تولید مکانیزم اسکلتی برای سوخت های جایگزین با استفاده از گراف رابطه ای هدایت شده با انتشار خطا و تجزیه و تحلیل حساسیت

A novel implementation for the skeletal reduction of large detailed reaction mechanisms using the directed relation graph with error propagation and sensitivity analysis (DRGEPSA) is developed and presented with examples for three hydrocarbon components, n-heptane, iso-octane, and n-decane, relevant to surrogate fuel development. DRGEPSA integrates two previously developed methods, directed relation graph-aided sensitivity analysis (DRGASA) and directed relation graph with error propagation (DRGEP), by first applying DRGEP to efficiently remove many unimportant species prior to sensitivity analysis to further remove unimportant species, producing an optimally small skeletal mechanism for a given error limit. It is illustrated that the combination of the DRGEP and DRGASA methods allows the DRGEPSA approach to overcome the weaknesses of each, specifically that DRGEP cannot identify all unimportant species and that DRGASA shields unimportant species from removal. Skeletal mechanisms for n-heptane and iso-octane generated using the DRGEP, DRGASA, and DRGEPSA methods are presented and compared to illustrate the improvement of DRGEPSA. From a detailed reaction mechanism for n-alkanes covering n-octane to n-hexadecane with 2115 species and 8157 reactions, two skeletal mechanisms for n-decane generated using DRGEPSA, one covering a comprehensive range of temperature, pressure, and equivalence ratio conditions for autoignition and the other limited to high temperatures, are presented and validated. The comprehensive skeletal mechanism consists of 202 species and 846 reactions and the high-temperature skeletal mechanism consists of 51 species and 256 reactions. Both mechanisms are further demonstrated to well reproduce the results of the detailed mechanism in perfectly-stirred reactor and laminar flame simulations over a wide range of conditions. The comprehensive and high-temperature n-decane skeletal mechanisms are included as supplementary material with this article.

Combustion of hydrocarbon fuels currently provides 85% of the energy produced in the United States [1] and [2]. Renewable sources of energy are being pursued to supplement and eventually replace combustion-based sources, but hydrocarbons will remain the major component for the next few decades. In the current era of increasing environmental awareness and rising fuel costs, there is considerable demand to improve efficiency and reduce emissions of the next generation combustion technology. Fuel-flexible designs that can use both conventional and alternative fuels are also desired. Since computational modeling drives the design of engines and combustors for aerospace, transportation, and energy applications, accurate prediction of fuel combustion and pollutant emissions requires comprehensive detailed reaction mechanisms [3]. Liquid transportation fuels contain varying blends of many hydrocarbons. There has been a recent collaborative effort to develop surrogate models to emulate real fuels to accurately predict combustion properties. Such surrogate models typically contain mixtures of a small number of appropriate liquid hydrocarbons. However, detailed reaction mechanisms for surrogates of gasoline [4] and [5], diesel [6] and [5], and jet fuels [7], [8] and [9] typically contain large numbers of species and reactions. For instance, a recently developed detailed mechanism for C8-C16C8-C16n-alkane hydrocarbons contains 2115 species and 8157 reactions [10], while a mechanism for methyl-decanoate, a biodiesel surrogate, contains 2878 species and 8555 reactions [11]. Despite rapid advancements in computing power, it is generally formidable to integrate such detailed reaction mechanisms into large-scale computational simulations in terms of CPU time and memory requirements. Since the computational cost of chemistry scales by the third power of the number of species in the worst case when factorizing the Jacobian [12], such large sizes pose problems even in zero-dimensional modeling. In addition, the wide range of time scales (from nanosecond to second) and the nonlinear coupling between species and reactions induces stiffness when governing equations are solved [12]. Due to these computational demands, reduction of large mechanisms is necessary to facilitate practical simulations using realistic chemistry with modern computational tools. Skeletal reduction is typically the first step of mechanism reduction, where species and reactions deemed negligible to important phenomena over the range of conditions of interest (e.g., pressure, temperature, and equivalence ratio) are removed from the detailed mechanism. Much effort has been dedicated to the development of effective skeletal reduction techniques, as reviewed by Griffiths [13], Tomlin et al. [14], and Okino and Mavrovouniotis [15]. Classical skeletal reduction methods include sensitivity analysis [16], [17] and [18], principal component analysis [19], and detailed reduction [20]. Other important methods include lumping [21], [22] and [23], genetic algorithms [24] and [25], optimization [26], [27] and [28], and adaptive reduction approaches [29], [30], [31], [32] and [33]. While mechanism reduction via time scale analysis is a separate approach outside the scope of this paper, such methods can be employed to perform skeletal reduction as well. Computational singular perturbation (CSP)-based methods [34], [35] and [36] analyze the Jacobian matrix to decompose species relations into fast and slow components. Species are considered important if coupling is strong in either the fast or slow subspace. However, this approach can overestimate the importance of some species and produce skeletal mechanisms of larger size than other methods [37]. Another method similar to CSP is level of importance (LOI) analysis [38], [29], [39] and [40], which combines time scale analysis with sensitivity analysis to rank species importance. The most recent work [40] using LOI presented skeletal mechanisms for ethylene that are competitive with those generated using other methods [41], though the range of conditions considered in the LOI analysis was much narrower. The chemistry-guided reduction (CGR) [42] approach was recently presented and applied to a detailed mechanism for n-heptane [43]. This method combines lumping and necessity analysis applied to a compact starting mechanism. The necessity of species is based on reaction-flow analysis toward and from important species. Though the resulting mechanism sizes are competitive with those from other methods (and the current work), CGR is not explicitly error-controlled and the emphasis on a small starting mechanism could be a possible limitation of the method. Nagy and Turányi [44] developed the simulation error minimization connectivity method, based on the original connectivity method proposed by Turányi [18], which exhaustively analyzes sets of important species through Jacobian analysis and selects an optimal mechanism based on an error limit. The method was shown to provide minimal mechanism sizes for a given error but at a computational expense an order of magnitude above other methods [44]. This could limit the applicability of the approach to the particularly large mechanisms considered in the current work. The directed relation graph (DRG) method, originally proposed by Lu and Law [41], [45] and [37], recently received significant attention. This approach uses a directed graph to map the coupling of species and consequently find unimportant species for removal based on selected target species and an acceptable error threshold. It has been shown to be a particularly efficient and reliable method to reduce large reaction mechanisms [45]. Further development of the DRG method branched into two major directions: (1) DRG-aided sensitivity analysis (DRGASA) [46] and [47], from the original authors of the DRG method which performs sensitivity analysis on species not removed by DRG to further reduce the mechanism and (2) DRG with error propagation (DRGEP) [48], which considers the propagation of error due to species removal down graph pathways. Another method based on DRG, path flux analysis [49], was recently presented that uses both production and consumption fluxes to define the directed graph and identify important species. In the current work an approach that integrates the major aspects of DRGEP and DRGASA, DRG with error propagation and sensitivity analysis (DRGEPSA), is presented. It is illustrated that this combined approach overcomes the weaknesses of the two individual methods. The DRGEPSA method was initially presented by Raju et al. [50] and more recently by Niemeyer et al. [51] and [52]. We also note that a similar method combining DRGEP and DRGASA was also recently presented by Zsély et al. [53] for the ignition of natural gas mixtures, though not explored in detail as in the current work. In the following, the methodology and implementation of DRGEPSA for the skeletal reduction of large detailed reaction mechanisms is first discussed in Section 2. In particular, neat components important to surrogates of gasoline, diesel, and jet fuels are considered. The weaknesses of DRGEP and DRGASA, and the subsequent improvement of DRGEPSA, are demonstrated with a skeletal reduction of the n-heptane detailed mechanism of Curran et al. [54] and [55] in Section 3.1. Additional comparisons are then made in Section 3.2 using a skeletal reduction of the iso-octane detailed mechanism of Curran et al. [55] A skeletal mechanism for n-decane from the detailed mechanism of Westbrook et al. [10] covering a wide range of conditions is presented in Section 3.3. In addition, a high-temperature skeletal mechanism is presented to illustrate the capability of the DRGEPSA method for reduction based on a specific range of conditions. Conclusions based on the various skeletal reductions as well as suggestions for future work are given in Section 4.

In the present work the directed relation graph with error propagation and sensitivity analysis (DRGEPSA) method for skeletal mechanism reduction was presented and discussed. This approach, a combination of the DRGEP and DRGASA methods, utilizes the specific strengths of each individual method to diminish some of the weaknesses of each. DRGEP efficiently identifies and removes unimportant species while DRGASA incorporates sensitivity analysis to identify further unimportant species for removal at a greater computational expense. By combining the two methods, DRGEPSA is able to identify and remove more unimportant species than its precursors. In addition, the current implementation uses a limited number of user inputs to automatically generate optimally small skeletal mechanisms. An iterative error threshold selection procedure produces an optimal DRGEP skeletal mechanism for the given error limit before the sensitivity analysis (SA) phase further eliminates unimportant species. Though the DRGEP phase eliminates a larger number of species in general than DRG, the SA phase must run autoignition simulations for each of the limbo species. A large list of limbo species combined with a wide range of autoignition conditions under consideration could induce significant computational cost. Skeletal mechanisms of n-heptane were generated to illustrate the improvement of DRGEPSA over DRGEP and DRGASA, resulting in a final mechanism with 108 species compared to 173 and 153 species, respectively. Skeletal mechanisms of iso-octane were also presented to further illustrate the improvement of DRGEPSA over DRGEP and DRGASA, with final skeletal mechanisms of 165, 232, and 211 species, respectively. All skeletal mechanisms exhibited good ignition delay prediction compared to the detailed mechanisms, with the most noticeable discrepancies in the NTC regions. Two skeletal mechanisms for n-decane were generated using DRGEPSA from a large detailed mechanism for n-alkanes, covering n-octane through n-hexadecane. One skeletal mechanism covers a comprehensive set of temperature conditions at low to high pressures while the other mechanism is limited to high-temperature conditions, and both mechanisms covered lean to rich equivalence ratios. The resulting comprehensive skeletal mechanism consists of 202 species and 846 reactions while the high-temperature mechanism is much smaller with 51 species and 256 reactions. The large extent of reduction for both mechanisms illustrates the capability of the DRGEPSA method to reduce large mechanisms of surrogate fuels. Both the comprehensive and high-temperature skeletal mechanisms are included as supplementary material to this article. External validation of the n-decane skeletal mechanisms was performed using perfectly-stirred reactor (PSR) and laminar flame simulations. The comprehensive skeletal mechanism reproduced the results of the detailed mechanism in PSR with larger errors at higher pressure and rich conditions. The high-temperature skeletal mechanism also performed well, with larger errors at the lean, atmospheric pressure and rich, 40 atm pressure conditions. The comprehensive skeletal mechanism also performed quite well in predicting laminar flame speed with noticeable error at rich, higher pressure conditions. By comparison, the high-temperature skeletal mechanism fared slightly less better. Though only ignition chemical kinetics data were used in the mechanism reduction procedure, both mechanisms performed well predicting the extinction turning point in PSR and even for predicting laminar flame speed where transport phenomena are considered. It is further noted that if a posteriori validation is not satisfactory, the range of OIC values used to identify limbo species could be adjusted. One possible pitfall is the removal of certain important species with small induced error in ignition delay but greater importance in other combustion phenomena. Alternatively, PSR and/or PREMIX simulations could be included in the chemical kinetics data sampling and for error evaluation. While a significant reduction is achieved with the comprehensive skeletal mechanism (approximately 10–20% of the detailed mechanism) using DRGEPSA, the final mechanism is still too large to be used in full-scale three-dimensional simulations. Nagy and Turányi [44] suggested that removal of additional unimportant reactions could significantly improve the computational cost of simulations. An integrated reduction approach involving unimportant reaction removal, isomer lumping, time-scale reduction (e.g., quasi-steady-state assumption), diffusive species bundling, and other reduction methods, similar to the approach presented by Lu and Law [47] and [12], is required before realistic computational simulations are feasible with such skeletal mechanisms; this will be the subject of future work. However, the small size of the high-temperature skeletal mechanism illustrates the significant reduction capability when the input conditions are limited to the desired range. For instance, flame simulations rely largely on high-temperature chemistry such that a skeletal mechanism desired for this purpose could omit the complex low-temperature and NTC regime chemistry with acceptable error. The current high-temperature skeletal mechanism for n-decane with 51 species and 256 reactions could be used without further reduction in large-scale simulations.