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Numerical Investigation of Homogeneous Charge Compression Ignition (HCCI) Combustion with Detailed Chemical Kinetics Using On-the-Fly Reduction Kaiyuan He, Ioannis P. Androulakis, and Marianthi G. Ierapetritou* Department of Chemical and Biochemical Engineering, Rutgers, The State University of New Jersey, Piscataway, New Jersey 08854, United States ABSTRACT: An on-the-fly mechanism reduction approach is employed in this paper to integrate detailed chemical kinetics with a computational fluid dynamics (CFD) code. The reduction methodology employs an instantaneous element flux analysis to identify redundant species and reactions for given local conditions. The emphasis of this work is focused on the numerical study of homogeneous charge compression ignition (HCCI) engine combustion in CFD code KIVA-3V using a detailed n-heptane oxidation mechanism with 653 species and 2827 elementary reactions. The proposed on-the-fly reduction method predicts species concentrations, temperatures, and pressures with high fidelity compared to solutions obtained using the detailed mechanism. In the mean time, central processing unit (CPU) time on chemistry calculation is tremendously reduced, enabling integration of complex kinetic mechanisms in engine CFD. When detailed chemistry is combined with realistic flow simulation, accurate predictions of in-cylinder combustion behavior of HCCI engines are provided.
1. INTRODUCTION Homogeneous charge compression ignition (HCCI) has received increasing attention from the engine community as a promising alternative operation mode to conventional diesel and spark-ignition (SI) engines. Its potential to achieve diesel-like combustion efficiency and reduce NOx and soot emissions has been reported.13 However, the main obstacle in the application of HCCI is the lack of reliable ignition timing controlling strategies.3 The control issue stems from multiple ignition sites in the chamber and cycle-to-cycle variations.1,3,4 Various controlling strategies, including direct injection (DI),5 variable valve actuation (VVA),6 and exhaust gas recirculation79 have been investigated to achieve accurate ignition timing control. These strategies all introduce additional thermal and composition stratifications to the in-cylinder mixture. To achieve accurate numerical analysis of the stratified HCCI combustion, detailed kinetic mechanisms need to be incorporated in the reactive flow calculation. In recent studies, detailed chemical kinetic mechanisms have been developed to predict combustion behaviors, including ignition delay, combustion modes, and pollutant formation.1014 These detailed kinetic mechanisms provide a comprehensive description of fuel chemistry. However, they usually consist of hundreds of species and thousands of reactions. Therefore, integrating these detailed mechanisms in engine computational fluid dynamics (CFD) computations are expensive and oftentimes prohibitive. Numerous efforts have been devoted to tackling the complexity of this integration. These efforts can be divided into two major categories: detailed chemical kinetics with simplified flow models and complex CFD computations with simplified reaction schemes. Simplification of flow models is usually achieved using the so-called “zone” approach. The earliest example of this type of approximation was the single-zone model, which considered the entire engine cylinder to be a single cell.15 This model was proposed for HCCI engines, in which homogeneous charge was r 2011 American Chemical Society
used. However, although termed “homogeneous”, there are always some inhomogeneities in HCCI engines because of multiple sources.3 Thus, in later work, multi-zone models were developed to divide the combustion chamber into multiple zones based on temperature and compositions.16,17 Each zone represents a group of computational cells that have similar reactive conditions. The average temperature, pressure, and compositions of its member cells are used to specify the thermodynamic state of each zone. The zone approaches provide a good strategy to integrate detailed chemical kinetics in CFD. However, in-cylinder combustion behaviors cannot be accurately captured because of the fact that computational cells are grouped into zones, which results in a less fine resolution in the reacting flow simulation. This detailed characterization of in-cylinder behaviors is of particular importance to the understanding of multi-point ignition in HCCI engines induced because of spatial inhomogeneities in composition, temperature, and pressure. To solve the chemistry for each computational cell in CFD calculation, it is necessary to reduce the detailed kinetic mechanism. The goal is to alleviate the computational intensity while retaining an acceptable level of accuracy in the predictions of incylinder combustion behavior and parameters. Substantial efforts have been devoted to the reduction of detailed kinetic mechanisms. Approximation of chemistry computations encompasses a multitude of approaches, including mechanism reduction approaches, tabulation techniques, and quasi-steady-state approximation methods. Mechanism reduction approaches target the identification of redundancy in kinetic mechanisms, i.e., identifying redundant species and reactions for given system states. Mechanism reduction can be performed globally or dynamically. Global reduction approaches include globally lumping Received: February 24, 2011 Revised: July 7, 2011 Published: July 07, 2011 3369
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Energy & Fuels techniques,18 sensitivity analysis,1921 optimization-based approaches,22,23 and element flux analysis approaches.24 These global reduction approaches give rise to a skeletal kinetic mechanism, which is used for the entire simulation. However, when the system encounters wide-ranging reactive conditions, one skeletal mechanism is not able to cover the entire condition space. To develop locally accurate mechanisms, adaptive reduction and on-the-fly reduction approaches have been proposed. Active species are identified using various techniques, such as mathematical programming approaches,25 graph-based approaches,2530 and flux-based approaches.31 Another category of approximation methods is so-called tabulation approaches, which employ the idea of constructing a local approximation table and solving for system variables based on table look-up instead of integrating chemical source terms. This category includes in situ adaptive tabulation (ISAT),32 and store-andretrieve representations.33 The third category of chemistry approximation approaches replaces differential equations with algebraic equations to reduce stiffness of the kinetic ordinary differential equation (ODE) system. A commonly used technique in this category is the quasi-steady-state approximation (QSSA) approach.34,35 In the QSSA approach, fast evolving species are assumed to have zero source terms and their concentrations are described by algebraic equations. In doing so, both the dimension and the stiffness of the kinetic ODE system are reduced. Mechanism reduction approaches introduced above predict the reaction system with high fidelity compared to the detailed mechanism. However, these approaches either lack the capability to derive different reduced mechanisms for different conditions or are too expensive to be implemented on-the-fly in a realistic flow simulation. To arrive at a mechanism reduction approach that meets the requirements of both dynamic chemistry reduction and efficient on-the-fly implementation, we proposed a mechanism reduction approach based on element flux analysis in our previous work.31 The approach is based on the assumption that large element transition flux involves important species. Thus, active species are determined by sorting the flux between all sourcesink pairs in descending order and applying a cutoff. The proposed reduction method has been validated against corresponding detailed mechanisms in terms of ignition delay, species concentrations, NOx formation, and soot formation in both a plug-flow reactor model and simplified two-dimensional (2D) CFD.31,36 The on-the-fly scheme has been tested in simplified CFD models using several different fuel combustion mechanisms.37 Liang et al.29 and Shi et al.30 have implemented a dynamic adaptive chemistry (DAC) method to incorporate detailed mechanisms with over 500 species in CFD simulations. The main focus of this paper is to implement the flux-based onthe-fly reduction approach in CFD code to efficiently generate a locally accurate reduced mechanism for every computational cell and time step. When detailed chemistry is fully integrated with a realistic flow simulation, an accurate prediction of in-cylinder combustion behavior as well as combustion parameters, such as pressures, temperatures, and species compositions, can be obtained for HCCI engines. The fuel is n-heptane, and a detailed mechanism including 653 species and 2827 reactions3840 is used in the study. KIVA-3V41 is used as the CFD framework, and CHEMKIN42 is employed to formulate chemistry and transport. The DI mode of the HCCI engine using room-temperature, atmospheric-pressure spray is investigated. The initial conditions of the numerical model
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simulate the in-cylinder situation observed in laser-induced exciplex-fluorescence (LIEF) experiments.43
2. COMPUTATIONAL MODEL 2.1. On-the-Fly Mechanism Reduction Approach. The reduction scheme consists of element flux analysis and identification of active species and reactions based on flux magnitudes. In our previous work, we demonstrated how the concept of element flux analysis provides a pointer to quantify the activity of species and perform mechanism reduction.24,31 The instantaneous elemental flux of atom · A from species j to species k through reaction i, denoted as Αijk, is defined in eq 1. The total instantaneous flux between species j and k can · be calculated by summing Αijk over all of the reactions in which species j and k are involved, as represented in eq 2 Α_ijk ðtÞ ¼ qi ðtÞ
Αjk ðtÞ ¼
nA, j nA, k NA, i
ð1Þ
NR
∑ Α_ijk ðtÞ i¼1
ð2Þ
where qi(t) is the instantaneous rate of reaction i (mol/s), nA,j is the number of atoms A in species j, nA,k is the number of atoms A in species k, NA,i is the total number of atoms A in reaction i, and NR represents the number of reactions that these species participate as reactants or products. However, we demonstrated in our previous work31 that eqs 1 and 2 do not properly represent element flux for quasi-steadystate species induced by partial equilibrium reactions. This is due to the small net reaction rates of partial equilibrium reactions compared to their respective forward and reverse reaction rates. Therefore, the flux · pointer Αijk calculated through eq 1 is small, although very fast element transition is taking place between species j and k through reaction i. To avoid underestimation of element flux for these quasi-steady-state species, both the forward and reverse reaction rates are taken into account in the current work. Equation 1 has been modified as eq 3 Α_ijk ðtÞ ¼ ðjqifwd ðtÞj þ jqirev ðtÞjÞ
nA, j nA, k NA, i
ð3Þ
where qifwd and qirev are the reactions rates of forward and reverse reactions, respectively. The flux pointers computed using eq 3 weigh the connection between two species by means of element transition rates. When integrated in CFD calculations, flux analysis is performed for each computational cell at each time step, providing a metric to evaluate the local activity of all of the sourcesink pairs in the system. A userselected cutoff value is then applied on the list of sourcesink pairs, which are sorted in descending order according to their flux values. Species above the cutoff are considered to be significant and thus included in the reduced mechanism, while species below the cutoff are considered to be trivial for current local conditions. Therefore, only the ODEs of active species are needed to be solved for local chemistry, which substantially reduces central processing unit (CPU) time on chemistry computation. However, all of the species are transported, and all species concentrations are stored in the CFD calculation, so that when a different set of active species are identified at other time steps or computational cells, the required species concentrations can be readily retrieved to perform kinetic calculations for local chemistry. In our reduction procedure, given the active species set, only the reactions with all active species are kept in the reduced mechanism, while reactions with any of their participating species not included in the active species set are eliminated. The active species and reactions are then passed to CHEMKIN, where they are interpreted into a reduced mechanism for chemistry calculation. When the CFD code advances to the next computational 3370
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Figure 2. Two-dimensional numerical mesh of KIVA-3V simulations. Temperatures and species compositions in the cylinder area enclosed by the dash-line box are monitored in this work. The x axis and z axis represent the cell index in the radial and axial directions of the cylinder, respectively.
Figure 1. Procedures for integrating the on-the-fly reduction scheme in KIVA/CHEMKIN code. step, the flux analysis and mechanism reduction are repeated on the basis of new conditions. The on-the-fly reduction scheme largely reduces the complexity of the chemical kinetics; however, it was found in our precious study36 that mechanism interpretation and generation in CHEMKIN accounts for nearly 10% of the total CPU time. When larger mechanisms are used, this portion can increase up to 40% of the total CPU time, which constitutes a significant overhead. In this work, a chemical source term evaluation subroutine is introduced in the on-the-fly reduction scheme, targeting the overhead introduced by mechanism interpretation and generation. In the subroutine, rates of active reactions are retrieved from the full reaction rate array to evaluate the source terms of active species. The subroutine replaces its CHEMKIN counterpart, which requires interpretation and initialization of the mechanism. Therefore, when this subroutine is called, source terms of active species can be evaluated without mechanism interpretation in CHEMKIN. The source terms of active species are integrated to calculate the composition change and the heat release, which are passed to the CFD code where fluid mechanical processes, including convection and diffusion steps, are computed. In the meantime, concentrations of dormant species are kept unchanged and passed to the next computational step. The application of the on-the-fly reduction method in KIVA3V is schematized in Figure 1. A detailed description of the integration of flux analysis and CFD is available in ref 37, while in this paper, we will focus on the efficient integration of a highly complex kinetic mechanism in realistic CFD calculations. 2.2. CFD Model and Numerical Cases. Engine CFD code KIVA-3V is employed is this study to simulate HCCI engine combustion. The fuel is n-heptane, and a detailed n-heptane oxidation mechanism including 653 species and 2827 reactions3840 is used to describe the chemistry. Element flux analysis is performed for the mechanism at each time step for every computational cell. All of the sourcesink species pairs are sorted according to carbon flux in descending order. A userselected cutoff value is applied on the list of sourcesink pairs, which preserves a high portion, e.g., 99% of the total flux transition in the cell at that particular time step. Species above the cutoff are considered to be significant and thus included in the reduced mechanism, while species below the cutoff are frozen; i.e., their production/destruction rates are
Figure 3. Initial n-heptane concentration (g/cm3) distribution in the engine chamber (corresponding to the area enclosed by the dash-line box in Figure 2). set to be zero, for the current time step and computational cell. Thus, the cutoff is one critical parameter to determine before mechanism reduction is performed. In our previous study, a few trial runs using different cutoffs (90, 99, and 99.9%) have been performed for n-pentane and nheptane oxidation.24,31 The results suggested that higher cutoff retains more fidelity of the detailed mechanism while trading off simulation time. A 99% cutoff was determined to be an appropriate cutoff, which both retains good accuracy and keeps the reduced mechanism size tractable. Thus, 99% is used to determine active species in the current study. The numerical mesh used for the analysis is a 2D grid with 1052 cells at bottom dead center (Figure 2). Because of axial symmetry, only half of the engine chamber is simulated in the grid, with the z axis being the axial direction and the x axis being the radial direction. In a practical HCCI engine, inhomogeneities exist in both bulk gas and boundary layers because of various sources, including heat transfer, fuel spray vaporization, and turbulent transport during compression.44 The validation case that we examined is to simulate the DI mode using roomtemperature, atmospheric-pressure spray in HCCI engines. The initial condition of the numerical model is prescribed by the in-cylinder fuel concentration distribution obtained in LIEF experiments.43 When the fuel is injected into the chamber at room temperature, fuel vaporization is slow and, thus, a large portion of the fuel hits the piston in the liquid state. This portion of fuel vaporizes as the piston brings it up to the cylinder head during compression. Meanwhile, there are fuel droplets remaining on the injector, resulting in a moderately higher fuel concentration 3371
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Figure 4. Temperature and HRR profiles of the stratified case (solid lines) and the homogeneous case (dashed lines). near the injector. A numerical case simulating the fuel concentration inhomogeneity induced by fuel spray in this scheme is investigated in this study. The initial fuel concentration distribution in the cylinder is shown in Figure 3. The simulation starts from crank angle (CA) 80.0° after top dead center (ATDC). The fuel concentration is stratified with a global equivalence ratio of 0.32, and the temperature is uniformly 498 K in the chamber at 80.0° ATDC. The equivalence ratio ranges from 1.6 to 0.1, covering the span of fuel concentrations encountered in HCCI engines operated in DI mode. This case is designed to study the in-cylinder combustion behavior under inhomogeneous fuel concentrations. The stratified HCCI combustion also provides an ideal test case to validate the adaptability of the proposed on-the-fly reduction method in addressing different reactive conditions. The inhomogeneous case is compared to a homogeneous case, with the same initial charge as the global average of the inhomogeneous case, an equivalence ratio of 0.32, and temperature of 498 K, at 80.0° ATDC. The simulation is performed on a Unix platform with Intel Xeon 3.0 GHz CPU.
3. RESULTS AND DISCUSSION 3.1. Effects of Charge Stratification on the Average Temperature and Pressure. When homogeneous charge is used in
HCCI engines, ignition occurs uniformly across the engine chamber, which results in a high pressure-rise rate (PRR) and short combustion duration. Too high of a PRR might cause engine knock; thus, sometimes it is necessary to introduce inhomogeneities to lower PRR and extend combustion duration.1,3,7,8 The average in-cylinder temperature, heat release rate (HRR), and pressure of the two cases are shown in Figures 4 and 5. Both stratified and homogeneous cases exhibit pronounced cool flame behavior (from 45° to 43° ATDC). A significant amount of heat is released in the cool flame stage, and the temperature was increased by 50100 K. The main ignition occurs earlier in the stratified case because of the fact that the fuel-rich region releases more heat than the homogeneous chamber in the pre-ignition stage (CA from 35° to 33°). The stratified charge also extends the duration of heat release by nearly 2 CAs. This is due to non-instantaneous ignition in the stratified case, which will be illustrated in the following sections. As indicated by arrows in Figure 4, a significant amount of heat is released after the main ignition in the stratified case, which results in a longer heat release duration and lower peak HRR in the stratified case.
Figure 5. Pressure profile of the stratified case (solid lines) and the homogeneous case (dashed lines).
3.2. Effects of Charge Stratification on In-Cylinder Combustion Behaviors. To analyze the underlying mechanism of the
effects of stratification on HCCI combustion, it is necessary to capture in-cylinder temperature and species composition distributions at different CAs. When the detailed chemistry for each computational cell is solved, the on-the-fly reduction model tracks compositions of all species and thus enables a detailed characterization of the in-cylinder combustion behavior. Incylinder temperature, fuel concentration, and oxygen concentration distributions at different CAs are shown in Figures 6 and 7. In the stratified case, the fuel vaporization results in a stratification of the equivalence ratio in the chamber, with a high fuel concentration near the cylinder center and a low fuel concentration near the wall. At the early stage of the compression, endothermic n-heptane decomposition represents the main chemical activity, which results in a lower temperature in fuelrich regions. When the cylinder is further compressed, incylinder temperature elevates and fuel-rich regions exhibit lowtemperature flame behavior. The heat released from the lowtemperature oxidation reactions elevates the temperature of fuelrich regions to a higher level than fuel-lean regions. The chamber finally ignites in the region between fuel-rich and fuel-lean regions. In the homogeneous case, as shown in Figure 7, multiple ignition sites are developed simultaneously around CA 32.7° ATDC. These ignition sites cover a large portion of the chamber, generating a near-instantaneous thermal explosion. This thermal explosion results in a high PRR and HRR, which might cause engine knock.3,4 On the contrary, the subsonic flame propagation in the inhomogeneous case extends the burn duration and gives rise to a less steep pressure rise. 3.3. Detailed Chemical Kinetics at Different Regions of the HCCI Engine. To understand the underlying chemical kinetics of the ignition, detailed reaction activity and species evolution have to be monitored at each stage of the combustion. The flux analysis proposed in this work provides a framework to quantitatively evaluate species activities at each time step. Representative species were selected from different pathways of n-heptane oxidation to monitor the activity of each pathway. The different oxidation pathways of n-heptane were investigated in refs 10 and 38 and summarized in Figure 8. At low temperature, two oxygen 3372
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Figure 6. In-cylinder temperature and n-heptane concentration distributions at different CAs of the stratified case. The x axis and z axis represent the cell index in the radial and axial directions of the cylinder, respectively. The arrow indicates the only ignition region in the stratified case.
Figure 7. In-cylinder temperature and n-heptane concentration distributions at different CAs of the homogeneous case. The x axis and z axis represent the cell index in the radial and axial directions of the cylinder, respectively. The arrow indicates one of the three ignition regions in the homogeneous case.
molecules are added to the primary n-heptane radicals, forming keto-hydroperoxide radicals. When the temperature increases, the hydroperoxide radicals decompose to olefin and cyclic ether, instead of reacting with another oxygen molecule. At high temperature, β-scission of the primary n-heptane radicals becomes dominant. Three representative species, as highlighted in Figure 8, were selected from low-temperature, medium-temperature, and high-temperature pathways, respectively, to monitor the activity of each pathway. The high-temperature species is the direct product of β-scission of the primary n-heptane radical. The medium-temperature species corresponds to cyclic ether from hydroperoxide radical decomposition. The low-temperature species is the product of second oxygen addition to the hydroperoxide radical. The activities of the selected species are monitored using the summation of their instantaneous influx and outflux at each time step. The instantaneous influx and outflux of each species provide a measure of species activity and depict species evolution. The carbon flux flowing in and out of the chosen species at the ignition region of each case is traced. The total flux transitions through the selected three species are compared and plotted with the temperature and n-heptane concentration in Figures 9 and 10. In the autoignition region of the stratified case, the n-heptane concentration is slightly lower than the homogeneous case. The high-temperature pathway is the most active pathway in the combustion. The low- and medium-temperature pathways have similar flux magnitudes, both being approximately 25% of the high-temperature pathway. It should also be noticed that most of the transitions through
these three species take place in the cool flame stage, while the oxidation of smaller hydrocarbons dominates the main ignition. In the homogeneous case, a different evolution was observed. The high-temperature pathway dominates the entire combustion process, with low- and medium-temperature pathways less than 5% of its activity. Significant flux values are observed in the main ignition stage, which results in a steeper temperature rise in the homogeneous case. This observation agrees with the in-cylinder combustion pattern shown in Figures 6 and 7. The simultaneous combustion in the homogeneous case results in a higher temperature-rise rate compared to the inhomogeneous charge in the stratified case. The detailed characterization of in-cylinder behavior and element transitions presented above provides an analysis of HCCI combustion, which involves multiple ignition points and distinct chemical kinetics. When the detailed chemistry is solved using the proposed on-the-fly reduction method, species evolutions can be predicted in addition to average in-cylinder parameters, while CPU time is tremendously reduced. The number of species used at each time step of the stratified case is presented in Figure 11. It can be seen that, in the early compression stage, mechanism size increases as the in-cylinder temperature is elevated. Large mechanisms are required during the period between cool flame ignition and main ignition, where substantial chemical transitions are taking place to build up a radical pool for combustion. At the main ignition, the mechanism size dropped noticeably because of the fact that a radical pool has already been built up in the preignition stage and large species have been 3373
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Figure 10. Flux analysis of selected species for the autoignition region (highlighted in Figure 7) in the homogeneous case.
Figure 8. n-Heptane oxidation pathways at different temperature regimes.
Figure 11. Number of species in the reduction mechanism for each time step of the stratified case.
Figure 9. Flux analysis of selected species for the autoignition region in the stratified case.
decomposed to smaller species, hence substantially reducing the mechanism size. After the main ignition, the mechanisms reduce to a very small size, with only a few species involved. The average species number of all of the reduced mechanisms used for the stratified combustion simulation is 93.8, as compared to 653 species in the detailed mechanism. Because the species number used for each time step is dramatically lowered in the on-the-fly scheme, a good fidelity to the detailed mechanism is maintained in the reduced mechanisms. Figure 12 compares the pressure profiles predicted by the detailed mechanism and the on-the-fly reduction scheme for the stratified case. It can be seen that the
on-the-fly reproduces the detailed results with good fidelity. Both the low-temperature ignition stage (near CA 44.5°) and the main ignition stage (after CA 33.5°) are accurately predicted by the on-the-fly reduction scheme. In comparison to the pressure profile predicted by the detailed mechanism, the onthe-fly scheme returns an average error of 3.7% and a maximum error of 9.4% for the homogeneous case and 3.1 and 8.7%, respectively, for the stratified case. Similar accuracy is observed for temperatures and key species concentrations as well. CPU time of the simulation using the detailed mechanism, the on-the-fly scheme using mechanism interpretation in CHEMKIN, and the on-the-fly scheme using the newly introduced species source term evaluation subroutine is compared in Figure 13. Mechanism interpretation accounts for a large portion of total CPU time (42%), constituting a significant overhead. The simulation using the detailed n-heptane mechanism takes more than 2 months in the current KIVA-3V simulation, while the on-the-fly reduction scheme is finished within 5 days. The CPU time used to solve the chemistry is reduced by a factor of 20, while the overall CPU time is reduced by a factor of 18. The overhead induced by flux analysis and species source term 3374
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Figure 12. Pressure profiles predicted by the detailed mechanism (solid line) and the on-the-fly scheme (dashed line) for the stratified case.
Figure 13. CPU time for simulation using the detailed mechanism, onthe-fly reduction, and on-the-fly reduction using the new species source term evaluation subroutine.
evaluation accounts for only 2.5% of the total CPU time using the new subroutine.
’ CONCLUSION An on-the-fly reduction scheme is implemented to integrate detailed chemistry and CFD simulations. A detailed nheptane mechanism including 653 species and 2827 reactions is used in the simulation of HCCI engine combustion. Using the proposed on-the-fly reduction method, detailed chemistry is solved for each computational cell and each time step of the CFD simulation. A stratified HCCI combustion case was investigated numerically and compared to a homogeneous HCCI case. In-cylinder combustion behaviors as well as combustion parameters, such as pressures, temperatures, and species compositions, in HCCI combustion are captured. Multiple ignition sites are predicted in the homogeneous case, while only one ignition site is observed in the stratified case. Flux analysis is employed to investigate the underlying chemical
reaction scheme of different regions. It was found that hightemperature oxidation pathways of n-heptane are the most active in both stratified and homogeneous HCCI combustion. However, the high-temperature pathways are less dominant in the stratified combustion, with one-third flux transitions going through low- and medium-temperature pathways. When the detailed chemistry for each computational cell and time step is solved, the on-the-fly reduction model provides a detailed characterization of in-cylinder combustion behaviors of HCCI engines, which is essential to predict multiple ignition sites and distinct chemical kinetics at different regions during the combustion process. The cutoff used to determine active species enables the user to choose their own level of trade-off between accuracy and efficiency. The on-the-fly framework provides an efficient yet accurate mechanism reduction approach to take advantage of detailed chemistry in the investigation of complex reactive flows. The flux analysis employed to identify redundancy in this framework keeps the overhead of mechanism reduction at a minimum. Thus, this flux-based reduction framework is suitable for on-the-fly reduction in highly complex reactive flow models.
’ AUTHOR INFORMATION Corresponding Author
*Telephone: (732) 445-2971. Fax: (732) 445-2581. E-mail: marianth@ soemail.rutgers.edu.
’ ACKNOWLEDGMENT The authors gratefully acknowledge financial support from ExxonMobil R&E Co., National Science Foundation (NSF) Chemical, Bioengineering, Environmental, and Transport Systems (CBET) Grant 0730582, and Office of Naval Research (ONR) Contract N00014-10-10440. 3375
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