Development of a simplified n-heptane/methane model for high-pressure direct-injection natural gas marine engines

Abstract

High-pressure direct-injection (HPDI) of natu- ral gas is one of the most promising solutions for future ship engines, in which the combustion process is mainly controlled by the chemical kinetics. However, the employment of detailed chemical models for the multi-dimensional combustion simulation is significantly expensive due to the large scale of the marine engine. In the present paper, a reduced n-heptane/methane model consisting of 35-step reactions was constructed using multiple reduction approaches. Then this model was further reduced to include only 27 reactions by utilizing the HyChem (Hybrid Chemistry) method. An overall good agreement with the experimentally measured ignition delay data of both n-heptane and methane for these two reduced models was achieved and reasonable predictions for the measured laminar flame speeds were obtained for the 35-step model. But the 27-step model cannot predict the laminar flame speed very well. In addition, these two reduced models were both able to reproduce the experimentally measured in-cylinder pressure and heat release rate profiles for a HPDI natural gas marine engine, the highest error of predicted combustion phase being 6.5%. However, the engine-out CO emission was over-predicted and the highest error of predicted NO_x emission was less than 12.9%. The predicted distributions of temperature and equivalence ratio by the 35-step and 27-step models are similar to those of the 334-step model. However, the predicted distributions of OH and CH₂O are significantly different from those of the 334-step model. In short, the reduced chemical kinetic models developed provide a high-efficient and dependable method to simulate the characteristics of combustion and emissions in HPDI natural gas marine engines.

Graphical abstract

Keywords

high-pressure direct-injection / natural gas / chemical kinetics / combustion modelling / marine engine

1 Introduction

In recent decades, lower pollutant emissions and better fuel economy are the primary research targets to meet the increasingly stringent emission regulations for internal combustion engines (ICEs) and tackle the potential oil shortage problem in the near future. Therefore, there is a worldwide interest in looking for clean alternative fuels for ICEs [1]. Natural gas has attracted great attention due to its advantages of worldwide reserves and suitable combustion features in both spark-ignited and compression ignition (CI) engines [2]. Lots of research have revealed that a high thermal efficiency and low pollutant emissions can be obtained for the natural gas engines [3,4]. However, owing to its high-octane number and low reactivity, natural gas is difficult to be ignited in CI engines compared to diesel fuel. As a result, when natural gas is taken as the fuel supply in CI engines, an additional ignition source like a spark plug or high-reactivity fuel should be implemented [5–10].

Different types of natural gas engines have been summarized in Ref. [11]. There are primarily three kinds of operating modes for natural gas engines, which are pure natural gas engines, low-pressure dual-fuel engines, and high-pressure direct-injection (HPDI) dual-fuel engines. In pure natural gas engines, natural gas is ignited by a spark plug. Engine knock occurs at high or elevated loads and misfire may occur at low load. Therefore, for pure natural gas engines, load expansion is an urgent problem [12]. In low-pressure dual-fuel engines, the engine operates with premixed natural gas and direct-injection pilot diesel, and the natural gas is typically introduced through the intake port during the intake stroke. Although knock and misfire are inhibited significantly by the pilot diesel, the power output and thermal efficiency are still limited by knock, and the low-load condition is also confronted with the instability problem [13,14]. In HPDI dual-fuel engines, both natural gas and pilot diesel are injected into the cylinder near the top dead center. Pilot diesel is injected into the cylinder prior to natural gas. When natural gas is injected into the cylinder, pilot diesel has been spontaneously ignited. The natural gas is entrained into the pilot flame and ignited. For HPDI dual-fuel engines, the performance can even match conventional diesel engines, while the emissions are lower. However, the original emissions of NO_x and soot in the cylinder are still higher than the limited values of regulations [4,15].

Experiment methodology plays an important role in improving the performance and emissions in natural gas engines. However, due to the complex combustion process in ICEs, a single experiment method is not sufficient to explore the detailed combustion processes within the engine chamber, such as the ignition process, emission formation process, and combustion kinetics process [16,17]. Therefore, the computational fluid dynamic (CFD) approach is usually adopted. There has been a continuous interest in the development of a better understanding of the detailed combustion process in ICEs, in which the CFD is frequently employed owing to its effectiveness and low expenses. To better predict the spray-combustion process occurring in engines, the chemical kinetic model should be adopted in CFD modeling. However, the detailed combustion kinetic model is typically consisted of hundreds of species and reactions, making it difficult to be directly coupled with the CFD codes. In addition, real fuels like diesel, have hundreds of compositions, ranging from alkanes, alkenes, cyclic alkanes and alkenes, aromatics, and other stuff. Therefore, in order to better represent the chemical reactivity of diesel, n-heptane is usually employed as the surrogate fuel, due to its simple molecular structure and similar ignition/combustion feature with diesel [18,19]. For natural gas, which is primarily composed of methane and minimal fractions of hydrogen, ethane, propane, or other mixtures depending on the sources and refinement methods, researchers usually adopt methane to predict the combustion process of natural gas. Many efforts have been devoted to studying the ignition process of n-heptane and methane in laboratory devices such as shock tubes [6,20–27], flow reactors [28–30], rapid compression machines [31–34], and engines [35–37].

It is known that marine engines typically have much larger sizes compared to conventional automobile engines. As a result, the three-dimensional CFD modeling of the spray-combustion process for marine engines is significantly more expensive, especially when coupled with the detailed chemical kinetics model. Therefore, the development of reduced models with a compact size but a high reliability is urgently required. Lots of efforts have been made in the development of reduced n-heptane models. Seshadri [38] developed a skeletal n-heptane model with 23 species and 34 reactions and applied this model to study the structure of premixed n-heptane flames. Peters et al. [39] have developed a skeletal model for n-heptane oxidation with 30 species based on a 56-step model, which includes both low- and high-temperature chemistries. Furthermore, this model reproduces ignition delay times at various pressures and temperatures reasonably well. Tanaka et al. [33] have developed a reduced model for primary reference fuels and validated it with experimental data measured in a rapid compression engine (RCM) under a lean mixture condition. In this model, the intermediate reactions involving species with carbon numbers from 2 to 5 are omitted and alkylketoperoxide are considered to undergo a single oxidation reaction to form CO. This model is able to well predicted the ignition delay measured in the RCM but significantly underestimates the ignition delay measured in the shock tube. Li et al. [40] have developed a reduced n-heptane model composed of 20 species and 29 reactions. This model not only describes the two oxidation stages of heptyl, the chain branch, as well as the chain propagation processes but also includes the peroxidation process of small alkyl radicals. Su and Huang [41] have proposed a reduced n-heptane model with 40 species and 62 reactions, which reproduces the two-stage ignition process of n-heptane. The performance of this model generally agree well with those of the detailed model. Although the above models reproduce ignition delay times of n-heptane reasonably well, the methane sub-model is not included or validated.

Patel et al. [42] have also constructed a reduced n-heptane model consisting of 29 species and 52 reactions, in which the methane sub-model is also included. This model exhibits a similar predictive performance for the combustion of n-heptane with the detailed models, while the ignition delays of methane are underestimated. Maroteaux and Noel [43] have developed two reduced n-heptane models, including 61 and 26 reactions, respectively, and the methane sub-models are also included, which however, fails to well predict the ignition delays for methane. Lapointe et al. [44] have developed an 8-step core sub-model for n-heptane coupled with a C₀-C₄ sub-model, which is consisted of hundreds of species and reactions, making it difficult to be adopted in three-dimensional modeling.

Based on the literature review, the previous developed simplified n-heptane model containing fewer species and reactions cannot be applied to predict combustion characteristics of methane, whereas these models that can simultaneously predict combustion characteristics of n-heptane and methane containing too many species and reactions. If these models are applied to 3D CFD numerical simulation of large-scale dual fuel marine engines, too many computing resources would be wasted, which is not conducive to the development and optimization of large-scale dual fuel marine engines.

In summary, there has not been a reduced n-heptane/methane model that is compact enough (containing less than100 reactions) to predict the ignition delays of both n-heptane and methane simultaneously well, which limits the efficient and accurate simulation of large-size dual-fuel marine engines. Therefore, in the present paper, an attempt was made to develop an ultra-simplified n-heptane/methane model for marine engine simulation. First, a 35-step reduced chemical kinetic model for n-heptane/methane was constructed by using various model reduction approaches, including the reaction pathway analysis, sensitivity analysis, decoupling methodology, and chemical lumping methods. Then, based on the 35-step model, a 27-step model was developed by using the HyChem (hybrid chemistry) approach, specially aimed at the high-temperature regime. Both of these two reduced models were validated against the experimentally measured ignition delays, species concentration profiles, and laminar flame speeds. Finally, these two reduced models were coupled with the CFD code to predict the engine combustion and emissions for a marine engine. The currant development model can significantly reduce the CPU-time of marine engine simulations, which is of significance for the design and development of marine engines.

2 Model development

2.1 Development of the 35-step model

The reduced model is primarily based on the detailed n-heptane model developed by Curran et al. [18]. In this model, the oxidation process of n-heptane is composed of two primary pathways, i.e., the low-temperature combustion (LTC) and high-temperature combustion (HTC) processes. Based on the reaction pathway analysis, CH₂O, ·HO₂, and H₂O₂ were identified as the most important intermediate species for the LTC reactions of n-heptane, which dominated its ignition process. During the LTC period, much H₂O₂ was generated, which was then decomposed just before the HTC period, leading to the rapid growth of ·OH and laying the foundation for the high-temperature ignition. Although the combustion of methane does not exhibit an obvious LTC feature, species like CH₂O, ·HO₂, H₂O₂, and OH are also the most significant species for its ignition and heat release, which must be included in the reduced model.

A schematic diagram of the model is shown in Fig. 1. Fuel consumption is initiated by the abstraction of ·H from n-heptane by O₂ to form ·C₇H₁₅ and ·HO₂ (R1). Due to the symmetric molecular structure of n-heptane, there are four heptyl isomer products. Based on the lumping reduction approach, only ·C₇H₁₅ is employed in the reduced model to represent the four isomers. After the initial reaction stage, a small amount of ·H, ·HO₂, and ·OH are formed, which will dominate the further consumption of n-heptane by the H-abstraction reactions R2, R3, and R4. The sensitivity analysis demonstrates that R2 is less important for the ignition process of n-heptane in comparison to R3 and R4. Therefore, R2 is ignored in the reduced model.

(R1){\mathrm{C}}_{\mathrm{7}}{\mathrm{H}}_{\mathrm{16}}{\mathrm{+O}}_{\mathrm{2}}\mathrm{=}\cdot {\mathrm{C}}_{\mathrm{7}}{\mathrm{H}}_{\mathrm{15}}\mathrm{+}\cdot {\mathrm{HO}}_{\mathrm{2}}

(R2){\mathrm{C}}_{\mathrm{7}}{\mathrm{H}}_{\mathrm{16}}\mathrm{+}\cdot \mathrm{H=}\cdot {\mathrm{C}}_{\mathrm{7}}{\mathrm{H}}_{\mathrm{15}}{\mathrm{+H}}_{\mathrm{2}}

(R3){\mathrm{C}}_{\mathrm{7}}{\mathrm{H}}_{\mathrm{16}}\mathrm{+}\cdot {\mathrm{HO}}_{\mathrm{2}}\mathrm{=}\cdot {\mathrm{C}}_{\mathrm{7}}{\mathrm{H}}_{\mathrm{15}}{\mathrm{+H}}_{\mathrm{2}}{\mathrm{O}}_{\mathrm{2}}

(R4){\mathrm{C}}_{\mathrm{7}}{\mathrm{H}}_{\mathrm{16}}\mathrm{+}\cdot \mathrm{OH=}\cdot {\mathrm{C}}_{\mathrm{7}}{\mathrm{H}}_{\mathrm{15}}{\mathrm{+H}}_{\mathrm{2}}\mathrm{O}

·C₇H₁₅ is then combined with O₂ to form C₇H₁₅O₂ (R5), whose reaction is significantly sensitive to temperature. C₇H₁₅O₂ is primarily consumed via the isomerization process, generating C₇H₁₄OOH (R6). After the second O₂-addition reaction (R7), OOC₇H₁₄OOH is produced and then consumed by the decomposition reaction (R8), generating ·OC₇H₁₃OOH and OH.

(R5)\cdot {\mathrm{C}}_{\mathrm{7}}{\mathrm{H}}_{\mathrm{15}}{\mathrm{+O}}_{\mathrm{2}}{\mathrm{=C}}_{\mathrm{7}}{\mathrm{H}}_{\mathrm{15}}{\mathrm{O}}_{\mathrm{2}}

(R6)\cdot {\mathrm{C}}_{\mathrm{7}}{\mathrm{H}}_{\mathrm{15}}{\mathrm{=C}}_{\mathrm{7}}{\mathrm{H}}_{\mathrm{14}}\mathrm{OOH}

(R7){\mathrm{C}}_{\mathrm{7}}{\mathrm{H}}_{\mathrm{14}}{\mathrm{OOH+O}}_{\mathrm{2}}{\mathrm{=OOC}}_{\mathrm{7}}{\mathrm{H}}_{\mathrm{14}}\mathrm{OOH}

(R8){\mathrm{OOC}}_{\mathrm{7}}{\mathrm{H}}_{\mathrm{14}}\mathrm{OOH=}\cdot {\mathrm{OC}}_{\mathrm{7}}{\mathrm{H}}_{\mathrm{13}}\mathrm{OOH+}\cdot \mathrm{OH}

At a higher temperature, ·OC₇H₁₃OOH is further decomposed into C₅H₁₁CO, CH₂O, and ·OH in which C₅H₁₁CO will also be consumed by the decomposition reactions, forming the smaller hydrocarbon products. To simplify this process, the decomposition reactions of OC₇H₁₃OOH and C₅H₁₁CO are lumped into one reaction (R9).

(R9)·{\mathrm{OC}}_{\mathrm{7}}{\mathrm{H}}_{\mathrm{13}}{\mathrm{OOH\; =\; C}}_{\mathrm{3}}{\mathrm{H}}_{\mathrm{7}}{\mathrm{CO\; +\; CH}}_{\mathrm{2}}\mathrm{O\; +}·{\mathrm{C}}_{\mathrm{2}}{\mathrm{H}}_{\mathrm{3}}\mathrm{+}·\mathrm{OH}

At the high-temperature condition, the pyrolysis reactions become important. In the present paper, only the b-decomposition reactions of ·C₇H₁₅ and C₇H₁₄OOH are considered, and the corresponding pyrolysis reactions are lumped into R10 and R11.

(R10)\cdot {\mathrm{C}}_{\mathrm{7}}{\mathrm{H}}_{\mathrm{15}}{\mathrm{=C}}_{\mathrm{2}}{\mathrm{H}}_{\mathrm{4}}+\cdot {\mathrm{C}}_{\mathrm{2}}{\mathrm{H}}_{\mathrm{5}}+{\mathrm{C}}_{\mathrm{3}}{\mathrm{H}}_{\mathrm{6}}

(R11){\mathrm{C}}_{\mathrm{7}}{\mathrm{H}}_{\mathrm{14}}{\mathrm{OOH=C}}_{\mathrm{3}}{\mathrm{H}}_{\mathrm{6}}+{\mathrm{C}}_{\mathrm{3}}{\mathrm{H}}_{\mathrm{7}}\mathrm{CHO}+\cdot \mathrm{OH}

The skeletal C₂–C₄ sub-model is taken from the works of Gustavsson et al. [45] and Zheng et al. [46] as the bridge between the n-heptane and methane sub-models, based on which a 16-step methane sub-model was constructed as the base model. Finally, a reduced n-heptane/methane model composed of 33 species and 35 reactions was developed and the reaction rate coefficients of some reactions were optimized based on the approach proposed by Ra and Reitz [47] to better predict the experimental results, the detailed n-heptane model. The experimental data obtained by Ciezki et al. [20] and Heufer et al. [48] were used to optimize the reaction rate coefficients. The final reduced model is demonstrated in Table 1, whose thermodynamic data and transportation data are taken from Refs. [40,42,45,46].

2.2 Development of the 27-step model

In HPDI natural gas engines, which typically have a higher compression ratio than low pressure dual fuel engines, the temperature at the top dead center is higher (around 1000 K) than the conventional engines. As discussed in Section 2.1, during the HTC process, the LTC reaction pathway is less significant and n-heptane is primarily consumed by decomposition reactions, converting into small hydrocarbons. Therefore, the 35-step model was further reduced for the HTC regime by using the HyChem approach, which employed a physics-based understanding of the primary reaction pathways in fuel combustion. A more detailed introduction of the HyChem approach can be found in Ref. [49]. During the reduction, the O₂-addition reactions and the following LTC reaction pathway were removed, forming a new reduced n-heptane/methane model consisting of 23 species and 27 reactions. Since the LTC reactions for n-heptane were removed, the reaction rate parameters were further optimized based on sensitivity analysis. Noted that there was no change in the methane sub-model. The final reduced model is displayed in Table 2.

2.3 Validations of the 35-step and 27-step models

Validation of the reduced model was performed by comparing the experimental data with the prediction of a 79 species and 334-step reactions n-heptane/methane model [11]. The modeling target was a zero-dimensional combustion reactor under the constant-volume and adiabatic condition based on the SENKIN code. Figure 2 compares the experimental and calculated ignition delays for n-heptane at a wide range of ambient pressures from 1.3 MPa to 5.5 MPa and ambient temperatures from 700 K to 1200 K [23,48,50]. It is seen that the 35-step model demonstrates a better agreement with the experimental data than that of the 334-step model at 1.3 MPa and 3.8 MPa, especially in the low and intermediate temperature region. The 27-step model can well reproduce the ignition delay times for n-heptane at high temperatures and all research pressures. Figure 3 compares the calculated and measured ignition delays for methane [24] at an ambient pressure of 1.0 MPa and an initial temperature from 1300 K to 1700 K. The result demonstrates that there is no obvious negative temperature combustion region for methane combustion. The predicted ignition delay times of methane for the 35-step and 27-step models have a better agreement with the experimental data compared to the 334-step model under high equivalence ratio conditions, whereas the 334-step model performs better under low equivalence ratio conditions. In general, both of the two reduced models (35- and 27-step models) exhibited a good agreement with the experimental data. Figure 4 depicts the predicted and measured ignition delays of methane/n-heptane mixtures at an ambient pressure of 1.0 MPa and an equivalence ratio of 1.0. The result indicates that when the mole fraction of methane is 50% and 70%, the ignition delays of methane/n-heptane mixtures predicted by the three model are in good agreement with measured values. At a methane mole fraction of 90%, the ignition delays predicted by the 334-step model is slightly lower than measured values. The ignition delays predicted by the 35- and 27-step models agree well with experimental data at high temperatures. However, they are slightly lower than experimental data at low and medium temperatures.

Figures 5 and 6 compare the predicted species concentration profiles for the main species by the three reduced kinetic models in a constant volume chamber. Compared to the 334-step model, the generally lower n-heptane consumption rate and peak C₂H₄ concentration were predicted by the 35-step model. The consumption rate of methane for the 35-step model is also slightly slower than that of the 334-step model. However, the CH₂O profile of the 35-step model is much higher than that of the 334-step model. The reason for this is that a part of CH₃ for the 334-step model is oxidized to form CH₂ species, while for the 35-step model, CH₂O is the only oxidation species.

Comparisons between the calculated and experimental laminar flame speeds [51–62] of the n-heptane/air and methane/air mixtures at 0.1 MPa are plotted in Figs. 7 and 8, respectively. The predicted laminar flame speeds for the n-heptane/air mixture of the 334-step model are in good agreement with the experimental data obtained by Kumar et al. [51] and Dirrenberg et al. [55]. The 35-step model can reasonably reproduce the experimental data at the equivalence ratio of less than 1.3 for the n-heptane/air mixture. However, it significantly over-predicted the flame speed at the equivalence ratio of more than 1.3. The 27-step model cannot reproduce laminar flame speeds of the n-heptane/air mixture at all research equivalence ratio. For the methane/air flame as presented in Fig. 8, it is observed that the laminar flame speed predicted by the 334-step model agrees well with the experimental values, except those measured by Bradley et al. [57], which is higher at the lean-fuel side and lower at the rich-fuel side. However, the laminar flame speed predicted by the 35-step and 27-step models are in good agreement with experimental data obtained by Bradley et al. [56] at the equivalence ratio of less than 1.0, but they both significantly over-predict the experimental values under rich conditions.

3 Model validation in a marine engine

The reduced models are finally intended to be employed for multi-dimensional CFD modeling. The dual-fuel HPDI natural gas engine usually operates under around the stoichiometric- and lean burn conditions. As a result, it is preferable that the reduced n-heptane/methane is able to predict the ignition delay of n-heptane and laminar flame speed of methane well under such conditions. Based on previous validations, it is seen that these two newly developed reduced models can reasonably predict the experimental results under stoichiometric- and lean-burn conditions. In this section, they are further adopted for 3D CFD modeling validations.

The engine combustion experiment was conducted on a Man Diesel and Turbo 4T50ME-GI engine, which was a low-speed and two-stroke marine engine. The start and end of pilot fuel and natural gas injection were - 2/0°CA and - 1/17.6°CA, respectively, and the cyclic injection quantities of the pilot diesel fuel and natural gas were 0.13 and 26 g, respectively. The opening and closing timings of the scavenge ports and exhaust valve were - 217/-143°CA and - 248/-73.5°CA, respectively. The simulation started from the exhaust valve opening (EVO) for a whole cycle. The main specifications of the engine can be found in Table 3 and the detailed parameters can be found in Ref. [11]. The computational study was performed using the Converge code [63]. The initial and boundary conditions were set based on experimental data [64] and one-dimensional GT-Power data. For the engine simulation, the mesh was generated automatically by using an adaptive generation method with up to 5000000 grids. The SAGE solver was adopted to simulate the detailed combustion chemistry. The RNG k-e model was adopted to simulate the turbulence process. The extended Zeldovich model [65] and Hiroyasu soot model [66] were used to simulate NO_x and soot emissions, respectively. Detailed descriptions of the related sub-models used in the simulation can be found in Ref. [67]. It should be noted that all the boundary conditions in simulations were the same for the three reduced models. Table 4 lists the CPU-hour of the three models. Comparatively, it demonstrates that both the 27- and 35-step models can significantly reduce the computational expenses. Note that the current engine is in a large size, which needs more grids for simulations. With a higher grid number, the computational expenses will be further increased.

Figure 9 shows the measured and calculated pressure and heat release rate (HRR) profiles. The calculated pressure profiles of the three reduced models are in good agreement with the experimental data. Comparatively, the calculated HRR profiles of the 27- and 35-step models are slightly higher than that of the experimental data and the 334-step model, indicating that the combustion rates of both the 27- and 35-step models are also slightly higher. The previous study demonstrated that the combustion process of the HPDI natural gas engine was categorized into five stages, including the ignition delay period of the pilot-fuel, the premixed combustion period of the pilot-fuel, the rapid combustion period of methane, the mixing-controlled combustion period, and the post-combustion period [68]. It is noticed that the premixed combustion stage for the pilot fuel of the 27-step model is more intense than that of the other two models, owing to its predicted lower reactivity of n-heptane and thus the fuel-air mixing process is longer. However, the pilot-fuel ignition timing (the start of heat release rate) of the 27-step model is closer to the experimental data. Therefore, the maximum pressure (p_max) for the 27-step model is in better agreement with experimental data.

Comparisons of the predicted and measured primary parameters on combustion and engine performance are presented in Table 5. For key combustion parameters, the calculated CA10 and CA50 (CA10 and CA50 are defined as the crank angles that releases 10% and 50% of the heat.) for the three models are in good agreement with the experimental data, in which the highest error is less than 6.5% for both the 35- and 27-step model compared with the experimental data. In addition, both the 35- and 27-step models are able to reproduce the maximum combustion pressure (p_max) and the corresponding phase (p_{max phase}), and the 27-step model has a better prediction performance. For key engine performance parameters, the calculated power outputs and indicated specific fuel consumption (ISFC) of the 27- and 35-step models are in good agreement with the experimental data and the errors are less than 0.5%. This indicates that the 35- and 27-step models can be applied for the development of marine engines and prediction of important performance (such as power, fuel consumption) with a high credibility, despite of some deviations in its chemical kinetics (intermediate species, laminar flame speed) verification. Meanwhile, the important macroscopic combustion parameters of the engine captured by the 35-step model are also relatively accurate, which can be applied to the development of the combustion system for engines.

Table 6 presents the experimental and predicted engine-out emissions. Generally, the predicted NO_x emissions for the three reduced models are in good agreement with the experimental data, with the highest predicted error of less than 12.9%. At present, NO_x is the only pollutant emission limited to IMO Tier III, thus the present 35- and 27-step models can be employed for NO_x emission prediction.

In addition, similar predictions of HC and CO₂ emissions are also observed for three reduced models. However, the calculated CO emissions are significantly lower than the experimental values, owing to the predicted higher combustion rates, as shown in Fig. 5. Besides, the predicted soot emissions of the 27- and 35-step models are an order of magnitude higher than that of the 334-step model. Due to the complex combustion processes of engines, it is always difficult to accurately predict incomplete combustion products, such as HC, CO, and soot. Further improvement needs to be performed in the future.

Table 7 depicts the predicted in-cylinder temperature distributions for different models. The initial temperature distribution (0°CA) for the three models is almost the same. At 5°CA ATDC, the temperature distribution regions of the three models are similar. However, the local regions of the 35- and 27-step models have a higher temperature than that of the 334-step model. This indicates that the combustion process of the 35- and 27-step models are more intense. At 10°CA ATDC, the temperature distributions of the three models are also similar. However, the local high-temperature regions of the 35- and 27-step models become larger than that of the 334-step model, and the intense combustion process leads to a higher heat release rate (seen in Fig. 8).

Table 8 shows the predicted equivalence ratio distributions of the three models, which are almost the same at 0°, 5°, and 10°CA ATDC. At 15°CA ATDC, however, the equivalence ratio distributions of the three models differ owing to the more significant effect of in-cylinder turbulent flows. Due to the more intense combustion process of the 35- and 27-step models, the fuel distributions of the 35- and 27-step models are wider. Correspondingly, the high-temperature regions are larger than that of the 334-step model. Moreover, the combustion process of the 27-step model is more intense than that of the 35-step model, hence the high-temperature regions of the 27-step model are slightly larger than those of the 35-step model. At 20°CA ATDC, the high-temperature regions of the 27-step model are larger than those of the 35-step and the 334-step models, and the fuel distribution regions are wider than those of the 35- and 334-step models. The main differences in temperature and equivalence ratio distributions for the three models are marked by black circles.

Table 9 shows the OH distributions of the three models. From 0° to 10°CA ATDC, the ·OH distributions of the three models are almost the same. It is well known that ·OH is the most important radicals at the high-temperature combustion stage, thus the ·OH distribution is used to indicate the high-temperature combustion region in the present paper. As can be seen in Table 8, the burning region can be clearly distinguished from the unburning region. According to Ref. [69], the initial combustion stage of the HPDI engine belongs to premixed combustion, which can be demonstrated by the ·OH distributions at 0° and 5°CA ATDC. At 10°, 15°, and 20°CA ATDC, the ·OH distributions of the three models become different. It is interesting that high ·OH concentration regions of the 334-step model are larger than that of the 35- and 27-step model. The reason for this is that ·OH is concentrated on the edge of high-temperature regions, while the high-temperature regions of the 35- and 27-step models are distributed almost throughout the cylinder, thus the high ·OH concentration regions are smaller. The main differences of ·OH distribution for the three models are marked in black circles.

The CH₂O distributions of the three models are tabulated in Table 10. CH₂O is an important species at the low combustion stage for n-heptane, and it is also an important species for the oxidation process of methane. At 0°CA ATDC, the CH₂O distributions of the 35- and 27-step models are much larger than those of the 334-step model. For the 334-step model, only a small amount of CH₂O concentrates near the nozzle. At 5°CA ATDC, the OH distribution of the 334-step model becomes slightly larger, but it is still much smaller than those of the 35- and 27-step models, and the CH₂O concentration is also much lower than those of the 35- and 27-step model. At 10°CA ATDC, the combustion process intensifies, the formed CH₂O is instantly oxidized to HCO. Therefore, the CH₂O of the 334-step model disappears, and only a small amount of CH₂O concentrates near the nozzle for the 35- and 27-step models. At 15°CA and 20°CA ATDC, the CH₂O disappears in the cylinder for the 334- and 35-step models. However, the CH₂O concentration of the 27-step model increases at 15°CA ATDC. The main differences of CH₂O distribution for the three models are marked by black circles.

Tables 11 and 12 lists the predicted distribution of NO_x and soot in the combustion process. Due to the later ignition timing of the 27-step model, the NO_x formation is lower at 0°CA ATDC. At 10°CA, the NO_x distribution regions of the three models are similar. Due to the differences in the high-temperature distribution region, the NO_x distribution regions of the three models significantly differ at 20°CA and 30°CA ATDC. However, the area of NO_x distribution for the three models is similar. In general, the soot distribution regions of the three models are similar at different crank angles. However, the predicted soot concentration of the 334-step models is much lower than that of the 35- and 27-step models. The main differences in NO_x and soot distributions for the three models are marked by black circles.

In summary, the 35-step model can reproduce the ignition delay times of n-heptane at all research temperatures, while the 27-step model gives reasonable predictions of ignition delay times for n-heptane at high temperatures. Both of these two models give accurate predictions of ignition delay times for methane. The main species histories of n-heptane and methane cannot be well reproduced by both the 27- and 35-step model. In addition, the calculated laminar flame speeds of methane for the 35-step model are the same as those of the 27-step model, which are higher than experimental values. The 35-step model can reproduce the laminar flame speed of n-heptane at an equivalence ratio of less than 0.9, however, the 27-step model fails to predict the laminar flame speeds of n-heptane at all equivalence ratios.

However, for practical application like engine combustion simulation, these two newly developed models give reasonable predictions of ignition timings, in-cylinder pressures, HRRs, CA10, power output, indicated specific fuel consumption (ISFC), and soot emissions in a HPDI natural gas marine engine model. During the engine design process, efficient and robust CFD simulation is the key factor. In comparison to the 334-step model, the 27- and 35-step model are sufficient in the predictions of both the overall engine combustion performance and detailed in-cylinder combustion processes. As a consequence, for the complex combustion process in engines, whether a precise kinetic model is necessary for the research and development of ICEs remains to be further explored. After all, the complex model makes it very difficult for engine simulations. Of course, the 27- and 35-step reduced models also require to be further validated extensively in other engine operating conditions

4 Conclusions

In the present paper, two reduced n-heptane/methane models were constructed by employing various reduction approaches, including the reaction pathway analysis, sensitivity analysis, and the HyChem method. In addition, the reaction rate constants were optimized based on the sensitivity analysis of ignition delays. The reduced models were validated against experimental ignition delays, laminar flame speeds, and engine combustion and emission results.

The 27- and 35-step models can well predict the experimental ignition delays of the n-heptane/air and methane/air mixtures. The calculated laminar flame speeds of the n-heptane/air and methane/air mixtures for these two reduced models are only in agreement with the experimental data under the stoichiometric and lean mixture conditions.

The applications of the 27- and 35-step reduced models in the multi-dimensional CFD simulations can significantly shorten the CPU-hours. Both the 27- and 35-step models could reasonably predict the experimental engine combustion process and NO_x emissions. Besides, the distributions of temperature, equivalence ratio, OH, CH₂O, NO_x, and soot calculated by the 35- and 27-step models are in reasonable agreement with those calculated by the 334-step model at 0°CA ATDC. As a result, the present reduced n-heptane/methane models can be used for the future design of the HPDI natural gas marine engines.

In the future, owing to the complicated combustion process in engines, whether a precise kinetic model is necessary for the engine research and design needs to be further explored. After all, the more complicated model makes it more expensive and time-consuming for engine simulations. Of course, the 27- and 35-step reduced models also require to be further validated under more engine-related conditions.

References

[1] Luo M Y, Liu D. Kinetic analysis of ethanol and dimethyl ether flames with hydrogen addition. International Journal of Hydrogen Energy, 2017, 42(6): 3813–3823

[2] Ying Y Y, Liu D. Detailed influences of chemical effects of hydrogen as fuel additive on methane flame. International Journal of Hydrogen Energy, 2015, 40(9): 3777–3788

[3] Abdelaal M M, Hegab A H. Combustion and emission characteristics of a natural gas-fueled diesel engine with EGR. Energy Conversion and Management, 2012, 64: 301–312

[4] Florea R, Neely G D, Abidin Z, . Efficiency and emissions characteristics of partially premixed dual-fuel combustion by co-direct injection of NG and diesel fuel (DI²). In: SAE 2016 World Congress and Exhibition, Detroit, USA, 2016, 121606

[5] Wei H Q, Qi J Y, Zhou L, . Ignition characteristics of methane/n-heptane fuel blends under engine-like conditions. Energy & Fuels, 2018, 32(5): 6264–6277

[6] He Y Z, Wang Y D, Grégoire C, . Ignition characteristics of dual-fuel methane-n-hexane-oxygen-diluent mixtures in a rapid compression machine and a shock tube. Fuel, 2019, 249: 379–391

[7] McTaggart-Cowan G P, Huang J, Munshi S. Impacts and mitigation of varying fuel composition in a natural gas heavy-duty engine. SAE International Journal of Engines, 2017, 10(4): 1506–1517

[8] McTaggart-Cowan G P, Jones H L, Rogak S N, . The Effects of high-pressure injection on a compression-ignition, direct injection of natural gas engine. Journal of Engineering for Gas Turbines and Power, 2007, 129(2): 579–588

[9] Wagemakers A M L M, Leermakers C A J. Review on the effects of dual-fuel operation, using diesel and gaseous fuels, on emissions and performance. In: SAE 2012 World Congress and Exhibition, Detroit, USA, 2012, 92224

[10] Zeng K, Huang Z H, Liu B, . Combustion characteristics of a direct-injection natural gas engine under various fuel injection timings. Applied Thermal Engineering, 2006, 26(8–9): 806–813

[11] Liu H F, Li J R, Wang J T, . Effects of injection strategies on low-speed marine engines using the dual fuel of high-pressure direct-injection natural gas and diesel. Energy Science & Engineering, 2019, 7(5): 1994–2010

[12] Cho H M, He B Q. Spark ignition natural gas engines—a review. Energy Conversion and Management, 2007, 48(2): 608–618

[13] Roethlisberger R P, Favrat D. Investigation of the prechamber geometrical configuration of a natural gas spark ignition engine for cogeneration: part I. numerical simulation. International Journal of Thermal Sciences, 2003, 42(3): 223–237

[14] Zheng J B, Wang J H, Zhao Z B, . Effect of equivalence ratio on combustion and emissions of a dual-fuel natural gas engine ignited with diesel. Applied Thermal Engineering, 2019, 146: 738–751

[15] Huang Z H, Shiga S, Ueda T, . Effect of fuel injection timing relative to ignition timing on the natural-gas direct-injection combustion. Journal of Engineering for Gas Turbines and Power, 2003, 125(3): 783–790

[16] Demosthenous E, Borghesi G, Mastorakos E, . Direct numerical simulations of premixed methane flame initiation by pilot n-heptane spray autoignition. Combustion and Flame, 2016, 163: 122–137

[17] Demosthenous E, Mastorakos E, Stewart Cant R. Direct numerical simulations of dual-fuel non-premixed autoignition. Combustion Science and Technology, 2016, 188(4–5): 542–555

[18] Curran H J, Gaffuri P, Pitz W J, . A comprehensive modeling study of n-heptane oxidation. Combustion and Flame, 1998, 114(1–2): 149–177

[19] Zhang K W, Banyon C, Bugler J, . An updated experimental and kinetic modeling study of n-heptane oxidation. Combustion and Flame, 2016, 172: 116–135

[20] Ciezki H K, Adomeit G. Shock-tube investigation of self-ignition of n-heptane-air mixtures under engine relevant conditions. Combustion and Flame, 1993, 93(4): 421–433

[21] Davidson D F, Hanson R K. Interpreting shock tube ignition data. International Journal of Chemical Kinetics, 2004, 36(9): 510–523

[22] Fieweger K, Blumenthal R, Adomeit G. Self-ignition of S.I. engine model fuels: a shock tube investigation at high pressure. Combustion and Flame, 1997, 109(4): 599–619

[23] Gauthier B M, Davidson D F, Hanson R K. Shock tube determination of ignition delay times in full-blend and surrogate fuel mixtures. Combustion and Flame, 2004, 139(4): 300–311

[24] Hu E J, Li X T, Meng X, . Laminar flame speeds and ignition delay times of methane–air mixtures at elevated temperatures and pressures. Fuel, 2015, 158: 1–10

[25] Huang J, Hill P G, Bushe W K, Munshi S R. Shock-tube study of methane ignition under engine-relevant conditions: experiments and modeling. Combustion and Flame, 2004, 136(1–2): 25–42

[26] Liang J J, Zhang Z H, Li G S, . Experimental and kinetic studies of ignition processes of the methane–n-heptane mixtures. Fuel, 2019, 235: 522–529

[27] Wu Y T, Liu Y, Tang C L, . Ignition delay times measurement and kinetic modeling studies of 1-heptene, 2-heptene and n-heptane at low to intermediate temperatures by using a rapid compression machine. Combustion and Flame, 2018, 197: 30–40

[28] Davis S G, Law C K, Wang H. Propene pyrolysis and oxidation kinetics in a flow reactor and laminar flames. Combustion and Flame, 1999, 119(4): 375–399

[29] Held T J, Marchese A J, Dryer F L. A semi-empirical reaction mechanism for n-heptane oxidation and pyrolysis. Combustion Science and Technology, 1997, 123(1–6): 107–146

[30] Zhang Z H, Zhao H, Cao L, . Kinetic effects of n-heptane addition on low and high temperature oxidation of methane in a jet-stirred reactor. Energy & Fuels, 2018, 32(11): 11970–11978

[31] Griffiths J F, Halford-Maw P A, Rose D J. Fundamental features of hydrocarbon autoignition in a rapid compression machine. Combustion and Flame, 1993, 95(3): 291–306

[32] Minetti R, Carlier M, Ribaucour M, . A rapid compression machine investigation of oxidation and auto-ignition of n-heptane: measurements and modeling. Combustion and Flame, 1995, 102(3): 298–309

[33] Tanaka S, Ayala F, Keck J C. A reduced chemical kinetic model for HCCI combustion of primary reference fuels in a rapid compression machine. Combustion and Flame, 2003, 133(4): 467–481

[34] Grogan K P, Scott Goldsborough S, Ihme M. Ignition regimes in rapid compression machines. Combustion and Flame, 2015, 162(8): 3071–3080

[35] Aroonsrisopon T, Sohm V, Werner P, . An investigation into the effect of fuel composition on HCCI combustion characteristics. In: Powertrain and Fluid Systems Conference and Exhibition, San Diego, USA, 2002, 90919

[36] Aroonsrisopon T, Werner P, Waldman J O, . Expanding the HCCI operation with the charge stratification. In: 2004 SAE World Congress, Detroit, USA, 2004, 90264

[37] Andrae J, Johansson D, Björnbom P, . Co-oxidation in the auto-ignition of primary reference fuels and n-heptane/toluene blends. Combustion and Flame, 2005, 140(4): 267–286

[38] Seshadri K. Numerical and asymptotic studies of the structure of stoichiometric and lean premixed heptane flames. Combustion and Flame, 1997, 108(4): 518–536

[39] Peters N, Paczko G, Seiser R, . Temperature cross-over and non-thermal runaway at two-stage ignition of n-heptane. Combustion and Flame, 2002, 128(1–2): 38–59

[40] Li H L, Miller D L, Cernansky N P. Development of a reduced chemical kinetic model for prediction of preignition reactivity and autoignition of primary reference fuels. In: International Congress and Exposition, Detroit, USA, 1996, 90323

[41] Su W, Huang H. Development and calibration of a reduced chemical kinetic model of n-heptane for HCCI engine combustion. Fuel, 2005, 84(9): 1029–1040

[42] Patel A, Kong S C, Reitz R D. Development and validation of a reduced reaction mechanism for HCCI Engine Simulations. In: 2004 SAE World Congress, Detroit, USA, 2004, 90264

[43] Maroteaux F, Noel L. Development of a reduced n-heptane oxidation mechanism for HCCI combustion modeling. Combustion and Flame, 2006, 146(1–2): 246–267

[44] Lapointe S, Zhang K, McNenly M J. Reduced chemical model for low and high-temperature oxidation of fuel blends relevant to internal combustion engines. Proceedings of the Combustion Institute, 2019, 37(1): 789–796

[45] Gustavsson J, Golovitchev V I. Spray combustion simulation based on detailed chemistry approach for diesel fuel surrogate model. In: 2003 JSAE/SAE International Spring Fuels and Lubricants Meeting, Yokohama, Japan, 2003, 90284

[46] Zheng J C, Yang W Y, Miller D L, . A skeletal chemical kinetic model for the HCCI combustion process. In: SAE 2002 World Congress, Detroit, USA, 2002, 90920

[47] Ra Y, Reitz R D. A reduced chemical kinetic model for IC engine combustion simulations with primary reference fuels. Combustion and Flame, 2008, 155(4): 713–738

[48] Heufer K A, Olivier H. Determination of ignition delay times of different hydrocarbons in a new high pressure shock tube. Shock Waves, 2010, 20(4): 307–316

[49] Wang H, Xu R, Wang K, . A physics-based approach to modeling real-fuel combustion chemistry- I. evidence from experiments, and thermodynamic, chemical kinetic and statistical considerations. Combustion and Flame, 2018, 193: 502–519

[50] Fieweger K, Blumenthal R, Adomeit G. Shock-tube investigations on the self-ignition of hydrocarbon-air mixtures at high pressures. Symposium (International) on Combustion, 1994, 25(1): 1579–1585

[51] Kumar K, Freeh J E, Sung C J, . Laminar flame speeds of preheated iso-octane/O₂/N₂ and n-heptane/O₂/N₂ mixtures. Journal of Propulsion and Power, 2007, 23(2): 428–436

[52] Smallbone A J, Liu W, Law C K, . Experimental and modeling study of laminar flame speed and non-premixed counterflow ignition of n-heptane. Proceedings of the Combustion Institute, 2009, 32(1): 1245–1252

[53] Ji C S, Dames E, Wang Y L, . Propagation and extinction of premixed C5–C12 n-alkane flames. Combustion and Flame, 2010, 157(2): 277–287

[54] Kelley A P, Smallbone A J, Zhu D L, . Laminar flame speeds of C5 to C8 n-alkanes at elevated pressures: experimental determination, fuel similarity, and stretch sensitivity. Proceedings of the Combustion Institute, 2011, 33(1): 963–970

[55] Dirrenberger P, Glaude P A, Bounaceur R, . Laminar burning velocity of gasolines with addition of ethanol. Fuel, 2014, 115: 162–169

[56] Li G S, Liang J J, Zhang Z H, . Experimental investigation on laminar burning velocities and markstein lengths of premixed methane-n-heptane-air mixtures. Energy & Fuels, 2015, 29(7): 4549–4556

[57] Bradley D. Burning velocities, markstein lengths, and flame quenching for spherical methane-air flames: a computational study. Combustion and Flame, 1996, 104(1–2): 176–198

[58] Hassan M. Measured and predicted properties of laminar premixed methane/air flames at various pressures. Combustion and Flame, 1998, 115(4): 539–550

[59] Vagelopoulos C M, Egolfopoulos F N. Direct experimental determination of laminar flame speeds. Symposium (International) on Combustion, 1998, 27(1): 513–519

[60] Dyakov I V, Konnov A A, Ruyck J D, . Measurement of adiabatic burning velocity in methane-oxygen-nitrogen mixtures. Combustion Science and Technology, 2001, 172(1): 81–96

[61] Tahtouh T, Halter F, Mounaïm-Rousselle C. Measurement of laminar burning speeds and Markstein lengths using a novel methodology. Combustion and Flame, 2009, 156(9): 1735–1743

[62] Dirrenberger P, Le Gall H, Bounaceur R, . Measurements of laminar flame velocity for components of natural gas. Energy & Fuels, 2011, 25(9): 3875–3884

[63] Richards K J, Senecal P K, Pomraning E.CONVERGE Manual (Version 2.3), 2016

[64] Juliussen L R, Kryger M J, Andreasen A. MAN B&W ME‐GI engines recent research & results. In: Proceedings of the International Symposium on Marine Engineering (ISME), 2011

[65] Lavoie G A, Heywood J B, Keck J C. Experimental and theoretical study of nitric oxide formation in internal combustion engines. Combustion Science and Technology, 1970, 1(4): 313–326

[66] Hiroyasu H, Kadota T, Arai M. Development and use of a spray combustion modeling to predict diesel engine efficiency and pollutant emissions (part 1 combustion modeling). Bulletin of the JSME, 1983, 26(214): 569–575

[67] Li J R, Wang J T, Liu T, . An investigation of the influence of gas injection rate shape on high-pressure direct-injection natural gas marine engines. Energies, 2019, 12(13): 2571

[68] Larson C R. Injection study of a diesel engine fueled with pilot-ignited, directly-injected natural gas. Dissertation for the Doctoral Degree. Vancouver: University of British Columbia, 2003

[69] Jud M, Fink G, Sattelmayer T. Predicting ignition and combustion of a pilot ignited natural gas jet using numerical simulation based on detailed chemistry. In: ASME 2017 Internal Combustion Engine Division Fall Technical Conference (ICEF 2017), Seattle, USA, 132256

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