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2210 日本機械学会論文集 (B 編 ) 77 巻 783 号 (2011-11) 原著論文 No.2011-JBT-0600 * 1 Nissan Motor CO., Ltd.

1 2210 日本機械学会論文集 (B 編 ) 77 巻 783 号 ( ) 原著論文 No.2011-JBT-0600 * 1 Nissan Motor CO., Ltd , Okatsukoku, Atsugi-shi Kanagawa , Japan 1, 2 Development of Flame Propagation Model Considering Lewis Number Effect for Rich Fuel Mixture for Gasoline SI Engines Atsushi TERAJI *1 and Anand GURUPATHAM The purpose of this research is to include the phenomenon that occurs because of Wrinkle (Stretch) which naturally generates to the flame surface under a rich condition that promotes the burning speed. This happens in a gasoline fuel combustion that is heavier than air. In the present study, the unstable flame was formed due to the imbalance of the mass diffusion and the temperature diffusion of the fuel was modeled. The laminar burning speed model was developed by considering the stretch. The model has shown the capability to reproduce the heat generation (heat release rate) at high accuracy in comparison with experimental data. The simulation was carried out for both homogeneous and the stratification combustion and validated with experimental data. Considering the flame stretch made 3-D combustion simulation tool high accuracy from lean to rich fuel mixture condition. Key Words : Flame Propagation, Lewis Number Effect, CFD (1) (2) Lewis (3) (6) Lewis TI (Time-scale Interaction combustion model) (7) TI Lewis * *1 原稿受付 2011 年 7 月 18 日正員, 日産自動車 ( 株 ) パワートレイン開発本部 ( 神奈川県厚木市岡津古久 560-2) *2 Renault-Nissan Technology and Business Center, India. teraji@mail.nissan.co.jp 162

2 TI TI(Time-scale Interaction) Universal Coherent Flamelet Model( UCFM) (8) Characteristic Time-scale Combustion (9) ( CTC ) τ kin τ t Damköhler Da 1 Well Stirred CTC (Da > 1) UCFM 1 2 Lewis Lewis U L U L0 Markstein Karlovitz U L = 1 MaKa (1) U L0 Karlovitz Ka ( ) 1 ( ) lt 2 u 3 2 Ka = (2) δ L U L0 u l t δ L Markstein Ma Markstein L δ t Ma = L δ t (3) Markstein L Law Zeldovich Ze (10) Lewis Le Markstein Ma Ma = Ze ( 1 1 ) (4) 2 Le Zeldovich Ze Clavin (11) Ze = E ( ) a Tad T u R E a T u T ad Lewis α D AB Le = T 2 ad α D AB (6) (5) 163

3 2212 Table 1 Configuration of 3-D combustion simulation Combustion TI combustion (7) Laminar Burning Velocity Gülder formula (16) Burned Gas Post chemistry Dissociation Wall Quench FIST model (17) Wall Heat Transfer Extended Law of the Wall (18) Ignition ERC spark ignition model (19) Spray SSP (20) Turbulence model RNG k-ε Table 2 Specifications of experimental MPI engine Engine Type 4-Stroke, 4-Valve, Single Cylinder Combustion Chamber Pentroof type Bore Stroke 93mm 81.4mm Compression Ratio 10:1 Engine Speed 2400 rpm Engine Load WOT Spark Advance -30 deg.atdc Fuel iso-octane Lewis Lewis Le F Le O Lewis Le (15) ef f Le ef f = Le F +(1 + φ)le O 2 + φ (7) φ = Ze(φ 1) (8) (Le < 1) Markstein Ma (12) (13) UCFM (14) φ > Lewis TI(Time-scale Interaction) STAR-CD 1 40 (MPI: Multi-Point Injection) (GDI: Gasoline Direct Injection) MPI N2, CO2, H2O (MPI) (GDI) MPI

4 2213 Laminar burning velocity (m/s) Fig Kumar et al. [21] Huang et al. [22] Davis et al. [23] Gülder et al. [24] Holley et al. [25] Egolfopoulos et al. [26] Gülder formula [28] Keck formula [27] Eqiuivalence ratio Comparison of laminar burning velocity between Keck and Gülder formula with reference data Comb. duration (10-90%) [degree] Fig Equivalence ratio Experimental combustion duration under various fuel mixture conditions Heat release rate (J/deg.) Crank Angle (deg.atdc) (a) φ= UL =1.22 UL =1.92 UL0 UL Exp. w/o Lewis number effect w/ Lewis number effect Crank Angle (deg.atdc) (b) φ=1.4 Fig. 3 Comparisons of heat release rate under rich fuel mixture condition with and without Lewis number effect model 1 U L0 2 U L0 φ=1.1 φ > 1.4 U L0 φ=0.8 φ > 1.4 φ=1.0 Lewis Lewis 3 Lewis U L U L0 U L /U L0 U L /U L0 φ Lewis Lewis 165

5 (MPI) φ= rpm φ=2.0 5 LIF(Laser Induced Fluorescence) 30 Fuel injector 1 Exhaust Rear Fuel Fig. 4 Intake Front Fuel injector 2 Configuration of experimental MPI engine for stratified combustion validation Fig φ Equivalence ratio (a) Calculation 1.8 Lean (b) Experiment Rich Comparison of equivalent ratio distribution between calculation result and LIF experimental data at -30 deg.atdc w/o Lewis number effect w/ Lewis number effect Experiment 20 deg.atdc 15 deg.atdc 10 deg.atdc 5 deg.atdc Fig. 6 Comparison of flame propagation behavior between with and without consideration of Lewis number effect 166

2215 6 Lewis Lewis - Lewis 78 Lewis iso-octane Markstein Ma Ma < 0

0 Leeff Effective Lewis number Fig. 7 0.0 0.

0 Ka Ma Karlovitz number Markstein number Distributions of Karlovitz

5 (a) Unstretched LBV U L0 (b) Stretched LBV UL Fig.

6 Lewis Lewis - Lewis 78 Lewis iso-octane Markstein Ma Ma < 0 Lewis φ=1.4 Lewis Lewis φ > 1 Lewis 0.2 φ 1.8 Equivalence ratio Leeff Effective Lewis number Fig Ka Ma Karlovitz number Markstein number Distributions of Karlovitz number and Markstein number at spark advance of -30 deg.atdc 0.0 m/s 1.5 (a) Unstretched LBV U L0 (b) Stretched LBV UL Fig. 8 Distribution of unstretched and stretched laminar burning velocity at spark advance of - 30 deg.atdc 3 3 (GDI) deg. ATDC( ) -5deg.ATDC() 9 Lewis Lewis 10 Lewis 167

2216 Table 3 Specifications of experimental GDI engine Engine Type 4-Stroke, 4-Valve, Single Cylinder Combustion

6mm Compression Ratio 10:1 Engine Speed 1250 rpm Engine Load 220 kpa A/F 16.0 Spark Advance 20 deg.

atdc IT= -3 deg.atdc Fuel distribution 0.0 φ 2.0 Stretched LBV 0.0 2.0 UL Unstretched LBV 0.0 2.0 U L0 Fig.

atdc Pressure (MPa) Exp. 2.0 Cal. 1.5 1.0 0.5 0.0-60 0 60 120-60 0 60 0 120 Crank Angle (deg.

7 2216 Table 3 Specifications of experimental GDI engine Engine Type 4-Stroke, 4-Valve, Single Cylinder Combustion Chamber Pentroof type Bore Stroke 78mm 83.6mm Compression Ratio 10:1 Engine Speed 1250 rpm Engine Load 220 kpa A/F 16.0 Spark Advance 20 deg.atdc 1st Injection Timing -300 deg.atdc 2nd Injection Timing -35, -5 deg.atdc Fuel iso-octane IT= -35 deg.atdc IT= -3 deg.atdc Fuel distribution 0.0 φ 2.0 Stretched LBV UL Unstretched LBV U L0 Fig. 9 Comparisons of distributions of equivalence ratio, stretched and unstretched laminar burning velocity at 20 deg.atdc Pressure (MPa) Exp. 2.0 Cal Crank Angle (deg. ATDC) Crank Angle (deg. ATDC) (a) IT= -35deg.ATDC (b) IT= -5deg.ATDC Heat release rate (J/deg.) Fig. 10 Comparisons of pressure histories and heat release rates at different injection timing TI Lewis 1. TI Lewis

8 Lewis (1) S. Heller and G. Wachtmeister, Analysis and Modeling of Heat Transfer in the SI Engine Exhaust System During Warm-Up, SAE Paper (2007). (2) Z. Xu, J. Yi, S. Wooldridge, D. Reiche, E. Curtis and G. Papaioannou, Modeling the Cold Start of the Ford 3.5L V6 EcoBoost Engine, SAE Paper (2009). (3) T. Kitagawa, Effects of Pressure on Burning Velocity and Instabilities of Propane-Air Premixed Flames, JSME (Int.) Journal Series B, Vol. 48, (2005), pp (4) Y. Nomura and R. Shimizu, Fractal Analysis of Flame Front during the Early Stages of Propagation in a SI Engine, The 18th Internal Combustion Engine Symposium, (2005). (5) B. Emami, R. Liu, D. S. K. Ting and M. D. Checkel, Numerical Study on the Burning Velocity of a Spherical, Premixed Methane-Air Flame, SAE Paper (2005). (6) C. Mandilas, M. P. Ormsby, C. G. W. Sheppard and R. Wooly, Effects of Hydrogen Addition on Laminar and Turbulent Premixed Methane and iso-octane-air Flames, Proceedings of the Combustion Institute, Vol. 31(2007), pp (7) A. Teraji, Y. Imaoka, T. Tsuda, T. Noda, M. Kubo and S. Kimura, Development of a Time-scale Interaction Combustion Model and its Application to Gasoline and Diesel Engines, Proceedings of the Combustion Institute, Vol. 32(2009), pp (8) A. Teraji, T. Tsuda, T. Noda, M. Kubo, T. Itoh, Development of a Novel Flame Propagation Model (UCFM: Universal Coherent Flamelet Model) for SI Engines and its Application to Knocking Prediction, SAE Paper (2005). (9) S. C. Kong, Z. W. Han and R. D. Reitz, The Development and Application of a Diesel Ignition and Combustion Model for Multidimensional Engine Simulation, SAE Paper (1995). (10) C. K. Law and C. J. Sung, Structure, Aerodynamics, and Geometry of Premixed Flamelets, Progress in Energy and Combustion Science, Vol. 26(2000), pp (11) P. Clavin, Dynamic Behavior of Premixed Flame Fronts in Laminar and Turbulent Flows, Progress in Energy and Combustion Science, Vol. 11(1985), pp (12) O. C. Kwon, G. Rozenchan and C. K. Law, Cellular Instabilities and Self-acceleration of Outwardly Propagating Spherical Flames, Proceedings of the Combustion Institute, Vol. 29(2002), pp (13) S. K. Marley and W. L. Roberts, Measurements of Laminar Burning Velocity and Markstein Number Using High-speed Chemiluminescence Imaging, Combustion and Flame, Vol. 141(2005), pp (14) A. Teraji, T. Tsuda, T. Noda, M. Kubo and T. Itoh, Analysis and Prediction of Unburned HCs in a Lean-burn Engine, SAE Paper (2007). (15) M. Matalon, Flame Dynamics, Proceedings of the Combustion Institute, Vol. 32(2009), pp (16) Ö. L. Gölder, Correlations of Laminar Combustion Data for Alternative S. I. Engine Fuels, SAE Paper (1984). (17) T. Poinsot, D. C. Haworth and G. Bruneaux, Direct Simulation and Modeling of Flame-wall Interaction for Premixed Turbulent Combustion, Combustion and Flame, Vol. 95(1993), pp (18) C. Angelberger, T. Poinsot, and B. Delhay, Improving Near-wall Combustion and Wall Heat Transfer Modeling in SI Engine Computations, SAE Paper (1997). (19) G. Stiesch, Z. Tan, G. P. Merker, R. D. Reitz, Modeling the Effect of Split Injections on DISI Engine Performance, SAE Paper (2001). (20) K. Naitoh, and Y. Takagi, Synthesized Spheroid Particle(SSP) Method for Calculating Spray Phenomena in Direct-injection SI Engines, SAE Paper (1996). 169

9 2218 (21) K. Kumar, J.E. Freeh, C.J. Sung, and Y. Huang, Laminar Flame Speeds of Preheated iso-octane/o2/n2 and n-heptane/o2/n2 Mixtures, Journal of Propulsion and Power, No. 23(2007), pp (22) Y. Huang, C. J. Sung and J. A. Eng, Laminar Flame Speeds of Primary Reference Fuels and Reformer Gas Mixtures, Combustion and Flame, Vol. 139 (2004), pp (23) S. G. Davis and C. K. Law, Laminar Flame Speeds and Oxidation Kinetics of iso-octane-air and n-heptane-air Flames, Combustion Science and Technology, No. 140 (1999), pp (24) Ö. L. Gölder, Laminar Burning Velocities of Methanol, Ethanol and iso-octane-air Mixtures, Proceedings of the Combustion Institute, Vol. 19(1982), pp (25) A. T. Holley, Y. Dong, M. G. Andac, and F. N. Egolfopoulos, Combustion and Flame, Extinction of Premixed Flames of Practical Liquid Fuels: Experiments and Simulations, Vol. 144 (2006), pp (26) C. K. Law F. N. Egolfopoulos and D. X. Du, A Study on Ethanol Oxidation Kinetics in Laminar Premixed Flames, Flow Reactors, and Shock Tubes, Proceedings of the Combustion Institute, Vol. 24 (1992), pp (27) M. Metghalchi and J. C. Keck, Burning Velocities of Mixtures of Air with Methanol, isooctane, and Indolene at High Pressure and Temperature, Combustion and Flame, Vol. 48 (1982), pp (28) Ö. L. Gölder, Correlations of Laminar Combustion Data for Alternative S. I. Engine Fuels, SAE paper, No (1984). 170

: u i = (2) x i Smagorinsky τ ij τ [3] ij u i u j u i u j = 2ν SGS S ij, (3) ν SGS = (C s ) 2 S (4) x i a u i ρ p P T u ν τ ij S c ν SGS S csgs

: u i = (2) x i Smagorinsky τ ij τ [3] ij u i u j u i u j = 2ν SGS S ij, (3) ν SGS = (C s ) 2 S (4) x i a u i ρ p P T u ν τ ij S c ν SGS S csgs 15 C11-4 Numerical analysis of flame propagation in a combustor of an aircraft gas turbine, 4-6-1 E-mail: tominaga@icebeer.iis.u-tokyo.ac.jp, 2-11-16 E-mail: ntani@iis.u-tokyo.ac.jp, 4-6-1 E-mail: itoh@icebeer.iis.u-tokyo.ac.jp,