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Development of a skeletal mechanism for heavy-duty engines fuelled by diesel and natural gas
Accepted Manuscript Development of a skeletal mechanism for heavy-duty engines fuelled by diesel and natural gas Wensheng Zhao, Wenming Yang, Liyun Fan, Dezhi Zhou, Xiuzhen Ma PII: DOI: Reference:
S1359-4311(17)32604-2 http://dx.doi.org/10.1016/j.applthermaleng.2017.05.175 ATE 10490
To appear in:
Applied Thermal Engineering
Received Date: Revised Date: Accepted Date:
18 April 2017 22 May 2017 29 May 2017
Please cite this article as: W. Zhao, W. Yang, L. Fan, D. Zhou, X. Ma, Development of a skeletal mechanism for heavy-duty engines fuelled by diesel and natural gas, Applied Thermal Engineering (2017), doi: http://dx.doi.org/ 10.1016/j.applthermaleng.2017.05.175
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Development of a skeletal mechanism for heavy-duty
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engines fuelled by diesel and natural gas
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Wensheng Zhaoa,b, Wenming Yangb*, Liyun Fana*, Dezhi Zhoub, Xiuzhen Maa
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a. College of Power and Energy Engineering, Harbin Engineering University, Harbin 150001, China b. Department of Mechanical Engineering, National University of Singapore, 4 Engineering Drive 3, Singapore 117583, Singapore
Abstract The purpose of this work is to develop a skeletal dual-fuel mechanism for heavy-duty engines fuelled by diesel and natural gas. With diesel fuel modeled as n-heptane, and natural gas modeled as methane, the skeletal mechanism was constructed by coupling the two skeletal mechanisms reduced detailed mechanisms: n-heptane and methane mechanisms. Directed relation graph error propagation and sensitivity analysis, computational singular perturbation and reaction rate adjustment methods were employed for mechanism reduction. The final skeletal dual-fuel mechanism is composed of 61 species and 199 reactions. So as to validate the fidelity of the novel skeletal dual-fuel mechanism, zero-dimension ignition delay testing against shock tube experimental results and 3-dimensional engine validation about in-cylinder pressures, heat release rates and NOx and CO emissions against engine testing results were performed under various operating conditions. The validation results indicate that the dual-fuel mechanism can accurately reproduce the ignition behaviors, combustion characteristics and emission trends in heavy-duty diesel/NG dual-fuel engines. Besides, a parallel computing method based on the round-robin algorithm was developed which can significantly save the time for calculating. Combined with the new developed skeletal dual-fuel mechanism, the 3D CFD simulation for the combustion in heavy-duty engines can be done in a reasonable computational time.
Keywords: Natural gas; Pilot diesel; Dual-fuel skeletal mechanism; heavy-duty engines
1. Introduction Diesel engines are widely used in numerous applications throughout the world. With rapid depleting of fossil fuels and increasingly strict emission regulations, alternative fuels for diesel engines have attracted more and more attention [1-4]. Due to its abundant reserves, high fuel economy and relatively low emissions, natural gas (NG) has been emerging as a promising alternative fuel in recent years, especially in ship propulsion [5-7]. The diesel/NG dual-fuel engines adopt natural gas as primary fuel, while using a small amount of diesel as pilot fuel to ignite NG and air mixture [8-9]. Conventional diesel engines can be retrofitted to diesel/NG dual-fuel engines with some modifications, which make it possible for the dual-fuel engines to utilize the high compression ratios of original diesel engines, thus achieving high thermal efficiency as well as relatively lower nitrogen oxides (NOx) and particulate matter * Corresponding authors Email addresses: [email protected] (WM Yang), [email protected] (LY Fan)
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emissions [10]. Hence, the dual-fuel engines have been research hotspot for many researchers and engine manufacturers. So far, quite a number of studies have been devoted to investigate the combustion of NG in compress ignition engines with diesel as the pilot fuel. Papagiannakis et al. [11] converted a single-cylinder high-speed Lister LV1 diesel engine to a dual-fuel engine by injecting the NG to the intake manifold of the engine and experimentally investigated the effects of NG percentage on the in-cylinder pressure, HRR, peak cylinder pressure, total brake specific fuel consumption, NOx, carbon monoxide (CO), unburned hydrocarbons (HC) and soot emissions. Carlucci et al. [12] tested a single cylinder diesel/NG dual-fuel engine and analyzed the effect of CNG and diesel fuel injection pressure, the pilot fuel injection quantity, on the combustion development and engine performance, in terms of specific emission levels and fuel consumption under different working conditions. Cordiner et al. Mittal et al. [13] investigated the exhaust emissions characteristics, i.e. HC, CO, NOx, soot, particulate matter (PM) and carbon dioxide (CO2), under diesel and dual fuel operations at different operating conditions on a six-cylinder diesel/NG dual fuel engine. Yang et al. [14] studied the impact of pilot diesel injection timing on the combustion noise and particle emissions characteristics of a diesel/NG dual-fuel heavy-duty engine at low load. However, solely by means of experiments, it can be rather costly and time-consuming to understand and optimize the engine performance and exhaust emissions in dual-fuel engines. Numerical simulation of the IC engines has shown to be a very quick and economical method for understanding the details of the complex spray, evaporation, combustion, and pollutant formation processes. Various types of models have been developed, including zero-dimensional (or thermodynamic) models, multi-zone models, and multi-dimensional computational fluid dynamics (CFD) models coupled with detailed chemistry. Rahimi et al. [15] optimized a chemical kinetic mechanism for an n-heptane and natural gas blend by modifying the reaction rate parameters with the genetic algorithm method, and verified the modeling results against experimental results with a zero-dimensional HCCI combustion model. The agreement between experimental and modeling results was found to be acceptable within the examined conditions. Papagiannakis et al. [16] examined the effect of compression ratio (CR) and diesel fuel injection timing (IT) on the performance and exhaust emissions of a dual-fuel single-cylinder research engine, which is fuelled with diesel and methane by utilizing a two-zone phenomenological combustion model. The model was tested and validated against experimental data obtained from a fumigated methane–diesel dual-fuel engine, operating with constant CR, diesel fuel IT, engine speed at partial-load conditions for various methane-diesel fuel mass ratios. Nonetheless, it has been found that the zero-dimensional model often predicts a very fast combustion rate once ignition occurs and is unable to capture the correct combustion phasing [17]. A zonal model can predict a reasonable overall combustion rate but it requires empirical adjustments in formulating zones [18]. Thus, a detailed chemistry-based CFD model can be a better tool to simulate different aspects of in-cylinder processes, if the computational time is
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acceptable. Singh et al. [19] numerically studied the combustion and emissions of dual-fuel engines with KIVA3V code, and identified the capabilities and limitations of the present combustion model to simulate premixed combustion of air and natural gas. Donateo et al. [20] modified the SHELL and the Characteristic Time Combustion model in the KIVA3V code, and verified the capability of the simulation code in predicting the emissions trends when changing pilot specification and engine configuration parameters. Moreover, a computer-aided procedure in finding optimal solutions was performed in the framework of the Modefrontier environment. Maghbouli et al. [21] investigated the combustion process under knocking conditions in a dual-fuel diesel-NG engine utilizing KIVA-3V incorporated with detailed chemical reaction model. A reduced chemical kinetics mechanism was developed by combining two previously published reduced mechanisms [22-23]. However, the meshes of the engine bowl for CFD modeling is very rough because of the lack of detailed parameters of the bowl geometry. Moreover, there is only validation for in-cylinder pressure and heat release rate (HRR), while short of the validation of ignition delay time which is a crucial parameter to represent the combustion process. Hockett et al. [24] constructed a reduced chemical kinetic mechanism composed of 141 species and 709 reactions to simulate the combustion of both natural gas and diesel fuels in a dual-fuel engine using the CONVERGE software, and the ignition delay time, in-cylinder pressure and HRR were validated. The results showed that the reduced mechanism accurately reproduces the chemical kinetic behavior of the detailed mechanism. Moreover, based on this mechanism, three-dimensional Reynolds-averaged Navier-Stokes-based engine simulations can be conducted within a reasonable computational time (less than 24 h). Nevertheless, the bore of heavy-duty engines is much larger than that of the GM 1.9L light-duty engine used in the paper, which means an exponential increase of the amount of the meshes for CFD modeling, and then an unreasonable computational time. So this mechanism is still not skeletal enough for large-bore dual-fuel engines. The objective of the present work is to develop a skeletal chemical kinetic mechanism which can be used in multidimensional CFD simulations of the combustion and emission formation process in the heavy-duty multi-cylinder diesel/NG dual-fuel engines. To ensure the reliability of this novel mechanism, validation for ignition delay times was performed against reflected shock tube experiments, and validation for in-cylinder pressure and HRR were conducted against heavy-duty dual-fuel engine experiments using multidimensional CFD simulations with a modified KIVA-4 code incorporated with CHEMKIN. Furthermore, a parallel computing method based on the round-robin algorithm was embedded into the coupled KIVA4-CHENMKIN code for a higher computation speed. 2. CHEMICAL REACTION MECHANISM REDUCTION PROCESS In the present study, the new reduced dual-fuel mechanism was developed from two published mechanisms: the Golovitchev diesel mechanism and the GRI-Mech 3.0 natural gas mechanism. The Golovitchev mechanism [25, 26] comprises of 82 species and 347 elementary chemical reactions, and in this mechanism, n-heptane was
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considered a surrogate of the diesel fuel because of their similar cetane numbers and heating values. The GRI-Mech 3.0 which consists of 53 species and 325 reactions, is an optimized mechanism designed to model natural gas combustion, including NO formation and reburn chemistry [27]. Methods of the direct relation graph with error propagation and sensitivity analysis (DRGEPSA), computational singular perturbation (CSP) algorithm, reaction rate adjustment have been employed to generate a reduced dual-fuel chemical reaction mechanism. First, the Golovitchev mechanism and GRI-mech 3.0 mechanism were reduced utilizing the DRGEPSA method, respectively. Then, the two reduced mechanisms were coupled together whereby reactions for C4-C7 species were derived from the reduced n-heptane mechanism; reactions for C2-C3 species were a combination of the two reduced mechanisms and the reaction rates of any duplicated reactions in the two mechanisms were chosen from the n-heptane mechanism to make sure that soot formation from diesel combustion is accurately represented; reactions for H2/CO/C1 species were taken from the reduced NG mechanism. At last, the new constructed skeletal dual-fuel mechanism was validated through reflected shock tube experiments and engine tests under different working conditions. The mechanism reduction procedure was demonstrated in Fig. 1. Following the above process, the DRGEPSA method [28-30], was firstly utilized for the reduction of n-heptane and NG mechanisms, through which unimportant species and reactions can be recognized efficiently and crucial features of global characteristics can be kept simultaneously [31]. The DRGEPSA method consists of two phases: the DRGEP and SA. In the first phase, the DRGEP approach is applied to map the coupling of species in a reaction system through a directed relation graph, in which the graph vertices represent species and directed edges between vertices represent the coupling of species. Next, the overall interaction coefficient for all species relative to the target species can be calculated, and a threshold value is introduced to categorize these species. The species with a lower overall interaction coefficient is considered unimportant to the target species and can be removed, while the others will be retained. As the second phase of DRGEPSA, the sensitivity analysis (SA) algorithm is utilized to classify limbo species and then eliminate those additional unimportant species whose overall interaction coefficients higher than the threshold of DRGEP but lower than the threshold of SA. Obviously, the proper selection of the target species are crucial to the entire reduction process. Synthetically considering the time consumed and the reduction accuracy, the target species for n-heptane mechanism reduction were identified as NC7H16, CO, CO2, O2, N2 and C2H2, while the DRGEP error tolerances were identified as 10%, 20%, 30%, 40% and 50%. The reduction process was sampled through 63 initial conditions with 3 initial pressures (P=20bar, 60bar and 100bar), 7 initial temperatures (T=700-1800 K) and 3 equivalence ratios (φ=0.5, 1.0 and 2.0). Fig. 2 illustrates the ignition delay times of n-heptane predicted both by the Golovitchev mechanism and the reduced one based on the DRGEPSA. The ignition delay time is defined as the time interval needed from
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its initial temperature to the temperature with an increase of 400 K [32]. As presented in Fig. 2, the ignition delay times calculated by the reduced mechanism based on DRGEPSA agree well with those of original chemical reaction mechanism. Actually there was no distinction among the reduction results of all the five error tolerances and their overall arithmetical mean error (AME) was only 0.88%, and thus, the DRGEPSA reduced mechanism with 0.88% AME was chosen. The final DRGEPSA reduced mechanism for n-heptane was composed of 55 species and 264 reactions. Whereas typical natural gas contains very high methane by volume, and thus exhibits properties very similar to those of methane [33], the present work models natural gas as pure methane. Therefore, the target species for NG mechanism reduction were defined as CH4, CO, CO2, O2, N2, NO, NO2 and AR, while the error tolerances of DRGEP, equivalence ratios, initial pressures and temperatures were exactly the same as settings of n-heptane mechanism reduction. Particularly, species NO and NO2 were regarded as the target species to keep the NOx formation predicted accurately in consideration of the fact that NG is the primary fuel in the pilot ignited dual-fuel engines. Fig. 3 demonstrates the comparison of the NG ignition delay times predicted by the GRI-Mech 3.0 mechanism and the reduced one based on DRGEPSA. The DRGEPSA reduced mechanism of 10% error tolerance was picked out for its minimum AME and acceptable number of reactions. The final DRGEPSA reduced mechanism for NG was formed of 40 species and 248 reactions. Subsequently, a method based on CSP algorithm [34, 35] was applied to calculate the importance index which indicates the normalized contribution of a reaction to the production rate of a species. This method can effectively remove species with small time scales by means of recognizing the fast species and the time scales of different modes which may not be fully identified in DRGEPSA method. Similarly, a threshold value is used to assist in eliminating reactions deemed nonsignificant in regard to a core set of species. The target species of CSP were consistent with those of DRGEPSA, as well as the error tolerances. The ignition delay time of n-heptane predicted both by the original mechanism and the CSP reduced one was presented in Fig. 4, and it can be found that the calculated ignition delay times of the further reduced mechanism based on CSP show good accordance with those of original reaction mechanism, especially for 10% and 30% error tolerances. Further, the overall AME of the mechanism with 10% error tolerance is 4.18% less than that of the 30% one, with an increase of merely 4 chemical kinetic reactions. Therefore, the CSP reduced mechanism generated by 10% error tolerance was adopted, and the final CSP reduced mechanism for n-heptane was composed of 49 species and 160 reactions. Fig. 5 demonstrates the NG ignition delay times predicted by the original mechanism as well as the CSP reduced one. There was no difference among the CSP reduction results of all the five error tolerances, and thus the final CSP reduced mechanism for NG was made up of 40 species and 146 reactions with an overall AME of 9.73%. Next, the above two CSP reduced mechanisms were integrated together through the
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aforementioned methodology, forming a multi-component chemical mechanism with 61 species amongst 199 reactions. And yet, the introduced species and reactions and the change of intermediate reaction pathways could cause random changes on the new mechanism in terms of its combustion prediction capability. With the purpose of maintaining its prediction accuracy while keeping the small size of this mechanism, it is quite essential to regulate the reactions by tuning the reaction rates of some particular reactions. Therefore, sensitivity analysis was implemented again utilizing SENKIN code to ascertain the reactions that significantly influence the ignition delay for both n-heptane and NG. Considering that both of the original mechanisms were not highly detailed, there existed errors with real ignition delay time predictions for both them, and thus the initial conditions were defined with reference to shock tube experimental data to prevent error propagation and amplification. The target tolerance for the final mechanism was defined as 30% for both n-heptane and NG. Those crucial reactions and their corresponding pre-exponential factors (A factor) before and after the adjustment are listed in Table 1. Because the reactions related to the small species such as the C1-C2 species could affect the ignition delay predictions of both NG and n-heptane, the sensitivity analysis and reaction rate adjustment were first conducted for methane over 53 shock tube experimental data points obtained from the literature [36], covering for pressures of 20bar, and 40bar, temperatures from 1412 to 1720 K and equivalence ratios of 0.5, 1.0 and 2.0. The pre-exponential factors were systematically tuned based on a variety of above-mentioned initial conditions. As presented in Table 1, reactions R1-R4 were the most sensitive reactions for NG ignition delay prediction and their pre-exponential factors were regulated to make the largest discrepancy was below 30%. As such, a second step sensitivity analysis and reaction rate adjustment was implemented for n-heptane in air over 27 shock tube experimental data points obtained from the literature [37, 38], covering for pressures of 13.5bar, 19.3bar, 40bar and 41bar, temperatures from 746 to 1138 K and equivalence ratios of 0.5 and 1.0. Since the diesel fuel was used as pilot fuel, only fuel lean and stoichiometric conditions (φ=0.5 and 1.0) for n-heptane were taken into account. In order to achieve accurate ignition delay predictions of n-heptane and maintaining the prediction accuracies of NG simultaneously, only reactions with C5-C7 species were tuned. As shown in Table 1, reactions R5-R9 were the most sensitive reactions for n-heptane ignition delay prediction. Following the above procedure, parametric adjustment on the pre-exponential factor A was conducted and the final diesel/NG dual-fuel mechanism which includes only 61 species participating in 199 reactions was developed. The robustness of the dual-fuel mechanism will be shown in the following sections by its validation under different conditions. These validations will guarantee that the new developed skeletal mechanism is trustworthy for capturing the combustion characteristics in terms of the heat-release and ignition delay of real diesel fuel and NG.
3. Results and discussion
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3.1 Ignition delay validations The validation of the novel skeletal dual-fuel reaction mechanism was first performed on the ignition delay time predictions for NG/air mixtures. Furthermore, the validation for NG was focused on the ignition delay time predictions at high temperatures and pressures, in view of that in diesel/NG dual-fuel engines, the NG is primary fuel and ignited by the pilot fuel under the top dead center (TDC) conditions with high temperatures and pressures. Fig. 6 shows the ignition delay times of NG obtained by the experimental data, skeletal dual-fuel and GRI-Mech 3.0 mechanisms. As presented in Fig. 6, the ignition delay plots indicate that the skeletal dual-fuel mechanism accurately mimic the experimental data for both mixtures across the range of pressures, temperatures, and equivalence ratios. The maximum error of -32.8% appears at 1456k, 40bar, under stoichiometric conditions. For all the other conditions presented, the error deviation across the whole testing domain is less than 30%. The relatively large discrepancies are discovered to appear in high temperature of 1400-1500k and at high pressure zone (40bar) for all the equivalence ratios. Moreover, ignition delay time predictions of original GRI-Mech 3.0 mechanism present huge errors, and that is because the validation of this mechanism mainly targeted predictions in high temperatures (1350-1800k) and low pressures (0.25-7.6bar). Fig. 7 presents the comparisons of the 0-D ignition delay times for n-heptane/air mixtures under fuel lean and stoichiometric conditions against the experimental data, skeletal dual-fuel and Golovitchev n-heptane mechanisms. From Fig. 7, it can be clearly found that the ignition delay time predictions of the skeletal dual-fuel mechanism fit well with experimental data. The relatively large deviations are observed at 13.5bar and high temperature zone (1100-1300k) under fuel lean conditions. The largest discrepancy is -29.7%, when T=928k, P=19.3bar and φ=1.0. Overall, the results in Fig. 6 and Fig. 7 suggest that the skeletal dual-fuel mechanism can be used in predicting the ignition delay process in diesel/NG dual-fuel engines. 3.2 Engine validations 3.2.1 Engine specifications A 6-cylinder turbocharged heavy-duty diesel engine was retrofitted to a diesel/NG dual-fuel engine with limited changes, including introducing a multi-point injection system to inject NG into the intake manifold and replacing a valve camshaft with different cam profile to regulate the valve timing and valve overlap angle. The engine test bed used in this investigation is shown in Fig. 8 and the detailed engine specifications are listed in Table 2. 3.2.2 Simulation Tool and parallel computing A coupled KIVA4-CHEMKIN code was employed to conduct engine combustion simulations. Important sub-models implemented in this KIVA4-CHEMKIN code include the heat transfer model based on Han and Reitz formulation [39], the RNG k-ε turbulence model [40] and a diesel spray model developed by the author [41] based on the Kelvin–Helmholtz Rayleigh–Taylor (KHRT) spray breakup model [42]. Moreover, three basic conservation equations need to be solved in KIVA4, namely
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continuity equation, energy equation, and momentum equation [43]. The former two equations are shown in Eq. (1)-(2). Continuity equation m ( mu) ( D( m )) mC S m1 t
(1)
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where u is the fluid velocity vector, is the total mass density, m is the mass
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density of species m, is the vector operator, D is the diffusion coefficient in
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Fick’s Law, mC is the chemical source term, S is the spray source term and is
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the Dirac delta function. Energy equation ( I ) (2) ( uI ) p u J QC Q S t where I is the specific internal energy, excluding chemical energy contribution, J
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is the heat flux vector, is the turbulent dissipation rate, Q C is the chemical
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source term due to chemical heat release and Q S is the spray source term.
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In the above equations, mC and Q C which are related to detailed chemical
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kinetics need to be obtained by solving a large number of ordinary differential equation (ODE) problems at each global time step, and yet the ODE integrations occupy most of the total wall-clock time for the simulation [44].
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Furthermore, the Q C can be described as m
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QC Qi j 1
(3)
k
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Qi ei wW i i i 1
(4)
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here m is the cell number of the mesh, Qi is the chemical source term due to
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chemical heat release of each cell, k is the number of species in the chemical
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reaction mechanism, ei is the internal energy of species i , wi is the net
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production rate, and Wi is the molecular weight of species i .
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In the original KIVA4 code, the CPU needs to calculate Qi for each cell serially,
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and with the increase of the grid cell quantity, the computational time grows geometrically. To save the computational time, a parallel computing method based on the round-robin algorithm was embedded into the coupled KIVA4-CHENMKIN
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code, which helps to get state variables for calculating Q C in parallel. The
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comparison of serial and parallel computation to obtain state variables is illustrated in Fig. 9. The in-cylinder pressure prediction results by serial and parallel computational methods are presented in Fig. 10, and it can be explicitly observed that they have alike prediction accuracy. Moreover, through this parallel computational method, simulation time for a typical case, from the inlet valve closure (IVC) to the exhaust valve open, was approximately three times less with 12 cores on NUS HPC clusters than simulation with single-core serial computation, as shown in Fig. 11, although it is not an ideal hyperbolic scaling of simulation time with number of processors. 3.2.3 Engine validation results The 3D CFD simulations for engine combustion were performed at a fixed engine speed of 2006 rpm with different loads of 25%, 50% and 75% and 100%, and compared with the measured data acquired in the present investigation. Since the in-cylinder pressure and HRR histories as a function the crank angle are the most important combustion characteristics, they were adopted as validation criteria. The experimental operating conditions for dual-fuel engine are presented in Table 3, and the sector mesh used for CFD simulation with KIVA4 is shown in Fig. 12. The comparison between the measured data and the simulation results are graphically demonstrated in Fig. 13. For an intuitionistic and clear display of the validation results, the in-cylinder pressure curves under 25%, 50% and 75% load plotted with experimental data have been smoothed with sixth or eighth Gaussian fitting algorithm, and R2, which is the index for goodness of fit, are all greater than 0.996, meaning that the fitting is quite well. Since the fitting result leaves much to be desired, there is no smoothing with the one at 100% load. From Fig. 13, it can be obviously seen that good agreements for in-cylinder pressure and HRR are achieved, which indicates the validity of this new developed dual-fuel mechanism to simulate the combustion characteristics of diesel and NG in heavy-duty dual-fuel engines. The normalized validation results on NOx and CO emissions are plotted in Fig. 14. I t can be observed that compared to the normalized experimental results, the trends for the formation of NOx and CO emissions can be correctly predicted among four load conditions.. Furthermore, limited to the experimental apparatus, the experimental data of soot emissions could not be obtained, and thus its validation cannot be performed. And based on the above observations, the new developed skeletal dual-fuel mechanism is validated.
4. Conclusion A skeletal diesel/NG dual-fuel mechanism containing 61 species and 199 reactions was developed for heavy-duty engines in this study. Firstly, a reduced mechanism for
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diesel was constructed from a published mechanism, and it was then coupled with a reduced NG mechanism generated from GRI-Mech 3.0 mechanism. Sensitive analysis and reaction rate adjustment were utilized to optimize the ignition delay predictions of this coupled dual-fuel mechanism. Next, a series of vigorous validations were performed including ignition delay testing against the shock tube experimental data, as well as 3D engine simulations against engine testing results under different conditions. The validation results indicate that the dual-fuel mechanism is valid in reproducing the ignition behaviors, combustion characteristics and NOx and CO emission trends in heavy-duty diesel/NG dual-fuel engines. Besides, a parallel computing method based on the round-robin algorithm was implemented and embedded into the coupled KIVA4-CHENMKIN code, through which the computational time can be greatly accelerated. With this parallel computational method and the new developed compact dual-fuel mechanism, the 3D CFD simulation for the combustion in heavy-duty engines can be done in a reasonable computational time. Abbreviations
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NG NOx CO
natural gas nitrogen oxides carbon monoxide
HC
hydrocarbon compounds
PM
particulate matters
CO2 CFD CR
carbon dioxide computational fluid dynamics compression ratio
HRR heat release rate AME arithmetical mean error DRGEPSA direct relation graph with error propagation and sensitivity analysis CSP computational singular perturbation KHRT Kelvin–Helmholtz Rayleigh–Taylor IVC inlet valve closure TDC top dead center
Acknowledgements The authors gratefully acknowledge financial support from China Scholarship Council.
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List of Figure Captions Figure 1. Procedure used to generate the skeletal dual-fuel mechanism Figure 2. Influence of pressure on n-heptane ignition delay times at φ=0.5, 1.0, 2.0, target error tolerance 10%, 30%, 50%, and comparisons between Golovitchev mechanism and reduced mechanism based on DRGEPSA Figure 3. Influence of pressure on NG ignition delay times at φ=0.5, 1.0, 2.0, target error tolerance 10%, 30%, 50%, and comparisons between GRI-Mech 3.0 mechanism and reduced mechanism based on DRGEPSA Figure 4. Influence of pressure on n-heptane ignition delay times at φ=0.5, 1.0, 2.0, target error tolerance 10%, 30%, 50%, and comparisons between Golovitchev mechanism and reduced mechanism based on CSP Figure 5. Influence of pressure on NG ignition delay times at φ=0.5, 1.0, 2.0, target error tolerance 10%, 30%, 50%, and comparisons between GRI-Mech 3.0 mechanism and reduced mechanism based on CSP Figure 6. Ignition delay validation for NG at different equivalence ratios and initial pressures Figure 7. Ignition delay validation for diesel at different equivalence ratios and initial pressures Figure 8. The engine test bed used in this investigation Figure 9. Comparison of serial and parallel computation to obtain state variables Figure 10. The in-cylinder pressure prediction results by serial and parallel computational methods under same operating conditions Figure 11. The simulation time with different CPU core numbers Figure 12. The sector mesh at TDC for engine simulation Figure 13. Comparison of in-cylinder pressure and HRR between engine test data and simulation results under 25%, 50%, 75% and 100% load at 2006 rpm Figure 14. Comparison of NOx and CO emissions between engine testing and numerical results
DRGEPSA 55 species and
Valeri n-heptane 82 species and 347 reactions
DRGEPSA 40 species and
GRI-MECH 3.0 53 species and 325 reactions
Validation
CSP
49 species and 160 reactions
CSP
40 species and 146 reactions
264 reactions
248 reactions
Coupled skeletal mechanism
Coupling and Reaction Rate Adjustment
61 species and 199 reactions
Fig. 1. Procedure used to generate the skeletal dual-fuel mechanism
2000 1
1600
1200
T (K)
800
(a) 0.1
Ignition Delay Time (s)
P=20bar 60bar
0.01
100bar
1E-3 1E-4 1E-5
Line: Golovitchev n-heptane mechanism Symbol : error 10% Symbol : error 30% Symbol : error 50%
1E-6 1E-7 0.6
0.8
1.0
1.2
1.4
1000/T (K-1) 2000 1
1600
1200
T (K)
800
(b) 0.1
Ignition Delay Time (s)
P=20bar
0.01
60bar
1E-3
100bar
1E-4 1E-5
Line: Golovitchev n-heptane mechanism Symbol : error 10% Symbol : error 30% Symbol : error 50%
1E-6 1E-7 0.6
0.8
1.0
1.2
1.4
1000/T (K-1) 2000 1
1600
1200
T (K)
800
(c) 0.1
Ignition Delay Time (s)
P=20bar
0.01
60bar
1E-3
100bar
1E-4 1E-5
Line: Golovitchev n-heptane mechanism Symbol : error 10% Symbol : error 30% Symbol : error 50%
1E-6 1E-7 0.6
0.8
1.0
1.2
1.4
1000/T (K-1)
Fig. 2. Influence of pressure on n-heptane ignition delay times at φ=0.5, 1.0, 2.0, target error tolerance 10%, 30%, 50%, and comparisons between Golovitchev mechanism and reduced mechanism based on DRGEPSA
2000 100 10
1600
1200
T (K)
800
(a) P=20bar 60bar
Ignition Delay Time (s)
1 100bar
0.1 0.01 1E-3 1E-4
Line: GRI-Mech 3.0 mechanism Symbol : error 10% Symbol : error 30% Symbol : error 50%
1E-5 1E-6 1E-7 0.6
0.8
1.0
1.2
1.4
1000/T (K-1)
2000 100 10
1600
1200
T (K)
800
(b) P=20bar
60bar
Ignition Delay Time (s)
1
100bar
0.1 0.01 1E-3 1E-4
Line: GRI-Mech 3.0 mechanism Symbol : error 10% Symbol : error 30% Symbol : error 50%
1E-5 1E-6 1E-7 0.6
0.8
1.0
1.2
1.4
1000/T (K-1)
2000 100 10
1600
1200
T (K)
800
(c) P=20bar
60bar
Ignition Delay Time (s)
1 100bar
0.1 0.01 1E-3 1E-4
Line: GRI-Mech 3.0 mechanism Symbol : error 10% Symbol : error 30% Symbol : error 50%
1E-5 1E-6 1E-7 0.6
0.8
1.0
1.2
1.4
1000/T (K-1)
Fig. 3. Influence of pressure on NG ignition delay times at φ=0.5, 1.0, 2.0, target error tolerance 10%, 30%, 50%, and comparisons between GRI-Mech 3.0 mechanism and reduced mechanism based on DRGEPSA
2000 1
1600
1200
T (K)
800
(a) 0.1
Ignition Delay Time (s)
P=20bar 60bar
0.01
100bar
1E-3 1E-4 1E-5
Line: Golovitchev n-heptane mechanism Symbol : error 10% Symbol : error 30% Symbol : error 50%
1E-6 1E-7 0.6
0.8
1.0
1.2
1.4
1000/T (K-1) 2000 1
1600
1200
T (K)
800
(b) 0.1
Ignition Delay Time (s)
P=20bar
0.01
60bar
1E-3
100bar
1E-4 1E-5
Line: Golovitchev n-heptane mechanism Symbol : error 10% Symbol : error 30% Symbol : error 50%
1E-6 1E-7 0.6
0.8
1.0
1.2
1.4
-1
1000/T (K ) 2000 1
1600
1200
T (K)
800
(c) 0.1
Ignition Delay Time (s)
P=20bar
0.01
60bar
1E-3
100bar
1E-4 1E-5
Line: Golovitchev n-heptane mechanism Symbol : error 10% Symbol : error 30% Symbol : error 50%
1E-6 1E-7 0.6
0.8
1.0
1.2
1.4
1000/T (K-1)
Fig. 4. Influence of pressure on n-heptane ignition delay times at φ=0.5, 1.0, 2.0, target error tolerance 10%, 30%, 50%, and comparisons between Golovitchev mechanism and reduced mechanism based on CSP
2000 100 10
1600
1200
T (K)
800
(a) P=20bar 60bar
Ignition Delay Time (s)
1 100bar
0.1 0.01 1E-3 1E-4
Line: GRI-Mech 3.0 mechanism Symbol : error 10% Symbol : error 30% Symbol : error 50%
1E-5 1E-6 1E-7 0.6
0.8
1.0
1.2
1.4
1000/T (K-1) 2000 100 10
1600
1200
T (K)
800
(b) P=20bar
60bar
Ignition Delay Time (s)
1
100bar
0.1 0.01 1E-3 1E-4
Line: GRI-Mech 3.0 mechanism Symbol : error 10% Symbol : error 30% Symbol : error 50%
1E-5 1E-6 1E-7 0.6
0.8
1.0
1.2
1.4
1000/T (K-1)
2000 100 10
1600
1200
T (K)
800
(c) P=20bar
60bar
Ignition Delay Time (s)
1 100bar
0.1 0.01 1E-3 1E-4
Line: GRI-Mech 3.0 mechanism Symbol : error 10% Symbol : error 30% Symbol : error 50%
1E-5 1E-6 1E-7 0.6
0.8
1.0
1.2
1.4
1000/T (K-1)
Fig. 5. Influence of pressure on NG ignition delay times at φ=0.5, 1.0, 2.0, target error tolerance 10%, 30%, 50%, and comparisons between GRI-Mech 3.0 mechanism and reduced mechanism based on CSP
T (K) 1750 0.1
1700
1650
1600
T (K) 1550
1500
1450
1600
1500
1E-5 Experimental data GRI-Mech 3.0 NG mechanism Skeletal dual-fuel mechanism
Ignition Delay Time (s)
1E-4
1E-6
0.58
0.60
0.62
0.64
0.66
0.68
1E-3
1E-4
1E-5 Experimental data GRI-Mech 3.0 NG mechanism Skeletal dual-fuel mechanism
1E-6
1E-7
1E-7 0.62
0.70
0.64
0.66
1000/T (K-1)
1600
1550
0.70
0.72
T (K)
T (K) 1650
0.68
1000/T (K-1)
1500
1450
1400
1750
0.1
1700
1650
1600
1550
1500
1450
0.1 (d) P=40.0bar
(c) P=20.0bar 0.01
0.01
1E-3
1E-4
1E-5 Experimental data GRI-Mech 3.0 NG mechanism Skeletal dual-fuel mechanism
1E-6
Ignition Delay Time (s)
Ignition Delay Time (s)
1400
0.01
1E-3
1E-3
1E-4
1E-5 Experimental data GRI-Mech 3.0 NG mechanism Skeletal dual-fuel mechanism
1E-6
1E-7
1E-7 0.60
0.62
0.64
0.66
0.68
0.70
0.72
0.58
0.60
0.62
-1
T (K) 1700
1650
0.64
0.66
0.68
0.70
1000/T (K-1)
1000/T (K )
T (K)
1600
1550
1500
1560
0.1
1540
1520
1500
1480
1460
1440
0.1
(e) P=20.0bar
(f) P=40.0bar
0.01
0.01
1E-3
1E-4
1E-5 Experimental data GRI-Mech 3.0 NG mechanism Skeletal dual-fuel mechanism
1E-6
1E-7 0.59
0.60
0.61
0.62
0.63
0.64
1000/T (K-1)
0.65
0.66
0.67
Ignition Delay Time (s)
Ignition Delay Time (s)
1450
(b) P=40.0bar
(a) P=20.0bar 0.01
Ignition Delay Time (s)
1550
0.1
1E-3
1E-4
1E-5 Experimental data GRI-Mech 3.0 NG mechanism Skeletal dual-fuel mechanism
1E-6
1E-7 0.64
0.65
0.66
0.67
0.68
0.69
1000/T (K-1)
Fig. 6. Ignition delay validation for NG at different equivalence ratios and initial pressures
T (K)
T (K) 1300
1200
1100
1000
900
1200
800
1000
(a) P=13.5bar
1E-4 1E-5
Experimental data Golovitchev n-heptane mechanism Skeletal dual-fuel mechanism
1E-6
Ignition Delay Time (s)
1E-3
0.01 1E-3 1E-4 1E-5
Experimental data Golovitchev n-heptane mechanism Skeletal dual-fuel mechanism
1E-6 1E-7
1E-7 0.8
0.9
1.0
1.1
1.2
0.8
1.3
0.9
1.0
T (K) 1000
950
1.2
1.3
1.4
T (K)
900
850
800
1100
1000
900
800
1 (c) P=19.3bar
(d) P=40.0/41.0bar
0.1
0.1
0.01 1E-3 1E-4 1E-5
Experimental data Golovitchev n-heptane mechanism Skeletal dual-fuel mechanism
1E-6
Ignition Delay Time (s)
Ignition Delay Time (s)
1.1
1000/T (K-1)
1000/T (K-1)
1E-7 0.95
800
0.1
0.01
1050 1
900
(b) P=41.0bar
0.1
Ignition Delay Time (s)
1100
1
1
0.01 1E-3 1E-4 1E-5
Experimental data Golovitchev n-heptane mechanism Skeletal dual-fuel mechanism
1E-6 1E-7
1.00
1.05
1.10
1.15 -1
1000/T (K )
1.20
1.25
1.30
0.9
1.0
1.1
1.2
1.3
1000/T (K-1)
Fig. 7. Ignition delay validation for n-heptane at different equivalence ratios and initial pressures
Air inlet
Natural gas
Combustion analyzer
Flow meter Charge amplifier Diesel fuel
EGR cooler
Fuel meter Decoder
Dynamometer Exhaust gas
Opacimeter Opacimeter
Gasanalyzer analyzer Gas
Fig. 8. The engine test bed used in this investigation
Chemical kinetics solver
Chemical kinetics solver Integration
Integration cell m
cell 1
P,T,ρ,Y
The next time step
state variables obtained in series
Cell 1 The next time step
P,T,ρ,Y … P,T,ρ,Y P,T,ρ,Y
P,T, P,T, … ρ,Y ρ,Y
P,T, P,T, P,T, P,T, … … … ρ,Y ρ,Y ρ,Y ρ,Y
Slave core 1
Slave core 2
…
Slave core n
State variables obtained in parallel
Cell m Collect updated state variables for each cell from slave cores
Collect updated state variables for each cell
Master core
Transport equation solver
Transport equation solver
(a) State variables obtained in series
(b) State variables obtained in parallel
Fig. 9. Comparison of serial and parallel computation to obtain state variables
140
In-cylinder pressure (bar)
120 100
Serial core numbers 8 core numbers 12 core numbers 16
80 60 40 20 0 -60
-40
-20
0
20
40
60
Crank angle (deg ATDC)
Fig. 10. The in-cylinder pressure prediction results by serial and parallel computational methods under same operating conditions
Simulation CPU time (minutes)
1.2x104
1.0x104
8.0x103
6.0x103
4.0x103
2.0x103
0
4
8
12
16
CPU core numbers
Fig. 11. The simulation time with different CPU core numbers
Fig. 12. The sector mesh at TDC for engine simulation
-60
-50
-40
-30
-20
-10
0
10
20
30
40
50
60
-50
-40
-30
-20
-10
0
10
20
30
Experiment Simulation
25% load
40
50
80
50% load
60 160 140
200
100 20 50
10
70
120
60
100
50 80 40 60
30 20
HRR (J/CAD)
150 30
HRR (J/CAD)
40
In-cylinder pressure (bar)
In-cylinder pressure (bar)
-60 90
Experiment Simulation
50
60 250
40
10
20
0
0 -50
-40
-30
-20
-10
0
10
20
30
40
50
30
40
50
60
-60
-50
-40
Crank angle (deg ATDC) -60
-50
-40
-30
-20
-10
0
10
20
-30
-20
-10
0
10
20
30
40
50
Crank angle (deg ATDC) -60
-50
-40
-30
-20
-10
0
10
20
30
40
50
120 100
Experiment Simualtion
75% load
140
80 40
60 40
20
20
HRR (J/CAD)
100 60
In-cylinder pressure (bar)
In-cylinder pressure (bar)
80
100% load
Experiment Simulation
100
120
-50
-40
-30
-20
-10
0
10
20
Crank angle (deg ATDC)
30
40
50
0 60
60 200 180 160 140
80
120 60
100 80
40
60 40
20
20
0 -60
0 60
HRR (J/CAD)
-60
0 60
0 -60
-50
-40
-30
-20
-10
0
10
20
30
40
50
0 60
Crank angle (deg ATDC)
Fig. 13. Comparison of in-cylinder pressure and HRR between engine test data and simulation results under 25%, 50%, 75% and 100% load at 2006 rpm
2.0
1.5
Normalized CO emissions
Normalized NOx emissions
2.0 Experimental NOx emissions Normalized predicted NOx emissions
1.0
0.5
0.0
Experimental CO emissions Normalized predicted CO emissions 1.5
1.0
0.5
0.0 25%
50%
75%
Engine load
100%
25%
50%
75%
100%
Engine load
Fig. 14. Comparison of NOx and CO emissions between engine testing and numerical results
List of Table Captions Table 1. Adjusted pre-exponential factors of sensitivity reactions Table 2. Engine specifications Table 3. Experimental conditions
Table 1. Adjusted pre-exponential factors of sensitivity reactions Arrhenius rate constants
Reactions NG
Diesel
A
Modified A
R1
CH3+CH3(+M) = C2H6(+M)
6.77E+16
9.77E+16
R2
CH3+H2O2 = HO2+CH4
2.45E+04
1.05E+04
R3
CH3+O2 = O+CH3O
3.56E+13
1.06E+13
R4
CH3+O2<=>OH+CH2O
2.31E+12
1.31E+12
R5
NC7H16+OH = C7H15-2+H2O
6.00E+09
9.00E+09
R6
NC7H16+HO2 = C7H15-2+H2O2
3.30E+13
2.30E+14
R7
C7H15O2 = C7H14O2H
6.00E+11
3.20E+12
R8
C7H15-2 = CH3+C6H12
2.51E+13
9.51E+13
R9
C7H14O2HO2=C7KET21+OH
1.49E+13
3.49E+13
Table 2. Engine specifications Item
Specifications
Number of cylinder
6
Engine type
Turbocharged, water-cooled
Bore×stroke (mm)
126×130
Swept volume (L)
9.726
Connecting rod length (mm)
219
Compression ratio
17.0
Rated power (kW)
247@1900rpm
Rated torque (N.m )
1250@1400rpm
Injector nozzle number
7
Nozzle orifice diameter (mm)
0.15
Included spray angle (deg)
152
Table 3. Experimental conditions Type
Case 25% load
50% load
75% load
100% load
Engine speed (rpm)
2006
2006
2006
2006
Pressure at IVC (bar)
12.68
23.12
27.28
29.10
Injected diesel per cylinder (mg)
17.9
14.8
13.4
19.5
Natural gas per cylinder (mg)
26.6
72.3
98.0
109.3
Injection duration (CAD)
8.9
8.9
8.9
10.8
SOI (CAD ATDC)
-17
-17
-15.0
-14.0
Boost pressure (kPa abs)
114
196
230
248
Manifold temperature (°C)
43
44
49
45
0.372
0.497
0.555
0.528
Natural gas equivalence ratio
Highlights
A new skeletal mechanism for diesel/natural gas dual-fuel was constructed. This mechanism can be used for combustion simulation of heavy-duty dual-fuel engines. A parallel computing method greatly saving the computational time was developed. The mechanism was well validated against shock tube and engine experimental results.
S1359-4311(17)32604-2 http://dx.doi.org/10.1016/j.applthermaleng.2017.05.175 ATE 10490
To appear in:
Applied Thermal Engineering
Received Date: Revised Date: Accepted Date:
18 April 2017 22 May 2017 29 May 2017
Please cite this article as: W. Zhao, W. Yang, L. Fan, D. Zhou, X. Ma, Development of a skeletal mechanism for heavy-duty engines fuelled by diesel and natural gas, Applied Thermal Engineering (2017), doi: http://dx.doi.org/ 10.1016/j.applthermaleng.2017.05.175
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Development of a skeletal mechanism for heavy-duty
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engines fuelled by diesel and natural gas
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Wensheng Zhaoa,b, Wenming Yangb*, Liyun Fana*, Dezhi Zhoub, Xiuzhen Maa
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a. College of Power and Energy Engineering, Harbin Engineering University, Harbin 150001, China b. Department of Mechanical Engineering, National University of Singapore, 4 Engineering Drive 3, Singapore 117583, Singapore
Abstract The purpose of this work is to develop a skeletal dual-fuel mechanism for heavy-duty engines fuelled by diesel and natural gas. With diesel fuel modeled as n-heptane, and natural gas modeled as methane, the skeletal mechanism was constructed by coupling the two skeletal mechanisms reduced detailed mechanisms: n-heptane and methane mechanisms. Directed relation graph error propagation and sensitivity analysis, computational singular perturbation and reaction rate adjustment methods were employed for mechanism reduction. The final skeletal dual-fuel mechanism is composed of 61 species and 199 reactions. So as to validate the fidelity of the novel skeletal dual-fuel mechanism, zero-dimension ignition delay testing against shock tube experimental results and 3-dimensional engine validation about in-cylinder pressures, heat release rates and NOx and CO emissions against engine testing results were performed under various operating conditions. The validation results indicate that the dual-fuel mechanism can accurately reproduce the ignition behaviors, combustion characteristics and emission trends in heavy-duty diesel/NG dual-fuel engines. Besides, a parallel computing method based on the round-robin algorithm was developed which can significantly save the time for calculating. Combined with the new developed skeletal dual-fuel mechanism, the 3D CFD simulation for the combustion in heavy-duty engines can be done in a reasonable computational time.
Keywords: Natural gas; Pilot diesel; Dual-fuel skeletal mechanism; heavy-duty engines
1. Introduction Diesel engines are widely used in numerous applications throughout the world. With rapid depleting of fossil fuels and increasingly strict emission regulations, alternative fuels for diesel engines have attracted more and more attention [1-4]. Due to its abundant reserves, high fuel economy and relatively low emissions, natural gas (NG) has been emerging as a promising alternative fuel in recent years, especially in ship propulsion [5-7]. The diesel/NG dual-fuel engines adopt natural gas as primary fuel, while using a small amount of diesel as pilot fuel to ignite NG and air mixture [8-9]. Conventional diesel engines can be retrofitted to diesel/NG dual-fuel engines with some modifications, which make it possible for the dual-fuel engines to utilize the high compression ratios of original diesel engines, thus achieving high thermal efficiency as well as relatively lower nitrogen oxides (NOx) and particulate matter * Corresponding authors Email addresses: [email protected] (WM Yang), [email protected] (LY Fan)
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emissions [10]. Hence, the dual-fuel engines have been research hotspot for many researchers and engine manufacturers. So far, quite a number of studies have been devoted to investigate the combustion of NG in compress ignition engines with diesel as the pilot fuel. Papagiannakis et al. [11] converted a single-cylinder high-speed Lister LV1 diesel engine to a dual-fuel engine by injecting the NG to the intake manifold of the engine and experimentally investigated the effects of NG percentage on the in-cylinder pressure, HRR, peak cylinder pressure, total brake specific fuel consumption, NOx, carbon monoxide (CO), unburned hydrocarbons (HC) and soot emissions. Carlucci et al. [12] tested a single cylinder diesel/NG dual-fuel engine and analyzed the effect of CNG and diesel fuel injection pressure, the pilot fuel injection quantity, on the combustion development and engine performance, in terms of specific emission levels and fuel consumption under different working conditions. Cordiner et al. Mittal et al. [13] investigated the exhaust emissions characteristics, i.e. HC, CO, NOx, soot, particulate matter (PM) and carbon dioxide (CO2), under diesel and dual fuel operations at different operating conditions on a six-cylinder diesel/NG dual fuel engine. Yang et al. [14] studied the impact of pilot diesel injection timing on the combustion noise and particle emissions characteristics of a diesel/NG dual-fuel heavy-duty engine at low load. However, solely by means of experiments, it can be rather costly and time-consuming to understand and optimize the engine performance and exhaust emissions in dual-fuel engines. Numerical simulation of the IC engines has shown to be a very quick and economical method for understanding the details of the complex spray, evaporation, combustion, and pollutant formation processes. Various types of models have been developed, including zero-dimensional (or thermodynamic) models, multi-zone models, and multi-dimensional computational fluid dynamics (CFD) models coupled with detailed chemistry. Rahimi et al. [15] optimized a chemical kinetic mechanism for an n-heptane and natural gas blend by modifying the reaction rate parameters with the genetic algorithm method, and verified the modeling results against experimental results with a zero-dimensional HCCI combustion model. The agreement between experimental and modeling results was found to be acceptable within the examined conditions. Papagiannakis et al. [16] examined the effect of compression ratio (CR) and diesel fuel injection timing (IT) on the performance and exhaust emissions of a dual-fuel single-cylinder research engine, which is fuelled with diesel and methane by utilizing a two-zone phenomenological combustion model. The model was tested and validated against experimental data obtained from a fumigated methane–diesel dual-fuel engine, operating with constant CR, diesel fuel IT, engine speed at partial-load conditions for various methane-diesel fuel mass ratios. Nonetheless, it has been found that the zero-dimensional model often predicts a very fast combustion rate once ignition occurs and is unable to capture the correct combustion phasing [17]. A zonal model can predict a reasonable overall combustion rate but it requires empirical adjustments in formulating zones [18]. Thus, a detailed chemistry-based CFD model can be a better tool to simulate different aspects of in-cylinder processes, if the computational time is
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acceptable. Singh et al. [19] numerically studied the combustion and emissions of dual-fuel engines with KIVA3V code, and identified the capabilities and limitations of the present combustion model to simulate premixed combustion of air and natural gas. Donateo et al. [20] modified the SHELL and the Characteristic Time Combustion model in the KIVA3V code, and verified the capability of the simulation code in predicting the emissions trends when changing pilot specification and engine configuration parameters. Moreover, a computer-aided procedure in finding optimal solutions was performed in the framework of the Modefrontier environment. Maghbouli et al. [21] investigated the combustion process under knocking conditions in a dual-fuel diesel-NG engine utilizing KIVA-3V incorporated with detailed chemical reaction model. A reduced chemical kinetics mechanism was developed by combining two previously published reduced mechanisms [22-23]. However, the meshes of the engine bowl for CFD modeling is very rough because of the lack of detailed parameters of the bowl geometry. Moreover, there is only validation for in-cylinder pressure and heat release rate (HRR), while short of the validation of ignition delay time which is a crucial parameter to represent the combustion process. Hockett et al. [24] constructed a reduced chemical kinetic mechanism composed of 141 species and 709 reactions to simulate the combustion of both natural gas and diesel fuels in a dual-fuel engine using the CONVERGE software, and the ignition delay time, in-cylinder pressure and HRR were validated. The results showed that the reduced mechanism accurately reproduces the chemical kinetic behavior of the detailed mechanism. Moreover, based on this mechanism, three-dimensional Reynolds-averaged Navier-Stokes-based engine simulations can be conducted within a reasonable computational time (less than 24 h). Nevertheless, the bore of heavy-duty engines is much larger than that of the GM 1.9L light-duty engine used in the paper, which means an exponential increase of the amount of the meshes for CFD modeling, and then an unreasonable computational time. So this mechanism is still not skeletal enough for large-bore dual-fuel engines. The objective of the present work is to develop a skeletal chemical kinetic mechanism which can be used in multidimensional CFD simulations of the combustion and emission formation process in the heavy-duty multi-cylinder diesel/NG dual-fuel engines. To ensure the reliability of this novel mechanism, validation for ignition delay times was performed against reflected shock tube experiments, and validation for in-cylinder pressure and HRR were conducted against heavy-duty dual-fuel engine experiments using multidimensional CFD simulations with a modified KIVA-4 code incorporated with CHEMKIN. Furthermore, a parallel computing method based on the round-robin algorithm was embedded into the coupled KIVA4-CHENMKIN code for a higher computation speed. 2. CHEMICAL REACTION MECHANISM REDUCTION PROCESS In the present study, the new reduced dual-fuel mechanism was developed from two published mechanisms: the Golovitchev diesel mechanism and the GRI-Mech 3.0 natural gas mechanism. The Golovitchev mechanism [25, 26] comprises of 82 species and 347 elementary chemical reactions, and in this mechanism, n-heptane was
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considered a surrogate of the diesel fuel because of their similar cetane numbers and heating values. The GRI-Mech 3.0 which consists of 53 species and 325 reactions, is an optimized mechanism designed to model natural gas combustion, including NO formation and reburn chemistry [27]. Methods of the direct relation graph with error propagation and sensitivity analysis (DRGEPSA), computational singular perturbation (CSP) algorithm, reaction rate adjustment have been employed to generate a reduced dual-fuel chemical reaction mechanism. First, the Golovitchev mechanism and GRI-mech 3.0 mechanism were reduced utilizing the DRGEPSA method, respectively. Then, the two reduced mechanisms were coupled together whereby reactions for C4-C7 species were derived from the reduced n-heptane mechanism; reactions for C2-C3 species were a combination of the two reduced mechanisms and the reaction rates of any duplicated reactions in the two mechanisms were chosen from the n-heptane mechanism to make sure that soot formation from diesel combustion is accurately represented; reactions for H2/CO/C1 species were taken from the reduced NG mechanism. At last, the new constructed skeletal dual-fuel mechanism was validated through reflected shock tube experiments and engine tests under different working conditions. The mechanism reduction procedure was demonstrated in Fig. 1. Following the above process, the DRGEPSA method [28-30], was firstly utilized for the reduction of n-heptane and NG mechanisms, through which unimportant species and reactions can be recognized efficiently and crucial features of global characteristics can be kept simultaneously [31]. The DRGEPSA method consists of two phases: the DRGEP and SA. In the first phase, the DRGEP approach is applied to map the coupling of species in a reaction system through a directed relation graph, in which the graph vertices represent species and directed edges between vertices represent the coupling of species. Next, the overall interaction coefficient for all species relative to the target species can be calculated, and a threshold value is introduced to categorize these species. The species with a lower overall interaction coefficient is considered unimportant to the target species and can be removed, while the others will be retained. As the second phase of DRGEPSA, the sensitivity analysis (SA) algorithm is utilized to classify limbo species and then eliminate those additional unimportant species whose overall interaction coefficients higher than the threshold of DRGEP but lower than the threshold of SA. Obviously, the proper selection of the target species are crucial to the entire reduction process. Synthetically considering the time consumed and the reduction accuracy, the target species for n-heptane mechanism reduction were identified as NC7H16, CO, CO2, O2, N2 and C2H2, while the DRGEP error tolerances were identified as 10%, 20%, 30%, 40% and 50%. The reduction process was sampled through 63 initial conditions with 3 initial pressures (P=20bar, 60bar and 100bar), 7 initial temperatures (T=700-1800 K) and 3 equivalence ratios (φ=0.5, 1.0 and 2.0). Fig. 2 illustrates the ignition delay times of n-heptane predicted both by the Golovitchev mechanism and the reduced one based on the DRGEPSA. The ignition delay time is defined as the time interval needed from
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its initial temperature to the temperature with an increase of 400 K [32]. As presented in Fig. 2, the ignition delay times calculated by the reduced mechanism based on DRGEPSA agree well with those of original chemical reaction mechanism. Actually there was no distinction among the reduction results of all the five error tolerances and their overall arithmetical mean error (AME) was only 0.88%, and thus, the DRGEPSA reduced mechanism with 0.88% AME was chosen. The final DRGEPSA reduced mechanism for n-heptane was composed of 55 species and 264 reactions. Whereas typical natural gas contains very high methane by volume, and thus exhibits properties very similar to those of methane [33], the present work models natural gas as pure methane. Therefore, the target species for NG mechanism reduction were defined as CH4, CO, CO2, O2, N2, NO, NO2 and AR, while the error tolerances of DRGEP, equivalence ratios, initial pressures and temperatures were exactly the same as settings of n-heptane mechanism reduction. Particularly, species NO and NO2 were regarded as the target species to keep the NOx formation predicted accurately in consideration of the fact that NG is the primary fuel in the pilot ignited dual-fuel engines. Fig. 3 demonstrates the comparison of the NG ignition delay times predicted by the GRI-Mech 3.0 mechanism and the reduced one based on DRGEPSA. The DRGEPSA reduced mechanism of 10% error tolerance was picked out for its minimum AME and acceptable number of reactions. The final DRGEPSA reduced mechanism for NG was formed of 40 species and 248 reactions. Subsequently, a method based on CSP algorithm [34, 35] was applied to calculate the importance index which indicates the normalized contribution of a reaction to the production rate of a species. This method can effectively remove species with small time scales by means of recognizing the fast species and the time scales of different modes which may not be fully identified in DRGEPSA method. Similarly, a threshold value is used to assist in eliminating reactions deemed nonsignificant in regard to a core set of species. The target species of CSP were consistent with those of DRGEPSA, as well as the error tolerances. The ignition delay time of n-heptane predicted both by the original mechanism and the CSP reduced one was presented in Fig. 4, and it can be found that the calculated ignition delay times of the further reduced mechanism based on CSP show good accordance with those of original reaction mechanism, especially for 10% and 30% error tolerances. Further, the overall AME of the mechanism with 10% error tolerance is 4.18% less than that of the 30% one, with an increase of merely 4 chemical kinetic reactions. Therefore, the CSP reduced mechanism generated by 10% error tolerance was adopted, and the final CSP reduced mechanism for n-heptane was composed of 49 species and 160 reactions. Fig. 5 demonstrates the NG ignition delay times predicted by the original mechanism as well as the CSP reduced one. There was no difference among the CSP reduction results of all the five error tolerances, and thus the final CSP reduced mechanism for NG was made up of 40 species and 146 reactions with an overall AME of 9.73%. Next, the above two CSP reduced mechanisms were integrated together through the
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aforementioned methodology, forming a multi-component chemical mechanism with 61 species amongst 199 reactions. And yet, the introduced species and reactions and the change of intermediate reaction pathways could cause random changes on the new mechanism in terms of its combustion prediction capability. With the purpose of maintaining its prediction accuracy while keeping the small size of this mechanism, it is quite essential to regulate the reactions by tuning the reaction rates of some particular reactions. Therefore, sensitivity analysis was implemented again utilizing SENKIN code to ascertain the reactions that significantly influence the ignition delay for both n-heptane and NG. Considering that both of the original mechanisms were not highly detailed, there existed errors with real ignition delay time predictions for both them, and thus the initial conditions were defined with reference to shock tube experimental data to prevent error propagation and amplification. The target tolerance for the final mechanism was defined as 30% for both n-heptane and NG. Those crucial reactions and their corresponding pre-exponential factors (A factor) before and after the adjustment are listed in Table 1. Because the reactions related to the small species such as the C1-C2 species could affect the ignition delay predictions of both NG and n-heptane, the sensitivity analysis and reaction rate adjustment were first conducted for methane over 53 shock tube experimental data points obtained from the literature [36], covering for pressures of 20bar, and 40bar, temperatures from 1412 to 1720 K and equivalence ratios of 0.5, 1.0 and 2.0. The pre-exponential factors were systematically tuned based on a variety of above-mentioned initial conditions. As presented in Table 1, reactions R1-R4 were the most sensitive reactions for NG ignition delay prediction and their pre-exponential factors were regulated to make the largest discrepancy was below 30%. As such, a second step sensitivity analysis and reaction rate adjustment was implemented for n-heptane in air over 27 shock tube experimental data points obtained from the literature [37, 38], covering for pressures of 13.5bar, 19.3bar, 40bar and 41bar, temperatures from 746 to 1138 K and equivalence ratios of 0.5 and 1.0. Since the diesel fuel was used as pilot fuel, only fuel lean and stoichiometric conditions (φ=0.5 and 1.0) for n-heptane were taken into account. In order to achieve accurate ignition delay predictions of n-heptane and maintaining the prediction accuracies of NG simultaneously, only reactions with C5-C7 species were tuned. As shown in Table 1, reactions R5-R9 were the most sensitive reactions for n-heptane ignition delay prediction. Following the above procedure, parametric adjustment on the pre-exponential factor A was conducted and the final diesel/NG dual-fuel mechanism which includes only 61 species participating in 199 reactions was developed. The robustness of the dual-fuel mechanism will be shown in the following sections by its validation under different conditions. These validations will guarantee that the new developed skeletal mechanism is trustworthy for capturing the combustion characteristics in terms of the heat-release and ignition delay of real diesel fuel and NG.
3. Results and discussion
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3.1 Ignition delay validations The validation of the novel skeletal dual-fuel reaction mechanism was first performed on the ignition delay time predictions for NG/air mixtures. Furthermore, the validation for NG was focused on the ignition delay time predictions at high temperatures and pressures, in view of that in diesel/NG dual-fuel engines, the NG is primary fuel and ignited by the pilot fuel under the top dead center (TDC) conditions with high temperatures and pressures. Fig. 6 shows the ignition delay times of NG obtained by the experimental data, skeletal dual-fuel and GRI-Mech 3.0 mechanisms. As presented in Fig. 6, the ignition delay plots indicate that the skeletal dual-fuel mechanism accurately mimic the experimental data for both mixtures across the range of pressures, temperatures, and equivalence ratios. The maximum error of -32.8% appears at 1456k, 40bar, under stoichiometric conditions. For all the other conditions presented, the error deviation across the whole testing domain is less than 30%. The relatively large discrepancies are discovered to appear in high temperature of 1400-1500k and at high pressure zone (40bar) for all the equivalence ratios. Moreover, ignition delay time predictions of original GRI-Mech 3.0 mechanism present huge errors, and that is because the validation of this mechanism mainly targeted predictions in high temperatures (1350-1800k) and low pressures (0.25-7.6bar). Fig. 7 presents the comparisons of the 0-D ignition delay times for n-heptane/air mixtures under fuel lean and stoichiometric conditions against the experimental data, skeletal dual-fuel and Golovitchev n-heptane mechanisms. From Fig. 7, it can be clearly found that the ignition delay time predictions of the skeletal dual-fuel mechanism fit well with experimental data. The relatively large deviations are observed at 13.5bar and high temperature zone (1100-1300k) under fuel lean conditions. The largest discrepancy is -29.7%, when T=928k, P=19.3bar and φ=1.0. Overall, the results in Fig. 6 and Fig. 7 suggest that the skeletal dual-fuel mechanism can be used in predicting the ignition delay process in diesel/NG dual-fuel engines. 3.2 Engine validations 3.2.1 Engine specifications A 6-cylinder turbocharged heavy-duty diesel engine was retrofitted to a diesel/NG dual-fuel engine with limited changes, including introducing a multi-point injection system to inject NG into the intake manifold and replacing a valve camshaft with different cam profile to regulate the valve timing and valve overlap angle. The engine test bed used in this investigation is shown in Fig. 8 and the detailed engine specifications are listed in Table 2. 3.2.2 Simulation Tool and parallel computing A coupled KIVA4-CHEMKIN code was employed to conduct engine combustion simulations. Important sub-models implemented in this KIVA4-CHEMKIN code include the heat transfer model based on Han and Reitz formulation [39], the RNG k-ε turbulence model [40] and a diesel spray model developed by the author [41] based on the Kelvin–Helmholtz Rayleigh–Taylor (KHRT) spray breakup model [42]. Moreover, three basic conservation equations need to be solved in KIVA4, namely
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continuity equation, energy equation, and momentum equation [43]. The former two equations are shown in Eq. (1)-(2). Continuity equation m ( mu) ( D( m )) mC S m1 t
(1)
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where u is the fluid velocity vector, is the total mass density, m is the mass
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density of species m, is the vector operator, D is the diffusion coefficient in
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Fick’s Law, mC is the chemical source term, S is the spray source term and is
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the Dirac delta function. Energy equation ( I ) (2) ( uI ) p u J QC Q S t where I is the specific internal energy, excluding chemical energy contribution, J
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is the heat flux vector, is the turbulent dissipation rate, Q C is the chemical
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source term due to chemical heat release and Q S is the spray source term.
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In the above equations, mC and Q C which are related to detailed chemical
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kinetics need to be obtained by solving a large number of ordinary differential equation (ODE) problems at each global time step, and yet the ODE integrations occupy most of the total wall-clock time for the simulation [44].
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Furthermore, the Q C can be described as m
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QC Qi j 1
(3)
k
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Qi ei wW i i i 1
(4)
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here m is the cell number of the mesh, Qi is the chemical source term due to
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chemical heat release of each cell, k is the number of species in the chemical
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reaction mechanism, ei is the internal energy of species i , wi is the net
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production rate, and Wi is the molecular weight of species i .
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In the original KIVA4 code, the CPU needs to calculate Qi for each cell serially,
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and with the increase of the grid cell quantity, the computational time grows geometrically. To save the computational time, a parallel computing method based on the round-robin algorithm was embedded into the coupled KIVA4-CHENMKIN
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code, which helps to get state variables for calculating Q C in parallel. The
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comparison of serial and parallel computation to obtain state variables is illustrated in Fig. 9. The in-cylinder pressure prediction results by serial and parallel computational methods are presented in Fig. 10, and it can be explicitly observed that they have alike prediction accuracy. Moreover, through this parallel computational method, simulation time for a typical case, from the inlet valve closure (IVC) to the exhaust valve open, was approximately three times less with 12 cores on NUS HPC clusters than simulation with single-core serial computation, as shown in Fig. 11, although it is not an ideal hyperbolic scaling of simulation time with number of processors. 3.2.3 Engine validation results The 3D CFD simulations for engine combustion were performed at a fixed engine speed of 2006 rpm with different loads of 25%, 50% and 75% and 100%, and compared with the measured data acquired in the present investigation. Since the in-cylinder pressure and HRR histories as a function the crank angle are the most important combustion characteristics, they were adopted as validation criteria. The experimental operating conditions for dual-fuel engine are presented in Table 3, and the sector mesh used for CFD simulation with KIVA4 is shown in Fig. 12. The comparison between the measured data and the simulation results are graphically demonstrated in Fig. 13. For an intuitionistic and clear display of the validation results, the in-cylinder pressure curves under 25%, 50% and 75% load plotted with experimental data have been smoothed with sixth or eighth Gaussian fitting algorithm, and R2, which is the index for goodness of fit, are all greater than 0.996, meaning that the fitting is quite well. Since the fitting result leaves much to be desired, there is no smoothing with the one at 100% load. From Fig. 13, it can be obviously seen that good agreements for in-cylinder pressure and HRR are achieved, which indicates the validity of this new developed dual-fuel mechanism to simulate the combustion characteristics of diesel and NG in heavy-duty dual-fuel engines. The normalized validation results on NOx and CO emissions are plotted in Fig. 14. I t can be observed that compared to the normalized experimental results, the trends for the formation of NOx and CO emissions can be correctly predicted among four load conditions.. Furthermore, limited to the experimental apparatus, the experimental data of soot emissions could not be obtained, and thus its validation cannot be performed. And based on the above observations, the new developed skeletal dual-fuel mechanism is validated.
4. Conclusion A skeletal diesel/NG dual-fuel mechanism containing 61 species and 199 reactions was developed for heavy-duty engines in this study. Firstly, a reduced mechanism for
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diesel was constructed from a published mechanism, and it was then coupled with a reduced NG mechanism generated from GRI-Mech 3.0 mechanism. Sensitive analysis and reaction rate adjustment were utilized to optimize the ignition delay predictions of this coupled dual-fuel mechanism. Next, a series of vigorous validations were performed including ignition delay testing against the shock tube experimental data, as well as 3D engine simulations against engine testing results under different conditions. The validation results indicate that the dual-fuel mechanism is valid in reproducing the ignition behaviors, combustion characteristics and NOx and CO emission trends in heavy-duty diesel/NG dual-fuel engines. Besides, a parallel computing method based on the round-robin algorithm was implemented and embedded into the coupled KIVA4-CHENMKIN code, through which the computational time can be greatly accelerated. With this parallel computational method and the new developed compact dual-fuel mechanism, the 3D CFD simulation for the combustion in heavy-duty engines can be done in a reasonable computational time. Abbreviations
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NG NOx CO
natural gas nitrogen oxides carbon monoxide
HC
hydrocarbon compounds
PM
particulate matters
CO2 CFD CR
carbon dioxide computational fluid dynamics compression ratio
HRR heat release rate AME arithmetical mean error DRGEPSA direct relation graph with error propagation and sensitivity analysis CSP computational singular perturbation KHRT Kelvin–Helmholtz Rayleigh–Taylor IVC inlet valve closure TDC top dead center
Acknowledgements The authors gratefully acknowledge financial support from China Scholarship Council.
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List of Figure Captions Figure 1. Procedure used to generate the skeletal dual-fuel mechanism Figure 2. Influence of pressure on n-heptane ignition delay times at φ=0.5, 1.0, 2.0, target error tolerance 10%, 30%, 50%, and comparisons between Golovitchev mechanism and reduced mechanism based on DRGEPSA Figure 3. Influence of pressure on NG ignition delay times at φ=0.5, 1.0, 2.0, target error tolerance 10%, 30%, 50%, and comparisons between GRI-Mech 3.0 mechanism and reduced mechanism based on DRGEPSA Figure 4. Influence of pressure on n-heptane ignition delay times at φ=0.5, 1.0, 2.0, target error tolerance 10%, 30%, 50%, and comparisons between Golovitchev mechanism and reduced mechanism based on CSP Figure 5. Influence of pressure on NG ignition delay times at φ=0.5, 1.0, 2.0, target error tolerance 10%, 30%, 50%, and comparisons between GRI-Mech 3.0 mechanism and reduced mechanism based on CSP Figure 6. Ignition delay validation for NG at different equivalence ratios and initial pressures Figure 7. Ignition delay validation for diesel at different equivalence ratios and initial pressures Figure 8. The engine test bed used in this investigation Figure 9. Comparison of serial and parallel computation to obtain state variables Figure 10. The in-cylinder pressure prediction results by serial and parallel computational methods under same operating conditions Figure 11. The simulation time with different CPU core numbers Figure 12. The sector mesh at TDC for engine simulation Figure 13. Comparison of in-cylinder pressure and HRR between engine test data and simulation results under 25%, 50%, 75% and 100% load at 2006 rpm Figure 14. Comparison of NOx and CO emissions between engine testing and numerical results
DRGEPSA 55 species and
Valeri n-heptane 82 species and 347 reactions
DRGEPSA 40 species and
GRI-MECH 3.0 53 species and 325 reactions
Validation
CSP
49 species and 160 reactions
CSP
40 species and 146 reactions
264 reactions
248 reactions
Coupled skeletal mechanism
Coupling and Reaction Rate Adjustment
61 species and 199 reactions
Fig. 1. Procedure used to generate the skeletal dual-fuel mechanism
2000 1
1600
1200
T (K)
800
(a) 0.1
Ignition Delay Time (s)
P=20bar 60bar
0.01
100bar
1E-3 1E-4 1E-5
Line: Golovitchev n-heptane mechanism Symbol : error 10% Symbol : error 30% Symbol : error 50%
1E-6 1E-7 0.6
0.8
1.0
1.2
1.4
1000/T (K-1) 2000 1
1600
1200
T (K)
800
(b) 0.1
Ignition Delay Time (s)
P=20bar
0.01
60bar
1E-3
100bar
1E-4 1E-5
Line: Golovitchev n-heptane mechanism Symbol : error 10% Symbol : error 30% Symbol : error 50%
1E-6 1E-7 0.6
0.8
1.0
1.2
1.4
1000/T (K-1) 2000 1
1600
1200
T (K)
800
(c) 0.1
Ignition Delay Time (s)
P=20bar
0.01
60bar
1E-3
100bar
1E-4 1E-5
Line: Golovitchev n-heptane mechanism Symbol : error 10% Symbol : error 30% Symbol : error 50%
1E-6 1E-7 0.6
0.8
1.0
1.2
1.4
1000/T (K-1)
Fig. 2. Influence of pressure on n-heptane ignition delay times at φ=0.5, 1.0, 2.0, target error tolerance 10%, 30%, 50%, and comparisons between Golovitchev mechanism and reduced mechanism based on DRGEPSA
2000 100 10
1600
1200
T (K)
800
(a) P=20bar 60bar
Ignition Delay Time (s)
1 100bar
0.1 0.01 1E-3 1E-4
Line: GRI-Mech 3.0 mechanism Symbol : error 10% Symbol : error 30% Symbol : error 50%
1E-5 1E-6 1E-7 0.6
0.8
1.0
1.2
1.4
1000/T (K-1)
2000 100 10
1600
1200
T (K)
800
(b) P=20bar
60bar
Ignition Delay Time (s)
1
100bar
0.1 0.01 1E-3 1E-4
Line: GRI-Mech 3.0 mechanism Symbol : error 10% Symbol : error 30% Symbol : error 50%
1E-5 1E-6 1E-7 0.6
0.8
1.0
1.2
1.4
1000/T (K-1)
2000 100 10
1600
1200
T (K)
800
(c) P=20bar
60bar
Ignition Delay Time (s)
1 100bar
0.1 0.01 1E-3 1E-4
Line: GRI-Mech 3.0 mechanism Symbol : error 10% Symbol : error 30% Symbol : error 50%
1E-5 1E-6 1E-7 0.6
0.8
1.0
1.2
1.4
1000/T (K-1)
Fig. 3. Influence of pressure on NG ignition delay times at φ=0.5, 1.0, 2.0, target error tolerance 10%, 30%, 50%, and comparisons between GRI-Mech 3.0 mechanism and reduced mechanism based on DRGEPSA
2000 1
1600
1200
T (K)
800
(a) 0.1
Ignition Delay Time (s)
P=20bar 60bar
0.01
100bar
1E-3 1E-4 1E-5
Line: Golovitchev n-heptane mechanism Symbol : error 10% Symbol : error 30% Symbol : error 50%
1E-6 1E-7 0.6
0.8
1.0
1.2
1.4
1000/T (K-1) 2000 1
1600
1200
T (K)
800
(b) 0.1
Ignition Delay Time (s)
P=20bar
0.01
60bar
1E-3
100bar
1E-4 1E-5
Line: Golovitchev n-heptane mechanism Symbol : error 10% Symbol : error 30% Symbol : error 50%
1E-6 1E-7 0.6
0.8
1.0
1.2
1.4
-1
1000/T (K ) 2000 1
1600
1200
T (K)
800
(c) 0.1
Ignition Delay Time (s)
P=20bar
0.01
60bar
1E-3
100bar
1E-4 1E-5
Line: Golovitchev n-heptane mechanism Symbol : error 10% Symbol : error 30% Symbol : error 50%
1E-6 1E-7 0.6
0.8
1.0
1.2
1.4
1000/T (K-1)
Fig. 4. Influence of pressure on n-heptane ignition delay times at φ=0.5, 1.0, 2.0, target error tolerance 10%, 30%, 50%, and comparisons between Golovitchev mechanism and reduced mechanism based on CSP
2000 100 10
1600
1200
T (K)
800
(a) P=20bar 60bar
Ignition Delay Time (s)
1 100bar
0.1 0.01 1E-3 1E-4
Line: GRI-Mech 3.0 mechanism Symbol : error 10% Symbol : error 30% Symbol : error 50%
1E-5 1E-6 1E-7 0.6
0.8
1.0
1.2
1.4
1000/T (K-1) 2000 100 10
1600
1200
T (K)
800
(b) P=20bar
60bar
Ignition Delay Time (s)
1
100bar
0.1 0.01 1E-3 1E-4
Line: GRI-Mech 3.0 mechanism Symbol : error 10% Symbol : error 30% Symbol : error 50%
1E-5 1E-6 1E-7 0.6
0.8
1.0
1.2
1.4
1000/T (K-1)
2000 100 10
1600
1200
T (K)
800
(c) P=20bar
60bar
Ignition Delay Time (s)
1 100bar
0.1 0.01 1E-3 1E-4
Line: GRI-Mech 3.0 mechanism Symbol : error 10% Symbol : error 30% Symbol : error 50%
1E-5 1E-6 1E-7 0.6
0.8
1.0
1.2
1.4
1000/T (K-1)
Fig. 5. Influence of pressure on NG ignition delay times at φ=0.5, 1.0, 2.0, target error tolerance 10%, 30%, 50%, and comparisons between GRI-Mech 3.0 mechanism and reduced mechanism based on CSP
T (K) 1750 0.1
1700
1650
1600
T (K) 1550
1500
1450
1600
1500
1E-5 Experimental data GRI-Mech 3.0 NG mechanism Skeletal dual-fuel mechanism
Ignition Delay Time (s)
1E-4
1E-6
0.58
0.60
0.62
0.64
0.66
0.68
1E-3
1E-4
1E-5 Experimental data GRI-Mech 3.0 NG mechanism Skeletal dual-fuel mechanism
1E-6
1E-7
1E-7 0.62
0.70
0.64
0.66
1000/T (K-1)
1600
1550
0.70
0.72
T (K)
T (K) 1650
0.68
1000/T (K-1)
1500
1450
1400
1750
0.1
1700
1650
1600
1550
1500
1450
0.1 (d) P=40.0bar
(c) P=20.0bar 0.01
0.01
1E-3
1E-4
1E-5 Experimental data GRI-Mech 3.0 NG mechanism Skeletal dual-fuel mechanism
1E-6
Ignition Delay Time (s)
Ignition Delay Time (s)
1400
0.01
1E-3
1E-3
1E-4
1E-5 Experimental data GRI-Mech 3.0 NG mechanism Skeletal dual-fuel mechanism
1E-6
1E-7
1E-7 0.60
0.62
0.64
0.66
0.68
0.70
0.72
0.58
0.60
0.62
-1
T (K) 1700
1650
0.64
0.66
0.68
0.70
1000/T (K-1)
1000/T (K )
T (K)
1600
1550
1500
1560
0.1
1540
1520
1500
1480
1460
1440
0.1
(e) P=20.0bar
(f) P=40.0bar
0.01
0.01
1E-3
1E-4
1E-5 Experimental data GRI-Mech 3.0 NG mechanism Skeletal dual-fuel mechanism
1E-6
1E-7 0.59
0.60
0.61
0.62
0.63
0.64
1000/T (K-1)
0.65
0.66
0.67
Ignition Delay Time (s)
Ignition Delay Time (s)
1450
(b) P=40.0bar
(a) P=20.0bar 0.01
Ignition Delay Time (s)
1550
0.1
1E-3
1E-4
1E-5 Experimental data GRI-Mech 3.0 NG mechanism Skeletal dual-fuel mechanism
1E-6
1E-7 0.64
0.65
0.66
0.67
0.68
0.69
1000/T (K-1)
Fig. 6. Ignition delay validation for NG at different equivalence ratios and initial pressures
T (K)
T (K) 1300
1200
1100
1000
900
1200
800
1000
(a) P=13.5bar
1E-4 1E-5
Experimental data Golovitchev n-heptane mechanism Skeletal dual-fuel mechanism
1E-6
Ignition Delay Time (s)
1E-3
0.01 1E-3 1E-4 1E-5
Experimental data Golovitchev n-heptane mechanism Skeletal dual-fuel mechanism
1E-6 1E-7
1E-7 0.8
0.9
1.0
1.1
1.2
0.8
1.3
0.9
1.0
T (K) 1000
950
1.2
1.3
1.4
T (K)
900
850
800
1100
1000
900
800
1 (c) P=19.3bar
(d) P=40.0/41.0bar
0.1
0.1
0.01 1E-3 1E-4 1E-5
Experimental data Golovitchev n-heptane mechanism Skeletal dual-fuel mechanism
1E-6
Ignition Delay Time (s)
Ignition Delay Time (s)
1.1
1000/T (K-1)
1000/T (K-1)
1E-7 0.95
800
0.1
0.01
1050 1
900
(b) P=41.0bar
0.1
Ignition Delay Time (s)
1100
1
1
0.01 1E-3 1E-4 1E-5
Experimental data Golovitchev n-heptane mechanism Skeletal dual-fuel mechanism
1E-6 1E-7
1.00
1.05
1.10
1.15 -1
1000/T (K )
1.20
1.25
1.30
0.9
1.0
1.1
1.2
1.3
1000/T (K-1)
Fig. 7. Ignition delay validation for n-heptane at different equivalence ratios and initial pressures
Air inlet
Natural gas
Combustion analyzer
Flow meter Charge amplifier Diesel fuel
EGR cooler
Fuel meter Decoder
Dynamometer Exhaust gas
Opacimeter Opacimeter
Gasanalyzer analyzer Gas
Fig. 8. The engine test bed used in this investigation
Chemical kinetics solver
Chemical kinetics solver Integration
Integration cell m
cell 1
P,T,ρ,Y
The next time step
state variables obtained in series
Cell 1 The next time step
P,T,ρ,Y … P,T,ρ,Y P,T,ρ,Y
P,T, P,T, … ρ,Y ρ,Y
P,T, P,T, P,T, P,T, … … … ρ,Y ρ,Y ρ,Y ρ,Y
Slave core 1
Slave core 2
…
Slave core n
State variables obtained in parallel
Cell m Collect updated state variables for each cell from slave cores
Collect updated state variables for each cell
Master core
Transport equation solver
Transport equation solver
(a) State variables obtained in series
(b) State variables obtained in parallel
Fig. 9. Comparison of serial and parallel computation to obtain state variables
140
In-cylinder pressure (bar)
120 100
Serial core numbers 8 core numbers 12 core numbers 16
80 60 40 20 0 -60
-40
-20
0
20
40
60
Crank angle (deg ATDC)
Fig. 10. The in-cylinder pressure prediction results by serial and parallel computational methods under same operating conditions
Simulation CPU time (minutes)
1.2x104
1.0x104
8.0x103
6.0x103
4.0x103
2.0x103
0
4
8
12
16
CPU core numbers
Fig. 11. The simulation time with different CPU core numbers
Fig. 12. The sector mesh at TDC for engine simulation
-60
-50
-40
-30
-20
-10
0
10
20
30
40
50
60
-50
-40
-30
-20
-10
0
10
20
30
Experiment Simulation
25% load
40
50
80
50% load
60 160 140
200
100 20 50
10
70
120
60
100
50 80 40 60
30 20
HRR (J/CAD)
150 30
HRR (J/CAD)
40
In-cylinder pressure (bar)
In-cylinder pressure (bar)
-60 90
Experiment Simulation
50
60 250
40
10
20
0
0 -50
-40
-30
-20
-10
0
10
20
30
40
50
30
40
50
60
-60
-50
-40
Crank angle (deg ATDC) -60
-50
-40
-30
-20
-10
0
10
20
-30
-20
-10
0
10
20
30
40
50
Crank angle (deg ATDC) -60
-50
-40
-30
-20
-10
0
10
20
30
40
50
120 100
Experiment Simualtion
75% load
140
80 40
60 40
20
20
HRR (J/CAD)
100 60
In-cylinder pressure (bar)
In-cylinder pressure (bar)
80
100% load
Experiment Simulation
100
120
-50
-40
-30
-20
-10
0
10
20
Crank angle (deg ATDC)
30
40
50
0 60
60 200 180 160 140
80
120 60
100 80
40
60 40
20
20
0 -60
0 60
HRR (J/CAD)
-60
0 60
0 -60
-50
-40
-30
-20
-10
0
10
20
30
40
50
0 60
Crank angle (deg ATDC)
Fig. 13. Comparison of in-cylinder pressure and HRR between engine test data and simulation results under 25%, 50%, 75% and 100% load at 2006 rpm
2.0
1.5
Normalized CO emissions
Normalized NOx emissions
2.0 Experimental NOx emissions Normalized predicted NOx emissions
1.0
0.5
0.0
Experimental CO emissions Normalized predicted CO emissions 1.5
1.0
0.5
0.0 25%
50%
75%
Engine load
100%
25%
50%
75%
100%
Engine load
Fig. 14. Comparison of NOx and CO emissions between engine testing and numerical results
List of Table Captions Table 1. Adjusted pre-exponential factors of sensitivity reactions Table 2. Engine specifications Table 3. Experimental conditions
Table 1. Adjusted pre-exponential factors of sensitivity reactions Arrhenius rate constants
Reactions NG
Diesel
A
Modified A
R1
CH3+CH3(+M) = C2H6(+M)
6.77E+16
9.77E+16
R2
CH3+H2O2 = HO2+CH4
2.45E+04
1.05E+04
R3
CH3+O2 = O+CH3O
3.56E+13
1.06E+13
R4
CH3+O2<=>OH+CH2O
2.31E+12
1.31E+12
R5
NC7H16+OH = C7H15-2+H2O
6.00E+09
9.00E+09
R6
NC7H16+HO2 = C7H15-2+H2O2
3.30E+13
2.30E+14
R7
C7H15O2 = C7H14O2H
6.00E+11
3.20E+12
R8
C7H15-2 = CH3+C6H12
2.51E+13
9.51E+13
R9
C7H14O2HO2=C7KET21+OH
1.49E+13
3.49E+13
Table 2. Engine specifications Item
Specifications
Number of cylinder
6
Engine type
Turbocharged, water-cooled
Bore×stroke (mm)
126×130
Swept volume (L)
9.726
Connecting rod length (mm)
219
Compression ratio
17.0
Rated power (kW)
247@1900rpm
Rated torque (N.m )
1250@1400rpm
Injector nozzle number
7
Nozzle orifice diameter (mm)
0.15
Included spray angle (deg)
152
Table 3. Experimental conditions Type
Case 25% load
50% load
75% load
100% load
Engine speed (rpm)
2006
2006
2006
2006
Pressure at IVC (bar)
12.68
23.12
27.28
29.10
Injected diesel per cylinder (mg)
17.9
14.8
13.4
19.5
Natural gas per cylinder (mg)
26.6
72.3
98.0
109.3
Injection duration (CAD)
8.9
8.9
8.9
10.8
SOI (CAD ATDC)
-17
-17
-15.0
-14.0
Boost pressure (kPa abs)
114
196
230
248
Manifold temperature (°C)
43
44
49
45
0.372
0.497
0.555
0.528
Natural gas equivalence ratio
Highlights
A new skeletal mechanism for diesel/natural gas dual-fuel was constructed. This mechanism can be used for combustion simulation of heavy-duty dual-fuel engines. A parallel computing method greatly saving the computational time was developed. The mechanism was well validated against shock tube and engine experimental results.