tube Chemical kinetics

1. Introduction Severe soot and NOx emissions had been always an issue in diffusion flames of diesel engines. In order to overcome this vital problem, not only natural gas, a low-carbon fuel, has been widely used as an alternative fuel in diesel engines. The new combustion modes Partially Premixed Compression Ignition (PPCI) [1,2], Reactivity Controlled Compression Ignition (RCCI) [3,4], Exhaust Gas Recirculation (EGR) [5] and after-treatment [6e9] that also improve fuel efficiency and reduce emissions from internal combustion engines are researched all the time. Natural gas can be used in diesel-ignited dual-fuel engines and HCCI engines. Since natural gas has a better anti-knock property than gasoline, gas engines can achieve a higher compression ratio and accordingly a higher thermal efficiency than gasoline engines [10,11]. However, due to the high auto-ignition temperature,

* Corresponding author. E-mail addresses: [email protected] (Z. Gong), [email protected] (L. Feng), [email protected] (L. Wei), [email protected] (W. Qu), 751983695@ qq.com (L. Li). https://doi.org/10.1016/j.energy.2020.117242 0360-5442/© 2020 Elsevier Ltd. All rights reserved.

natural gas is hard to be compression-ignited. Normally, gas engines utilize spark plugs or pilot-injection of a small amount of diesel (normally taking 1 to 5% of the total fuels heating value) to trigger the combustion of natural-gas in cylinders. The one with pilot diesel injection is called dual-fuel engine. The combustion of pilot diesel functions as a huge spark plug with high energy, which ensures the continuous reliable ignition and reduces cycle-to-cycle variations [12]. This combustion mode of Otto cycle dramatically reduces soot and NOx emission because the combustion temperature of natural-gas is obviously lower than that of diesel. Therefore, a great number of large four-stroke engines and low-speed twostroke dual-fuel marine engines adopt this combustion mode to meet the requirements of International Maritime Organization (IMO) Tire III emission regulations [13]. In dual-fuel engines, when pilot diesel ignites surrounding natural gas/air mixture, the mixture composition near ignition location is close to rich-diesel & leannatural-gas condition. Further, the overall diesel/natural-gas mixture is a over-lean mixture (excess air ratio>2.0) to avoid the possible pre-ignition of end-gas. Thus ignition characteristics of lean diesel/natural-gas mixture (rich-diesel & lean-natural-gas) need to be investigated because the combustion characteristics of

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this mixture plays a key role on the thermal efficiency and emission of engine. Besides the large-bore dual-fuel engines, natural-gas (lowreactivity fuel) and diesel (high-reactivity fuel) can be applied in HCCI engines, which are also named as Reactivity Controlled Compression Ignition (RCCI) engines, as well [14]. RCCI engine can achieve high thermal efficiency and low soot and NOx emissions thanks to its low-temperature and premixed combustion characteristics. Thus RCCI becomes a new advanced combustion strategy. In diesel/natural-gas RCCI engine, in-cylinder mixture composition is close to rich-natural-gas & lean-diesel condition. The ignition characteristics of rich-natural-gas & lean-diesel mixture should also be studied to provide the control methods of combustion phase for RCCI engine. The actual natural gas and diesel fuel consist of many complex compositions. For the convenience of theoretical research, methane is generally treated as the surrogate fuel of natural gas because methane takes up more than 90% volumetric fraction in natural gas in most gas sources [15]. N-heptane is normally the alternative fuel of diesel due to the close cetane numbers between n-heptane and diesel [16]. Thus it is necessary to examine the combustion characteristics of methane/n-heptane mixture with various blending ratios in detail. The ignition characteristics of methane and n-heptane have been investigated in many studies respectively [17e20]. However, only a few researches have concentrated on the ignition and combustion characteristics of methane/n-heptane mixture. Aggarwal et al. [21] studied the ignition of methane/n-heptane mixture based on a 42-species reduced reaction mechanism. The calculation conditions is similar to the operating conditions of HCCI diesel engine. They found the addition of a small amount of n-heptane could dramatically shorten IDT of methane mixture over the whole studied temperature range. But the addition of methane only had a minute influence on the IDT of n-heptane. Wei et al. [22] also simulated the effect of multivariable on ignition process of methane/n-heptane mixture under engine-like conditions based on a 44-species reduced reaction mechanism. They concluded that initial temperature and equivalence ratio played a key role on reaction rate and actual reaction temperature region. Liang et al. [23] investigated the effect of n-heptane replacement on methane’s ignition by shock tube and NUI mechanism under pressure of 10 bar and equivalence ratio of 1.0. They found that increasing n-heptane content advanced the time point of full methane consumption. Moreover, n-heptane had a stronger ability to react with free radicals, which was responsible for the earlier consumption of nheptane. Generally speaking, shock tube study of ignition properties of methane/n-heptane mixture was mainly conducted under middlepressure and stoichiometric-fuel conditions. Experimental study of methane/n-heptane mixture under low-pressure (near atmospheric-pressure) and lean-fuel conditions was scarce. The existed investigations concentrated on the replacement of methane with n-heptane when the overall equivalence ratio of methane/nheptane mixture was constant. The influence of extra addition of n-heptane into pure methane mixture (when methane content was constant) and the extra addition of methane into pure n-heptane mixture (when n-heptane content was constant), were also not analyzed. Therefore, shock tube and kinetic study on lean methane/ n-heptane mixture at low initial pressure needed to be proceeded to reveal the potential control strategies of combustion phase in diesel/natural-gas dual fuel engine and RCCI engine. Moreover, the high-pressure studies of methane/n-heptane mixture were limited to below 50 bar. However, in actual lowspeed two-stroke marine engine, in-cylinder pressure may reach 140 bar before auto-ignition process [24,25]. Thus numerical study

on methane/n-heptane mixture under this ultra-high-pressure of marine engine (close to 140 bar) should also be conducted based on detailed kinetic mechanism. In terms of the chemical reaction kinetics of methane/n-heptane mixture, current researches concluded that the stronger competitiveness of n-heptane compared with methane was responsible for the acceleration of oxidation process. However, the enhancement of system reactivity induced by n-heptane’s decomposition to form free radicals was not systematically studied. Furthermore, the discrepancies of autoignition and detailed reaction kinetics characteristics of n-heptane/ methane mixture between low-pressure & high-temperature conditions and low-temperature & high-pressure conditions were lacked and needed to be compared. Therefore, in present study, to provide the basic research data of IDT for lean methane/n-heptane mixture, and obtain the ignition control methods for dual-fuel marine engine and diesel/natural-gas RCCI engine, the shock tube and kinetic study on lean methane/nheptane mixture (equivalence ratio of 0.5) were conducted under low-pressure (2.0 bar) and temperature range from 1241 K to 1825 K. The effects of extra n-heptane’s addition and extra methane’s addition and n-heptane’s replacement on mixture’s IDT were compared and analyzed in detail. The ignition characteristics of lean methane/n-heptane mixture under ultra-high-pressure lowtemperature condition (p:40bar-140 bar & T:700 Ke1200 K) was investigated by a validated detailed kinetic mechanism as well. Chemical reaction kinetics analysis were also conducted to reveal the differences of auto-ignition properties and reaction kinetics characteristics of n-heptane/methane mixture between lowpressure & high-temperature and low-temperature & highpressure conditions. Moreover, internal principles of auto-ignition processes were investigated delicately from the point of view that n-heptane’s decomposition induced radicals formation and accelerated fuel oxidation processes. 2. Experimental and numerical methods 2.1. Shock tube facility The schematic of the shock tube in this study is shown in Fig. 1. The shock tube consists of a 4 m high-pressure driver section and a 3 m low-pressure driven section, with a connecting section in the middle of shock tube employed to separate the driver and driven section. The inner and outer diameter of shock tube are 100 mm and 130 mm respectively. Before each experiment, the whole shock tube is evacuated by a vacuum pump. Leakage rate of whole shock tube is less than 0.5 Pa/min. The mixtures of helium and nitrogen are introduced into high-pressure section as the driver gases. The combustible mixtures (CH4/n-C7H16/O2/AR), which are allowed to settle 12 h to ensure the homogeneity of reactants, are prepared in the mixing tank according to Dalton’s law of partial pressure. The heating systems are installed outside the mixing tank and the driven section and the connection pipe between them in order to promote the full vaporization of the reactants. The gases in mixing tank is introduced into low-pressure section directly. Initial pressure in driven and driver section before the arrival of incident shock wave is monitored by the vacuum gauge and pressure gauge respectively. Three fast-response piezoelectric sidewall pressure transducers (PCB 111A24) in the test section which locate at the fixed distance of 180 mm trigger the acquisition process of oscilloscope (TDS2000C) and measure the incident shock wave speed. The last sidewall pressure transducer near the end wall of test section records the pressure history during ignition period. In test section, OH* emission with the wavelength of 307 nm is recorded by a photomultiplier tube (PMT) through a narrow band pass filter. The

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Fig. 1. Schematic of shock tube.

chemical equilibrium software Gaseq [26] is adopted to calculate the pressure and temperature conditions behind the reflected shock wave. The largest uncertainty of the temperature behind the reflected shock wave is less than 25 K based on the error analysis method [27], which causes an uncertainty of the measured ignition delay times of less than 10%. As shown in Fig. 2, the pressure rise due to the arrival of reflected shock wave at the last pressure transducer is adopted to determine the onset of ignition. Ignition time point is based on the extrapolation of the maximum slope of the OH* emission signal to the zero. The definition of IDT is the time interval between the pressure rise and the extrapolation of the maximum slope of OH* emission [28,29]. The validation processes of authenticity in present shock tube setup and other details of experimental procedures have been described in previous literature [30e32]. 2.2. Mixture preparation In this study, the test mixtures are injected into mixing tank successively. Partial pressure of the n-heptane was less than 50% of its saturated vapor pressure in order to avoid possible condensation [33]. The purity of methane, oxygen, argon and n-heptane is 99.995%, 99.995%, 99.995% and 99% respectively. The following calculation methods for equivalence ratio are derived from He et al.

[34]. The definition of the equivalence ratio of main fuel (Fm) and the overall equivalence ratio of mixture (F) are as follows:

4m ¼

4¼

Xm =XO2 ðXm =XO2 Þstoic

(1)

2XC þ 0:5XH XO

(2)

where, Xm and XO2 means the mole amount of main fuel and oxygen. XC, XH and XO means the mole amount of C, H and O in mixture. The main fuel in mixture 100-0, 100-10 and 100-20 is methane. And the main fuel in mixture 0e100 and 50e100 is n-heptane. The studied mixture compositions are shown in Table 1. Mixture of 100-0, 95-5, 90-10,75-25, 50-50 and 0e100 means mole fraction of methane in mixtures is 100%, 95%, 90%, 75%, 50%, 0% respectively. Some methane is replaced by n-heptane when F is fixed to 0.5.10010 and 100-20 means mole fraction of added n-heptane is 10% and 20% of methane. Additional n-heptane is added into methane mixture when methane content is constant. Thus F also increases due to the addition of n-heptane. 50e100 means mole fraction of added methane is 50% of n-heptane. Additional methane is added into n-heptane mixture when n-heptane content is constant. F also increases to 0.545 because of the addition of methane. Replacing methane with small amount of n-heptane when F is constant, and adding extra n-heptane into methane mixture are similar to the in-cylinder mixture composition (rich-natural-gas & Table 1 Mixture compositions (Fm is the equivalence ratio of main fuel, F is the total equivalence ratio). Mixture (CH4þn-C7H16)

Fig. 2. Definition of ignition delay time.

100e0 100e10 100e20 95e5 90e10 75e25 50e50 0e100 50e100

Mole fraction (%) CH4

n-C7H16

O2

Ar

1.4 1.4 1.4 1.127 0.926 0.552 0.25 0 0.152

0 0.14 0.28 0.059 0.103 0.184 0.25 0.304 0.304

5.6 5.6 5.6 5.814 5.971 6.264 6.5 6.696 6.696

93 92.86 92.72 93 93 93 93 93 92.848

Fm

F

0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5

0.5 0.775 1.05 0.5 0.5 0.5 0.5 0.5 0.545

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lean-diesel) of diesel/natural-gas RCCI engine. Replacing methane with large amount of n-heptane, and adding extra methane into nheptane mixture are even closer to the actual mixture composition (rich-diesel & lean-natural-gas) in the in-cylinder local ignition region of micro-diesel-pilot natural-gas engine. In this study, replacing methane with n-heptane is simplified to “n-heptane’s replacement”. Extra addition of n-heptane into methane mixture is simplified to “n-heptane’s addition”. Similarly, extra addition of methane into n-heptane mixture is named as “methane’s addition”.

references, which demonstrates the validity and reliability of the measured results from present shock tube setup. 2.4. Error analysis In order to select the accurate reaction mechanism to study the chemical kinetics of methane/n-heptane mixture, the error analysis of experiments and mechanisms has been conducted. The calculation methods of errors are derived from He et al. [34]. Relative error of the ith experimental data point, which reflects the local performance of mechanisms, is calculated as follows:

2.3. Numerical modelling and mechanism validation The zero-dimensional, constant volume and adiabatic reactor in Chemkin-Pro is applied to calculate and analyze the ignition process of n-heptane/methane mixtures. Although the kinetic mechanisms for the ignition of n-heptane/methane mixture are rarely involved, the mechanisms for the ignition of pure methane mixture and pure n-heptane mixture have been widely studied. LLNL3.1 [35] and NUI [36] mechanisms are the representative n-heptane mechanism. Further, the n-heptane mechanism contains methane oxidation mechanism. Therefore, n-heptane oxidation mechanisms can be used for modelling the ignition of n-heptane/methane mixture. In order to validate the accuracy of n-heptane oxidation mechanism on predicting IDT of methane/n-heptane mixture, the IDT of methane and n-heptane modeled from LLNL3.1 and NUI mechanisms are compared to the measurements from Horning et al. [18] and Seery et al. [17] respectively. Fig. 3a shows the IDT of 0.4% nC7H16 þ 4.4% O2 þ 95.2% Ar with the pressure of 2.0 bar. The calculated values from LLNL3.1 and NUI mechanisms yield good agreement with the measurements from Horning et al., which indicates that these two mechanisms can predict well the IDT of nheptane. Fig. 3b shows the IDT of 9.1% CH4 þ 18.2% O2 þ 72.7% Ar with the pressure of 2.0 bar. It can be seen that LLNL3.1 and NUI mechanisms also agrees well with the measurements from Seery et al. Only GRI 3.0 mechanism [37] underestimates the IDT of methane. In general, LLNL3.1 and NUI mechanisms can be applied to calculate the IDT of n-heptane/methane mixture in later sections because it is good at predicting the IDT for both n-heptane and methane. Besides, the IDT for both n-heptane and methane from present shock tube setup is also very close to modeled values from n-C7H16 kinetic mechanisms and the measurements from previous

Ei ¼

timodel  texpi  100 texpi

(3)

where, Ei is the relative error of the ith data point, ti model and ti exp are the computed IDT and experimental IDT for the ith data point respectively. The mean and maximum absolute errors are also calculated to evaluate the overall performance of mechanisms. The expressions are as follows:

m¼

N 1 X jE j N i¼1 i

  Emax ¼ max Ei¼1;…;N 

(4)

(5)

where, m is the mean absolute error, N is the total number of experimental data points, Emax is maximum absolute error. 3. IDT of lean methane/n-heptane mixture under hightemperature low-pressure conditions 3.1. Experimental results and mechanism predictions The IDT of mixture in Table 1 under pressure of 2.0 bar and the initial temperature range from 1241 K to 1825 K is measured in present shock tube setup. The comparisons of measurements and computed data are shown in Fig. 4. IDT decreases obviously with the increase of initial temperature for all mixtures. Pure methane mixture and pure n-heptane mixture exhibits the longest and the shortest IDT respectively. When F is fixed to 0.5 (mixture: 100-0, 95-5, 90-10, 75-25, 50-50, 0e100), IDT decreases dramatically even

Fig. 3. Comparisons of the measurements in current study and other references and the computed results from kinetic mechanisms.

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Fig. 4. Comparisons of present measurements with the predictions from LLNL 3.1 mechanism and NUI mechanism (points for experimental measurements, lines for prediction data from mechanisms).

a little methane is replaced by n-heptane. The IDT reduces continuously with the increase of n-heptane content. But the reduction magnitude of IDT decreases gradually when n-heptane’s content is relatively high. The extra addition of 10% and 20% n-heptane into pure methane mixture (Fm ¼ 0.5) (mixture: 100-10, 100-20) also reduces the IDT of pure methane mixture. But the reduction magnitude of IDT caused by n-heptane’s addition is less than that caused by n-heptane’s replacement. The main reason is that n-heptane’s addition enriches mixture and delays ignition. Further, the extra addition of 50% methane into n-heptane mixture slightly raises the IDT of pure n-heptane mixture because F also increases a little. In other words, ignition of pure n-heptane mixture is delayed when methane is presented in ambient gas, which is consistent with the conclusions drawn by Schlatter et al. [38]. The comparison of IDT between the measurements from present shock tube setup and computed values from kinetic mechanisms is also shown in Fig. 4a and b. Fig. 4c shows the comparison between LLNL 3.1 and NUI mechanisms. Both LLNL3.1 and NUI mechanisms can capture the overall variation trend of IDT for all mixtures in experiment. NUI mechanism predicts a slight higher

IDT than LLNL 3.1 mechanism. The relative errors and absolute errors of mechanisms are shown in Fig. S1 and Table S1 of the Supplementary material respectively. Fig. S1 illuminates NUI mechanism slightly overestimate IDT than LLNL mechanism, especially under high n-heptane content condition (mixture compositions: 100-20, 50e100 and 0e100). Table S1 also demonstrates the mean and maximum absolute errors of LLNL mechanism are lower than that of NUI mechanism. Overall, the computed IDT of LLNL3.1 mechanism is more close to the present experimental measurements than that of NUI mechanism. Therefore, LLNL3.1 mechanism is selected to examine the chemical kinetics of nheptane/methane mixture. The effect of the addition of n-heptane on IDT is nonlinear. Therefore, in order to clarify the effect of mixture composition on IDT, detailed variations of computed IDT from LLNL3.1 mechanism are shown in Fig. 5. It can be seen that the influence of mixture composition on IDT under different initial temperatures is very similar. As mentioned above, replacing a small mole fraction of methane with n-heptane (mixture: 95-5) can promote ignition process and dramatically reduce IDT. With the increase of replacement fraction of n-heptane, IDT reduces constantly. The

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Moreover, n-heptane’s addition (mixture: 100-10, 100-20) also advances methane’s consumption. The effect of n-heptane’s fraction on raising the speed of methane’s consumption is not very remarkable when n-heptane content is relatively high. Fig. 6 also presents that, for pure methane mixture, methane content remains constant before ignition time point. For other mixtures which contain a small amount of n-heptane (mixture: 955, 100-10, 100-20, 90-10, 75-25, 50-50), methane content reduces slowly at early stage. Free radicals produced by n-heptane’s decomposition at early stage reacts with methane, which is responsible for the slow decrease of methane content. For the mixtures with high n-heptane content (mixture: 0e100, 50e100), methane fraction increases slightly firstly. The reason is that the combination of methyl and H forms methane at initial stage.

Fig. 5. Variations of IDT with various mixture compositions and initial temperature.

magnitude of the reduction of IDT becomes small when n-heptane content is high. N-heptane’s addition promotes the ignition of methane obviously. The promotion effect of the extra addition is weaker than that of the replacement. Methane’s addition slightly inhibits n-heptane’s ignition. 3.2. Chemical kinetic analysis In order to gain more insight into the ignition of n-heptane/ methane mixtures, chemical kinetic analysis was conducted through LLNL3.1 mechanism. Initial pressure and temperature are set as 2.0 bar and 1400 K respectively. 3.2.1. Variations of mole fraction of n-heptane and methane Fig. 6 demonstrates the variations of mole fraction of methane and n-heptane with various mixture compositions. All n-heptane is consumed fully at early stage. However, all methane is consumed fully until ignition time point. Fully consumption time point of methane is obviously latter than that of n-heptane. N-heptane’s replacement (mixture: 95-5, 90-10, 75-25, 50-50, 0e100) obviously accelerates methane’s consumption. With the increase of replacement fraction of n-heptane, methane reacts completely in advance.

3.2.2. Variations of mole fraction of free radicals Fig. 7 shows the comparisons of mole fraction of H, O, OH, HO2 and CH3 radicals. The formation of free radicals initiates at very late period for pure methane mixture (mixture: 100-0). By contrast, nheptane’s addition induces a rapid formation of radicals at initial stage (0.0001e0.01 ms). The increase of n-heptane’s content further raises the peak value of radical concentrations. And the time point of peak value also advances. The concentrations of H, O and OH increase rapidly near ignition time point, which is then sharply reduced to a specific value after that. On the contrary, the concentrations of HO2 and CH3 keep a high value before ignition time point and decreases to nearly zero after that. 3.2.3. Sensitivity analysis Sensitivity analysis on the IDT of n-heptane/methane mixture is conducted to examine the significant reactions in ignition process. The normalized sensitivity index is defined as follows [39]:

Si ¼

tð2ki Þ  tð0:5ki Þ 1:5tðki Þ

(6)

where, Si is the IDT sensitivity, t is the IDT, and ki is the rate of the ith reaction in the kinetic mechanism. Negative sensitivity index means that the increase of the rate constant of specific reaction will reduce the IDT. Positive sensitivity index represents increasing the rate constant of specific reaction can prolong the IDT. Fig. 8 demonstrates the normalized sensitivity of IDT with

Fig. 6. Variations of the mole fraction of n-C7H16 and CH4 from LLNL3.1 mechanism at P ¼ 2 bar and T ¼ 1400 K.

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Fig. 7. Mole fraction of H, O, OH, HO2 and CH3 under various mixture compositions at P ¼ 2 bar and T ¼ 1400 K.

Fig. 8. Normalized sensitivity of the IDT for various mixture compositions at P ¼ 2 bar and T ¼ 1400 K.

various mixture compositions. For the pure methane mixture (mixture: 100-0), the chain-branching reaction R1, H þ O2¼O þ OH, and R113, CH3þO2¼CH2O þ OH, have the high negative sensitivity index. The chain propagation reaction R109, CH3þHO2¼CH3O þ OH, in which the less reactive methyl is converted to the more reactive OH radical, also have relatively high negative sensitivity index. H-abstraction reaction R99, CH4þH]

CH3þH2, competes with R1 for the H radical. Thus R99 has the highest positive sensitivity index. Methyl combination reaction R151, 2CH3(þM) ¼ C2H6(þM), and methyl consumption reaction R110, CH3þHO2¼CH4þO2, consumes methyl radical, which inhibits ignition process. H-abstraction of methane attacked by OH radical (reaction R100, CH4þOH]CH3þH2O) also shows relatively high positive sensitivity index. N-heptane’s addition (mixture: 100-10) increases the negative sensitivity index of R1, R109, R105, R26 and R3 obviously. This is because n-heptane’s addition promotes radical formation (as shown in Fig. 7), which enhances the promotion effect of these reactions on ignition. The positive sensitivity index of R99, R100 and R13 also increases by reason of the early production of H and OH radicals and the increased peak value of radical concentrations. Moreover, for all methyl (CH3) and methane (CH4) related reactions (R1, R109, R105, R113, R99, R100, R110, R151, R98), with the increase of replacement fraction of n-heptane (mixture: 75-25, 5050, 0e100), the sensitivity index reduces obviously thanks to the decrease of methane content and the weakened effect of methane on ignition. H radical is produced from methane oxidation reaction, CH4/CH3/CH2O/HCO/H and CH4/CH3/CH2O/H2/H. Decreasing methane content prohibits the overall production of H, which reduces the sensitivity index of H related reaction (R1). The chain-branching reaction R1, H þ O2¼O þ OH is nearly the most important ignition promotion reaction for all mixtures. However, increasing n-heptane content gradually shifts the most important ignition inhibition reaction from the H-abstraction reaction of methane (R99 and R100) to HCO and HO2 radicals related reaction (R27 and R13). 3.2.4. ROP for H radical, methane and n-heptane ROP analysis for H radical and methane and n-heptane are conducted to reveal the effect of n-heptane addition on

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consumption and formation pathways of key species. The details are shown in Figs. 9e11. Fig. 9 shows H formation initiates near ignition time point (8 ms) for pure methane mixture (mixture: 1000). Key reactions for H formation are R3 (OH þ H2¼H2O þ H), R26 (HCO(þM) ¼ H þ CO(þM)), R111 (CH3þO]CH2O þ H), R24 (CO þ OH]CO2þH), and R2 (O þ H2¼H þ OH). The species H2, HCO, CH3 and CO are all produced by methane’s slow oxidation reaction, CH4/CH3/CH2O/H2, CH4/CH3/CH2O/HCO, CH4/CH3, CH4/CH3/CH2O/HCO/CO. However, when n-heptane is added, H radical is produced at initial stage (less than 0.05 ms). For the mixture with low n-heptane content (mixture: 100-10, 75-25), dominant reactions for H radical formation at initial stage are R111 (CH3þO]CH2O þ H) and R137 (CH2þO2¼>CO2þ2H). The decomposition reaction of nC7H16 produces CH3 and CH2 (NC7H16/C5H111/NC3H7/CH3/CH2(S)/CH2/H), which subsequently results in H radical formation. For the mixture with high content of nheptane (mixture: 50-50, 50e100, 0e100), dominant reaction for H formation at initial stage is the reverse reaction of R163, C2H4þH(þM)<¼>C2H5(þM). N-heptane decomposition produces C2H5 (NC7H16/C7H15-2/PC4H9/C2H5/H), which results in H formation. Then abundant H radical converts to OH radical by Hconsumption reaction R1, H þ O2¼O þ OH. These OH radical formed from R1 plays a key role on slow methane’s oxidation at initial stage (as shown in Fig. 10). With the increase of n-heptane’s content, the overall value of ROP for the reactions of H radical formation also increases at initial process, which is reponsible for the increase of H radical concentration (as shown in Fig. 7). In whole ignition process, main production and consumption reactions for H radical occurs near ignition time point and the reaction time is quite short for all mixtures, which demonstrates the rapid formation and

consumption of H near ignition time point (as shown in Fig. 7). ROP for methane are shown in Fig. 10. Key consumption reactions of methane are H-abstraction reaction of methane that is induced by O, H and OH radicals (R100: CH4þOH]CH3þH2O, R99: CH4þH]CH3þH2, R101: CH4þO]CH3þOH). The key formation reaction for methane is R98, CH3þH(þM) ¼ CH4(þM). The reaction time for these key reactions is very short and all these reactions occur near ignition time point, which explains the reason for the sharp decrease of methane content near ignition time point (as shown in Fig. 6). Fig. 10 also suggests n-heptane’s addition promotes the occurrence of key consumption and production reactions for methane at initial stage. For the mixture with high methane content (mixture: 100-10, 75-25, 50-50), the reactions of methane with H, OH and O radicals (R99, R100 and R101) dominate ignition at initial stage, which induce the slow decrease of methane content before ignition time point (as shown in Fig. 6). However, for the mixture with low methane content (mixture: 0e100, 50e100), at initial stage, the formation reaction of methane caused by the combination of methyl and H (R98) dominates ignition process, which slightly increases methane content (as shown in Fig. 6). In general, OH radical is the most significant radical for methane consumption at initial stage. The decomposition of n-heptane promotes the H and OH radical formation at this stage and induces the advance of slow methane oxidation (NC7H16/C7H152/PC4H9/C2H5/H/OH). ROP for n-heptane is shown in Fig. 11. All key consumption reactions of n-heptane proceed at initial stage, which explains the reason of the rapid decrease of n-heptane concentration (as shown in Fig. 6). At first, the dominant reactions for n-heptane consumption are n-heptane decomposition (R1970: NC7H16(þM) ¼ C5H11-1þC2H5(þM) R1971:

Fig. 9. ROP for H radical through the key reactions with various mixture compositions at P ¼ 2 bar and T ¼ 1400 K.

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Fig. 10. ROP for CH4 through the key reactions with various mixture compositions at P ¼ 2 bar and T ¼ 1400 K.

Fig. 11. ROP for n-C7H16 radical through the key reactions with various mixture compositions at P ¼ 2 bar and T ¼ 1400 K.

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NC7H16(þM) ¼ PC4H9þNC3H7(þM) R1969: NC7H16(þM) ¼ C6H13-1þCH3(þM)). These reactions finally induce the radical formation and enhance the whole system reactivity as mentioned above. As more and more n-heptane is consumed, the reactions of n-heptane with H and OH radicals become the dominant reactions for n-heptane consumption. Besides, with the increase of n-heptane content, the overall value of ROP of all these n-heptane consumption reactions also increases. In general, n-heptane decomposition produces free radicals firstly. Then H-abstraction reaction from n-heptane becomes significant, which consumes the residual n-heptane completely. In summary, n-heptane decomposition induces the production of H and OH radical and other free radicals at initial stage (as shown in Fig. 7), which results in subsequent H-abstraction reaction on nheptane (as shown in Fig. 11) and the advanced slow methane consumption (as shown in Fig. 6). The free radicals at initial stage formed from n-heptane decomposition enhances the whole system reactivity, which dramatically shortens the IDT. Further, from the perspective of engine performance, the ignition progress of diesel-ignited dual-fuel engine (ignition region is close to lean-natural-gas/rich-diesel condition) may be faster than that of diesel/natural-gas RCCI engine (in-cylinder mixture is leandiesel/rich-natural-gas) under similar thermodynamic conditions because the IDT reduces with increasing n-heptane’s content. For diesel-ignited dual-fuel engine, the ignition phase may not vary obviously when the injection mass of diesel changes. The main reason is the reduction degree of IDT of methane/n-heptane mixture decreases with the increase of n-heptane’s content when n-heptane’s content is high. By contrast, for diesel/natural-gas RCCI engine, the starting point of ignition progress varies apparently with the change of diesel’s content because the IDT of methane/nheptane mixture has close relationship with n-heptane’s content when n-heptane’s content is low. 4. IDT of lean methane/n-heptane mixture under highpressure low-temperature conditions In the present study, high-temperature low-pressure conditions represent p:2 bar & T:1241 Ke1825K. All high-pressure low-temperature conditions are defined as p:40bar-140 bar & T:700 Ke1200 K. The effect of initial temperature and mixture compositions on IDT of n-heptane/methane mixture has been investigated has been conducted under low-pressure high-temperature conditions (p:2 bar and T:1241 Ke1825K). However, the in-cylinder operating conditions before ignition process in lowspeed two-stroke marine dual-fuel engine with diesel fuel pilot is close to a high-pressure low-temperature condition (p:40bar140 bar & T:700 Ke1200 K). In-cylinder pressure of RCCI engine is also relatively high. Therefore, in order to provide the ignition control methods for diesel/natural-gas marine engine and RCCI engine, the variations of IDT of lean n-heptane/methane mixture under high-pressure low-temperature condition are investigated as well. The numerical method is utilized in this section. 4.1. Mechanism validation and numerical methods In order to select the proper mechanism which can accurately predict the IDT of n-heptane/methane mixture under high-pressure low-temperature conditions, the comparisons between measurements from references and the modeled results from various mechanisms are shown in Figs. 12 and 13. Fig. 12 shows the IDT of pure methane mixture with F of 0.4 and initial pressure of 50 bar and 100 bar. LLNL3.1, NUI and Sk88 [40] mechanisms slightly overestimate the IDT in low-temperature region compared with the measurements from Petersen et al. [41]. San Diego n-heptane

mechanism [42] underestimates the IDT within the whole temperature range. GRI3.0 mechanism slightly underestimates the IDT in high-temperature region compared with the measurements from Petersen et al. [41]. Fig. 13 suggests the IDT of pure n-heptane mixture with F of 1 and initial pressure of 50 bar and 55 bar. The computed values from NUI mechanism generally agrees well with the measurements from Davidson et al. [43] and Shen et al. [44] within the whole studied temperature range. Other mechanisms (including Liu mechanism [45]) shows more discrepancy with measurements. Therefore, NUI mechanism is selected to compute the IDT of n-heptane/methane mixture under high-pressure lowtemperature condition because NUI mechanism has a relatively high accuracy on predicting the IDT of methane mixture and nheptane mixture respectively at ultra-high-pressure and NTC region. The computation conditions are obtained based on the actual operating conditions of diesel/natural-gas marine engine [24,25] and RCCI engine [14]. Near top dead center (TDC), the in-cylinder temperature ranges from 700 K to 1200 K and pressure ranges from 40 bar to 140 bar. Thus the studied initial temperature and pressure are set in this range. Mixture compositions are shown in Table 2. Mole fraction of nitrogen is about 75% to simulate the actual air composition in engine. In micro-diesel-pilot natural-gas marine engine, mixture composition near the ignition region is rich-diesel & lean-natural-gas condition. In natural-gas/diesel RCCI engine, in-cylinder mixture composition is rich-natural-gas & leandiesel condition. Therefore, mixtures of 90-10, 80-20 and 70-30 simulates rich-natural-gas & lean-diesel condition. Similarly, mixture of 20e80 simulates rich-diesel & lean-natural-gas condition. 4.2. IDT for n-heptane/methane mixture at high-pressure condition Fig. 14 illuminates the computed IDT from NUI mechanism under high-pressure low-temperature condition (p:40bar-140 bar and T:700 Ke1200 K). For mixture with low n-heptane content (mixture: 90-10), NTC behavior is not obvious. When n-heptane content increases (mixture: 80-20, 70-30 and 20e80), NTC behavior becomes more pronounced. Moreover, IDT reduces apparently when initial pressure raises. This reduction degree of IDT becomes higher at elevated-temperature. Both pressure and temperature have remarkable influence on IDT in temperature range of 1000 Ke1200 K. When temperature decreases, IDT is mainly effected by pressure in NTC region (temperature range of 850 Ke1000 K). When temperature further reduces, temperature gradually becomes a more key role on IDT than pressure in lowtemperature region. The effect of mixture compositions on IDT with pressure of 60 and 100 bar are shown in Fig. 15. When n-heptane content increases, NTC behavior becomes more obvious. IDT also reduces rapidly. Mixture of 20e80 exhibits the shortest IDT, which means the IDT of rich-diesel & lean-natural-gas mixture is shorter than that of rich-natural-gas & lean-diesel mixture. 4.3. Mole fraction of n-heptane and methane and free radicals at high-pressure condition Mole fraction of methane and n-heptane is shown in Fig. 16. Under high-pressure low-temperature condition, both methane and n-heptane are consumed completely at the same time (near the ignition time point), which is obviously different from the variations under low-pressure high-temperature condition. Methane content reduces slightly firstly and rapidly decreased to zero near ignition time point. By contrast, the speed of the reduction of nheptane content is relatively uniform. The duration of n-heptane

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Fig. 12. Measurements and simulated IDT for methane under high-pressure condition.

Fig. 13. Measurements and simulated IDT for n-heptane under high-pressure condition.

Table 2 Mixture compositions under high-pressure low-temperature conditions (F is the total equivalence ratio). Mixture (CH4þn-C7H16)

90e10 80e20 70e30 20e80

F

Mole fraction (%) CH4

n-C7H16

O2

N2

3.31 2.33 1.68 0.258

0.37 0.58 0.72 1.032

21.32 22.09 22.6 23.71

75 75 75 75

0.5 0.5 0.5 0.5

consumption under high-pressure low-temperature condition is obviously longer than that of n-heptane under low-pressure hightemperature because temperature reduction obviously delays nheptane decomposition. Besides, end time point of n-heptane consumption is the same as that of methane consumption. The increase of initial temperature and n-heptane content advances the consumption of methane and n-heptane. Fig. 17 shows the variations of mole fraction of free radicals from NUI mechanism at P ¼ 60 bar. Only a very small amount of free radicals forms before ignition time point. Radical concentration in this stage at low-temperature condition is apparently less than that at high-temperature condition. Radical concentration raises rapidly instantly near ignition time point and reduces to a constant level after that. When mixture composition is 90-10, with the increase of initial temperature, peak value of free radicals content increases. When initial temperature is 900 K, with the increase of n-heptane content (from 10% to 80%), peak value of free radicals content raises. Time point of the increase of radical concentration advances as well.

4.4. ROP for methane and n-heptane at high-pressure condition ROP for methane and n-heptane from NUI mechanism is shown in Figs. 18 and 19. Table 3 shows the key reactions for the formation and consumption of these species. Fig. 18 suggests key reactions for methane consumption are R46, R45 and R44 (H-abstraction reactions induced by H, O, OH). Before ignition time point, R46 is responsible for slow methane consumption (as shown in Fig. 16), which means H-abstraction of methane is attacked by OH at this initial stage. The decomposition of n-heptane forms OH radical, which advances the slow oxidation reactions of methane (NC7H16/C7H152/C7H15e2O2/C7H14OOH24/C7H14OOH2e4O2/C7KET24/OH). Increasing initial temperature raises the values of ROP for methane as well. Fig. 19 shows under high-pressure low-temperature condition, duration time of n-heptane reactions is obviously longer than that of methane reactions. The significant reactions for n-heptane consumption are R4210, R4211, R4209 and R4212. Obviously different from low-pressure high-temperature condition, these H-abstraction reactions of n-heptane attacked by OH dominates ignition process under high-pressure low-temperature condition. Decomposition reactions of n-heptane are no longer the key consumption reactions. N-heptane decomposition is dramatically inhibited. Thus only a very small amount of OH radical is formed at initial stage (NC7H16 / C7H15-2 / C7H15e2O2 / C7H14OOH2-4 / C7H14OOH2e4O2 / C7KET24 / OH). Generally speaking, low-temperature condition weakens nheptane decomposition, which reduces the amount of OH at initial stage. N-heptane decomposition reactions are no longer the key

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Fig. 14. IDT for n-heptane/methane mixture with various initial pressure under high-pressure low-temperature condition.

Fig. 15. IDT for n-heptane/methane mixture with various mixture compositions under high-pressure low-temperature condition.

reactions for n-heptane consumption. H-abstraction reactions for n-heptane dominates ignition process. Moreover, severely weakened n-heptane decomposition also prolongs duration time of nheptane consumption, which brings the same end time point of full consumption of n-heptane and methane.

5. Conclusions To provide the control methods of ignition timing for dual-fuel (natural-gas/diesel) marine engine and HCCI engine, ignition characteristics of lean n-heptane/methane mixture (F of 0.5) under

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Fig. 16. Variations of mole fraction of n-C7H16 and CH4 from NUI mechanism at P ¼ 60 bar.

Fig. 17. Variations of mole fraction of H, O and OH from NUI mechanism at P ¼ 60 bar.

low-pressure of 2.0 bar and temperature range from 1241 K to 1825 K was investigated by shock tube and LLNL3.1 mechanism. To compare the differences of auto-ignition properties and reaction kinetic characteristics of n-heptane/methane mixture between low-pressure & high-temperature and low-temperature & highpressure conditions, NUI mechanism was also utilized to analyze the ignition characteristics under temperature range from 700 K to 1200 K and pressure range from 40 bar to 140 bar. Besides, from the point of view that n-heptane’s decomposition promoted radical’s formation and methane’s oxidation, the internal principles of ignition processes were also analyzed in detail. The conclusions can be summarized as following: (1) Under low-pressure high-temperature condition (p:2 bar & T:1241 Ke1825K), replacing a small amount of methane with n-heptane dramatically reduced IDT. IDT decreased with the increase of n-heptane replacement. The reduction degree of IDT decreased obviously when n-heptane content was high. N-heptane’s addition also reduced IDT of pure methane mixture. The IDT reduction induced by n-heptane’s addition was less than that induced by n-heptane’s replacement. Methane’s addition slightly increased IDT. LLNL3.1 mechanism showed n-heptane was consumed completely at start. By contrast, methane was rapidly consumed until ignition time point. Adding n-heptane induced a rapid formation of radicals at initial stage, which raised the sensitivity index

of these free radicals related reactions. Main consumption reactions for methane were H-abstraction reactions attacked by free radicals. For n-heptane, the decomposition reactions prevailed firstly, with H-abstraction reactions dominating ignition after that. N-heptane decomposition resulted in free radicals formation at initial stage, which induced n-heptane’s decomposition and advanced the methane’s slow oxidation. Thus the enhanced system reactivity shortened IDT dramatically. Previous studies considered that n-heptane had a stronger competitiveness for free radicals than methane, which was responsible for the early n-heptane consumption and the advance of ignition time point. Different from previous viewpoints, this study supports that n-heptane decomposition and subsequent Habstraction of n-heptane significantly enhanced system reactivity, which advanced methane’s oxidation. (2) Under high-pressure low-temperature condition (p:40bar140 bar & T:700 Ke1200 K), NUI mechanism showed increasing n-heptane content enhanced NTC behavior. And IDT also reduced obviously. Both methane and n-heptane were consumed completely near ignition time point. Increasing n-heptane content promoted radicals formation. Decomposition reactions were not dominant reactions for nheptane, with H-abstraction reactions attacked by OH radical dominating ignition process. This was obviously different from low-pressure high-temperature condition.

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Fig. 18. ROP for CH4 through the key reactions from NUI mechanism at P ¼ 60 bar.

Fig. 19. ROP for n-C7H16 through the key reactions from NUI mechanism at P ¼ 60 bar.

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Table 3 Key reactions for the consumption and formation of methane and n-heptane from NUI mechanism at P ¼ 60 bar. methane

n-heptane

R43: CH3þH(þM)<¼>CH4(þM) R44: CH4þH<¼>CH3þH2 R45: CH4þO<¼>CH3þOH R46: CH4þOH<¼>CH3þH2O R47: CH4þHO2<¼>CH3þH2O2 R49: CH3þHO2<¼>CH4þO2 R124: CH3OH þ CH3<¼>CH2OH þ CH4 R158: CH2O þ CH3<¼>HCO þ CH4 R168: HCO þ CH3<¼>CH4þCO R191: HOCHO þ CH3¼>CH4þCO þ OH R203: C2H6þCH3<¼>C2H5þCH4 R930: C2H3CHO þ CH3<¼>C2H3CO þ CH4

R4202: R4203: R4207: R4209: R4210: R4211: R4212: R4217: R4218: R4219: R4220: R4230: R4231:

The acquired ignition characteristics of methane/n-heptane mixture are helpful to provide ignition control methods for dualfuel marine engine and HCCI engine. It can be inferred that the ignition delay in actual diesel-ignited dual-fuel engine may be shorter than that in diesel/natural-gas RCCI engine under similar thermodynamic conditions. For diesel-ignited dual-fuel engine, when the injection mass of diesel changes, the ignition phase may not vary obviously. The ignition timing is mainly decided by incylinder thermodynamic conditions before TDC. By contrast, for diesel/natural-gas RCCI engine, both thermodynamic conditions and diesel’s content determine the actual ignition timing and ignition phase in engine combustion progress. Declaration of competing interest The authors declared that they have no conflicts of interest to this work. Acknowledges The work in this study was financially supported by the National Natural Science Foundation of China (Grant No. 51479028). Appendix A. Supplementary data Supplementary data to this article can be found online at https://doi.org/10.1016/j.energy.2020.117242. Abbreviations HCCI RCCI IMO IDT PMT NTC ROP

Fm F P T

homogeneous charge compression ignition reactivity controlled compression ignition international maritime organization ignition delay time photomultiplier tube negative temperature coefficient rate of production equivalence ratio of main fuel overall equivalence ratio of mixture initial pressure initial temperature

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