International Multidimensional Engine Modeling User s Group Meeting 24, Detroit, MI A PDF Method for Multidimensional Modeling of HCCI Engine Combustion: Effects of Turbulence/Chemistry Interactions on Ignition Timing and Emissions Y.Z. Zhang, E.H. Kung, and D.C. Haworth Department of Mechanical & Nuclear Engineering The Pennsylvania State University University Park, PA, USA Abstract In the limit of homogeneous reactants and adiabatic combustion, ignition timing and pollutant emissions in homogeneous-charge compression-ignition (HCCI) engines would be governed solely by chemical kinetics. As one moves away from this idealization, turbulence and turbulence/chemistry interactions (TCI) play increasingly important roles. Here the influence of TCI on autoignition and emissions of CO and unburned hydrocarbon (UHC) is examined using a three-dimensional time-dependent computational fluid dynamics (CFD) model that includes detailed chemical kinetics. TCI is accounted for using a hybrid probability density function (PDF) method. Variations in global equivalence ratio, wall temperature, swirl level, degree of mixture inhomogeneity (premixed versus direct injection, and startof-injection timing for direct-injection cases), and a top-ring-land crevice (TRLC) are investigated. In addition to providing new insight into HCCI combustion processes, this work also demonstrates the feasibility of bringing transported PDF methods to bear in modeling a geometrically complex threedimensional time-dependent turbulent combustion system. 1. Introduction Homogeneous-charge compression-ignition (HCCI) engines offer the potential for diesellike efficiency with low NOx and particulate emissions [1]. Outstanding issues include control of ignition timing, CO and hydrocarbon emissions, and transition to more conventional combustion modes at full load. An unresolved fundamental issue is the relative importance of hydrodynamics (turbulence) compared to chemical kinetics on the combustion process. Chemical kinetics clearly dominates under truly homogeneous conditions. But turbulence is expected to play an increasingly important role as conditions depart from this ideal. Both experimental [2] and computational [3] studies have shown that turbulence can influence ignition timing and emissions for practical HCCI engines. In a real engine, the temperature field is necessarily inhomogeneous as a result of wall heat transfer; the geometry of the combustion chamber, including crevice volumes, exacerbates this effect. Mixture composition may be inhomogeneous initially due to incomplete mixing among fuel, air, EGR, and residual products; and further composition inhomogeneity may develop as combustion proceeds as a result of the inhomogeneous temperature field. Several modeling approaches have been developed to explore the influences of inhomogeneities in temperature and composition and the role of turbulence in HCCI engines. These include multiple-zone models [4,5], stochastic models [6], and multidimensional models (computational fluid dynamics CFD) [3,7,8]. Complex-chemistry CFD studies that have explored hydrodynamic 1
effects include Refs. [3] and [8]; there a characteristic-timescale turbulent combustion model was used to account for turbulence/chemistry interactions. The aim of this research has been to elucidate further the role of turbulence/chemistry interactions (TCI) on HCCI autoignition and emissions. Toward that end, a state-of-the-art TCI model (a transported probability density function PDF method [9]) has been implemented in an unstructured-mesh finitevolume CFD solver, including detailed chemistry. The focus is on establishing trends and sensitivities rather than on quantitative comparison with experimental measurements. 2. Engine Configuration The engine is a two-valve pancake-chamber Cooperative Fuels Research (CFR) engine that has been modified for HCCI operation, including the addition of a fuel injector for direct in-cylinder injection [1]. Engine parameters and operating conditions are summarized in Table 1. 3. Physical and Numerical Models 3.1 CFD Codes Table 1 Engine configuration Configuration two-valve, pancakechamber CFR Bore/Stroke/Connecting 82.55/114.3/254. rod mm Compression ratio 15:1 Intake-valve 11 /214 ATDC opening/closing Exhaust-valve 51 /15 ATDC opening/closing Engine speed 1,8 r/min Fuel n-heptane Injector location, center of head, axial direction toward piston Injection duration (fuel 3.5, 345 K DI), fuel temperature Top-ring-land crevice 1 mm (radial) x 16.8 (where considered) mm (axial) Two three-dimensional time-dependent finitevolume CFD codes have been used: KIVA [11] and GMTEC [12]. A computational mesh and validated KIVA model, including fuel injector characterization and a state-of-the-art spray model (the LISA model [13]), is available for the CFR engine, while the PDF method has been implemented in GMTEC. For each case considered (Table 2), one full 72 engine cycle has been computed using KIVA. A second cycle then is run until 6 before TDC compression; at that point, both valves are fully closed. The KIVA-computed incylinder fields then are interpolated onto a GMTEC mesh. The PDF calculation is initialized, and the PDF model is run through the remainder of the compression stroke and combustion event until mass fractions of key species of interest are no longer changing: 4 after TDC generally suffices. 3.2 Chemical Kinetics A 4-species 165-reaction n-heptane mechanism has been employed [14]. Kinetic parameters and thermodynamic properties are implemented using the CHEMKIN libraries [15]. In both CFD codes, in situ adaptive tabulation (ISAT) [7,16] has been implemented to accelerate the computation of chemical source terms. 3.3 Turbulence and Turbulence/Chemistry Interactions The probability density function considered is the joint PDF of 4 species mass fractions and mixture enthalpy. The modeled PDF transport equation is solved using a hybrid particle/finite-volume method. The algorithms are described in detail in Refs. [12] and [17], and have been implemented in the GMTEC CFD code. Equations for mean velocity, mean pressure, mean absolute enthalpy, and turbulence quantities (here a two-equation k-ε model [18] with standard wall functions has been used) are solved using the finite-volume solver and are passed to the particle side of the calculation. On the particle side, a Lagrangian Monte Carlo method is used to solve for 2
species mass fractions and for enthalpy fluctuations. In all cases, standard values have been used for model coefficients [9,12,17]; there has been no tuning. Here the influence of TCI is investigated by comparing results obtained using the PDF method to those obtained using the same chemical mechanism implemented in the same finite-volume solver using cell-centered mean temperature and compositions directly in the elementary reaction mechanism (no TCI). Henceforth, cases computed with TCI will be denoted by PDF and those without TCI by FV. 3.4 Computational Considerations Calculations of chemical source terms dominate the computational effort. Two approaches have been used to accelerate the chemical kinetics: ISAT, and parallel computing. 4. Results and Discussion The influences on ignition timing, CO emissions, and unburned hydrocarbon (UHC) emissions of variations in global equivalence ratio, wall temperature, swirl level, degree of mixture inhomogeneity (premixed versus direct injection DI; start-of-injection SOI timing, for DI cases), and a TRLC are investigated. A summary of cases and global results is provided in Table 2. 4.1 Effect of Equivalence Ratio Variations in global equivalence ratio Φ are explored in cases PHI_2 (Φ =.2), PHI_25 (Φ =.25), and PHI_3 (Φ =.3). In all cases, the initial mixture composition is nearly homogeneous. The expected trends can be observed in Table 2 with increasing fuel-lean equivalence ratios: an advance in ignition timing, and decreases in CO and nonfuel UHC emissions. Computed global in-cylinder temperatures are plotted in Fig. 1 with (PDF) and without (FV) consideration of TCI. TCI has little influence on overall ignition timing and thermodynamics of the combustion process for these nearly homogeneous cases. However, even here, the influence of TCI on emissions cannot be ignored. With consideration of TCI, computed CO emissions increase by 16% and nonfuel UHC emissions by 5% for Case PHI_25; the differences are larger for Case PHI_3. These increases in emissions result mainly from the inhomogeneous in-cylinder temperature fields (wall heat transfer effects) and, to a lesser extent, from inhomogeneities in the initial mixture composition. 4.2 Effect of Wall Temperature The effect of a 5 C reduction in wall temperatures can be seen by comparing cases PHI_25 and TWAL_5 (Table 2 and Fig. 2). Again, the anticipated effects are found with decreasing wall temperature: a delay in ignition, lower peak temperature (not shown), and higher CO and nonfuel UHC emissions. The influence of TCI is similar to that discussed in Section 4.1: a small effect on global thermodynamics, and significant effects on emissions. 4.3 Effect of Swirl Swirl affects the turbulent mixing and combustion processes in several ways. Swirl influences mean and turbulent species transport, enhances wall heat transfer, and, if sufficiently strong, can serve to stratify the fuel/air/residual-gas mixture radially. Cases PHI_25 and SWRL_8 illustrate the effect of moderate (swirl ratio 2.) versus high (swirl ratio 8.) swirl with premixed reactants. The higher wall heat transfer rate and less homogeneous temperature and composition fields for the high-swirl case result in delayed ignition, lower peak temperature (not shown), and significantly higher pollutant emissions (Table 2, Fig. 3). The effects of TCI are comparable to those noted in the lower swirl cases. 4.4 Effect of Mixture Inhomogeneity Direct in-cylinder fuel injection with variation in SOI timing is explored in Cases SOI_112, SOI_18, and SOI_24 (Table 2, Fig. 4). 3
Inhomogeneity in the initial mixture composition field increases as injection is delayed towards TDC. For the cases investigated, later injection results in advanced ignition timing and higher emissions. The effects of TCI on both global thermodynamic quantities and on emissions are pronounced. For the latest SOI timing (24 ATDC), TCI results in a two-degree advance in the computed ignition timing, a 5 C increase in peak global in-cylinder temperature (not shown), a 26% increase in CO, and a 5% increase in nonfuel UHC emissions compared to computations that do not consider TCI. And while ignition is advanced with consideration of TCI, the peak heat release rate is lower with TCI (Fig. 4). 4.5 Effect of Top-Ring-Land Crevice The most dramatic effects result from consideration of a TRLC (Table 2, Fig. 5). The importance of the TRLC on HCCI emissions, in particular, has been the subject of earlier experimental [19] and modeling [2] studies. In general, the TRLC exacerbates spatial inhomogeneities in composition and temperature. Cases with a TLRC show high emissions and a non-negligible amount of unburned fuel at 4 ATDC (TRLC_18 versus SOI_18). There is a significant advance in ignition timing with versus without TCI; interestingly, this ignition advance appears to partially offset what otherwise would be a much larger difference in emissions. Particularly in cases where direct injection and a TRLC are considered simultaneously, it is essential to consider TCI effects in modeling HCCI autoignition and emissions. 4.6 ISAT An example illustrating the effectiveness of a storage/retrieval scheme [16] in accelerating the chemical source term calculations is provided in Fig. 6 for PDF case PHI_25. Here ISAT parameters have been set such that results obtained using ISAT are indistinguishable from those that have been obtained using direct integration of the chemical source terms [7]. ISAT is particularly effective before and after the main ignition event where table retrieve rates are high; during ignition there are steep spatial and rapid temporal variations in composition and temperature that result in a higher proportion of new table entries being generated. The overall speedup for this case is approximately a factor of 9. 5. Conclusions The influence of turbulence/chemistry interactions on autoignition and emissions of CO and UHC has been examined using a three-dimensional time-dependent CFD model. TCI is accounted for by considering the joint PDF of 4 chemical species and mixture enthalpy. Salient findings are as follows. For nearly homogeneous reactants with low to moderate swirl and no TRLC, TCI has little effect on ignition timing. However, even in that case the influence of TCI on emissions is not negligible. With increasing levels of swirl, higher degrees of mixture inhomogeneity, and for cases that include a TRLC, TCI effects become increasingly important and result in significant changes in ignition timing, global in-cylinder temperature and pressure, and emissions. Unburned fuel is a non-negligible contribution to UHC only in cases with high swirl or where a TRLC has been considered. The combination of consistent hybrid particle/finite-volume algorithms, detailed chemical kinetics, and chemistry acceleration strategies make PDF methods practicable for three-dimensional timedependent modeling of HCCI autoignition and emissions. The model will be exercised next to perform systematic quantitative comparisons with experimental measurements [1]. 4
Acknowledgements This research has been supported by the Department of Energy (DE-FC4-2AL67612), by the National Science Foundation (CTS-121573), by the General Motors R&D Center, and by the CD-adapco group. We are grateful to Profs. R.D. Reitz, C.J. Rutland, and D.E. Foster and to Dr. T. Aroonsrisopon of the University of Wisconsin- Madison Engine Research Center Center. References [1]. F. Zhao, T.W. Asmus, D.N. Assanis, J.E. Dec, J.A. Eng, P.M. Najt (Eds.), Homogeneous Charge Compression Ignition (HCCI) Engines: Key Research and Development Issues, Society of Automotive Engineers, Warrendale, PA, 23. [2]. M. Christensen, B. Johansson, SAE Paper No. 22-1-2864 (22). [3]. S.-C. Kong, R.D. Reitz, ASME Paper No. 2-ICE-36 (2). [4]. S.M. Aceves, D.L. Flowers, C.K. Westbrook, J.R. Smith, W.J. Pitz, R. Dibble, M. Christensen, B. Johansson, SAE Paper No. 2-1-327 (2). [5]. S.B. Fiveland, D.N. Assanis, SAE Paper No. 21-1-128 (21). [6]. M. Kraft, P. Maigaard, F. Mauss, M. Christensen, B. Johansson, Proc. Combust. Inst. 28 (2) 1195-121. [7]. M. Embouazza, D.C. Haworth, N. Darabiha, SAE Paper No. 22-1-2773 (22). Case 5 [8]. S.-C. Kong, R.D. Reitz, M. Christensen, B. Johansson, SAE Paper No. 23-1-188 (23). [9]. S.B. Pope, Prog. Energy Combust. Sci. 11 (1985) 119-192. [1]. T. Aroonsrisopon, P. Werner, V.M. Sohm, D.E. Foster, T. Ibara, T. Morikawa, M. Iida, J. Waldman, SAE Paper No. 24-1-1756 (24). [11]. A.A. Amsden, Los Alamos National Laboratory Report LA-13313-MS (1997). [12]. Y.Z. Zhang, D.C. Haworth, J. Comput. Phys. (24), to appear. [13]. D.P. Schmidt, I. Nouar, P.K. Senecal, C.J. Rutland, J.K. Martin, R.D. Reitz, SAE Paper No. 1999-1-496 (1999). [14]. N. Nordin, Thesis for the degree of Licenciate of Engineering, Chalmers University of Technology, Goteborg, Sweden (1998). [15]. R.J. Kee, F.M. Rupley, J.A. Miller, Sandia National Laboratories Report SAND89-89B (1989). [16]. S.B. Pope, Combust. Theory & Modelling 1 (1997) 41-63. [17]. S. Subramaniam, D.C. Haworth, Intern l. J. Engine Res. 1 (2) 171-19. [18]. S. H. El Tahry, J. of Energy 7 (1983) 345-353. [19]. M. Christensen, A. Hultqvist, B. Johansson, SAE Paper No. 21-1-1893 (21). [2]. S.M. Aceves, D.L. Flowers, F. Espinosa- Loza, J. Martinez-Frias, R.W. Dibble, M. Christensen, B. Johansson, R.P. Hessel, SAE Paper No. 22-1-2869 (22). Table 2. Summary of global results. CO and UHC values are at 4 ATDC. Equiv. T wall [K] IVC Premixed TRLC Ignition CO UHC ratio liner/ swirl or SOI Y/N timing 1 3 1 5 Φ head & ratio [ ATDC] [ ATDC] (fuel) piston FV/PDF FV/PDF FV/PDF UHC 1 3 (nonfuel) FV/PDF PHI_2.2 4/42 2. premixed N 1.2/1.2 7.9/7.12 2.96/3.74 1.98/2.2 PHI_25.25 4/42 2. premixed N -3.8/-3.8 1.46/1.7.21/.38.85/.89 PHI_3.3 4/42 2. premixed N -4.2/-4.2.16/.22./.2.36/.38 TWAL_5.25 35/37 2. premixed N -1/-1 3.2/3.45 1.2/2.9 1.13/1.19 SWRL_8.25 4/42 8. premixed N 1.4/1.4 7.73/7.88 19.55/22.1 2.83/2.91 SOI_112.25 4/42 2. 112 N -7/-9.14/.19./.1.35/.39 SOI_18.25 4/42 2. 18 N -9/-1.25/.39./.3.4/.42 SOI_24.25 4/42 2. 24 N -1/-12.43/.54./.4.41/.43 TRLC_18.25 4/42 2. 18 Y -9.5/-13.88/.91 11.7/11.3.69/.72
15 12 T[K] 9 FV Φ=.2 PDF Φ=.2 FV Φ=.25 PDF Φ=.25 FV Φ=.3 PDF Φ=.3 CO Mass Fraction.1.8.6.4 FV T wall =37K PDF T wall =37K FV T wall =42K PDF T wall =42K.2 6-45 -3-15 15 3-45 -3-15 15 3 Fig. 1. Computed global in-cylinder temperature with and without TCI: effect of equivalence ratio. Fig. 2. Computed global in-cylinder CO mass fraction with and without TCI: effect of wall temperature. UHC Mass Fraction.8.6.4.2 FV SR=8. PDF SR=8. FV SR=2. PDF SR=2. Heat Release Rate [J/Deg] 5 4 3 2 1 FV PDF -45-3 -15 15 3-4 -2 2 Fig. 3. Computed global in-cylinder nonfuel UHC with and without TCI: effect of swirl. Fig. 4. Computed global in-cylinder heat release rate with and without TCI for Case SOI_18. C 7 H 16 Mass Fraction.8.6.4.2 FV TRLC PDF TRLC FV No TRLC PDF No TRLC CPU time [s] 18 15 12 9 6 3 DI ISAT -2-1 1 2-3 -2-1 1 2 Fig. 5. Computed global in-cylinder unburned fuel mass fraction with and without TCI: effect of TRLC. Fig. 6. CPU time per computational timestep using direct integration (DI) versus ISAT for PDF case PHI_25. 6