Spark Ignition Engine Combustion Modeling Using a Level Set Method with Detailed Chemistry

Transcription

1 SAE TECHNICAL PAPER SERIES Spar Ignition Engine Combustion Modeling Using a Level Set Method with Detailed Chemistry Long Liang and Rolf D. Reitz University of Wisconsin Madison Reprinted From: Multi-Dimensional Engine Modeling 6 (SP-11) 6 SAE World Congress Detroit, Michigan April 3-6, 6 4 Commonwealth Drive, Warrendale, PA U.S.A. Tel: (74) Fax: (74) Web:

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3 Spar Ignition Engine Combustion Modeling Using a Level Set Method with Detailed Chemistry Copyright 6 SAE International Long Liang and Rolf D. Reitz University of Wisconsin-Madison ABSTRACT A level set method (G-equation)-based combustion model incorporating detailed chemical inetics has been developed and implemented in KIVA-3V for Spar- Ignition (SI) engine simulations for better predictions of fuel oxidation and pollutant formation. Detailed fuel oxidation mechanisms coupled with a reduced NO X mechanism are used to describe the chemical processes. The flame front in the spar ernel stage is traced using the Discrete Particle Ignition Kernel (DPIK) model. In the G-equation model, it is assumed that after the flame front has passed, the mixture within the mean flame brush tends to local equilibrium. The subgrid-scale burnt/unburnt volumes of the flame containing cells are traced for the primary heat release calculation. A progress variable concept is introduced into the turbulent flame speed correlation to account for the laminar to turbulent evolution of the spar ernel flame. To test the model, a homogeneous charge propane SI engine was modeled using a 1-species, 539-reaction propane mechanism, coupled with a reduced 9-reaction NOx mechanism for the chemistry calculations. Good agreement with experimental cylinder pressures and NOx data was obtained as a function of spar timing, engine speed and EGR levels. The model was also applied to a stratified charge two-stroe gasoline engine simulations, and good agreement with measured data was obtained. INTRODUCTION Multidimensional Computational Fluid Dynamics (CFD) modeling has become an indispensable tool in the design and analysis of low-emission, high-fuel-efficiency Internal Combustion Engines (ICE). Good understanding of the in-cylinder turbulent combustion is one of the ey factors for successful modeling. In this paper, we focus on the combustion modeling of homogeneous charge and stratified charge SI engines. The in-cylinder turbulent combustion in SI engines is a complicated aero-thermo-chemical process especially due to the turbulence and chemistry interactions on tremendously different time-scale and length-scale levels. There have been several approaches to model the premixed and partially premixed combustion occurring in SI engines. They can be classified into turbulent mixing controlled, flamelet and PDF approaches. Abraham et al. [1] proposed a characteristic timescale combustion (CTC) model which used -ε model for turbulent transport and a combination of a mixing-controlled and an Arrhenius-controlled species conversion rate. Flamelet models are another group of widely used methods which are either based on the progress variable, c, or on the non-reacting scalar, G []. The Bray-Moss-Libby (BML) model and the Coherent Flame Model (CFM) are based on the progress variable, c, which is viewed either as a normalized temperature or as a normalized product mass fraction [3]. As an example, Boudier et al. [4] implemented an extended version of CFM into KIVA to simulate turbulent flame ignition and propagation in SI engines, with focus on the evolution criterion from the laminar stage to the fully developed turbulent stage based on flame stretch effects. The model was validated by comparison with incylinder flame front contours in an experimental SI engine. The level set method (G-equation) is a powerful tool for describing interface evolution. With its application to combustion, Williams [5] first suggested a transport equation of a non-reactive scalar, G, for laminar flame propagation. Peters [,6] subsequently extended this approach to the turbulent flame regime. The turbulent G-equation concept has been successfully applied to SI engine combustion simulations by Deena et al. [7], Tan [8] and Ewald et al. [9]. In recent years, to better understand the fundamental engine combustion process and to further improve the versatility of multidimensional models, attention is being given to models incorporating comprehensive elementary chemical inetic mechanisms. A large amount of wor has been done on developing detailed chemical inetic mechanisms for fuel oxidation and pollutant formation [1]. Further, research on mechanism reduction and parallel computing techniques have made it computationally affordable to incorporate the reduced detailed chemical inetic mechanisms into multidimensional engine simulations. The objective of the current wor is to incorporate detailed chemical

4 inetics into the G-equation-based turbulent combustion model which was implemented into the KIVA-3V code by Tan et al. [11,1]. Specifically, for SI engine combustion, detailed fuel oxidation mechanisms coupled with a reduced NO X mechanism are applied behind the mean flame front for modeling post flame combustion and NO X formation. The chemical inetic mechanisms are also applied in front of the flame front for the potential capability of predicting the compression autoignition of the end-gas. Also, In the course of coupling detailed chemistry with the G-equation combustion model for the primary heat release calculation within the flame front, the laminar and turbulent flame speed correlations were required to be revisited and improved for a better description of the turbulent flame propagation process. THE MODELS COMBUSTION MODEL WITH DETAILED CHEMISTRY G-equation description of turbulent flame propagation In the flamelet modeling theory of premixed turbulent combustion by Peters [], two regimes of practical interest were addressed: the corrugated flamelet regime where the entire reactive-diffusive flame structure is assumed to be embedded within eddies of the size of the Kolmogorov length scale η ; and the thin reaction zone regime where the Kolmogorov eddies can penetrate into the chemically inert preheat zone of the reactive-diffusive flame structure, but cannot enter the inner layer where the chemical reactions occur. Peters derived level set equations applicable to both regimes, including the Favre averaged equations for the mean, G, and its variance, G, and a model equation for the flame surface area ratio, which in turn, gives an algebraic solution for the steady-state planar turbulent flame speed, S T. These equations together with the Reynolds averaged Navier-Stoes equations and the turbulence modeling equations, form a complete set to describe premixed turbulent flame front propagation []. Considering the Arbitrary Lagrangian-Eulerian (ALE) numerical method used in the KIVA code, Tan [1] modified the convection term of the G transport equation to account for the velocity of the moving vertex, v vertex. Thus, the equation set suitable for KIVA implementation is: G + ( v u ) f v vertex G = S T G D tκ G t G u + ( v f vvertex ) G = ( Dt G ) t ε + Dt( G) cs G (1) () ST ab 4 3 l ab 4 3 l u l = ab 4 3 SL b1 lf b1 lf sll F where v f 1 (3) is the fluid velocity vector, D t is the turbulent diffusivity, and a 4, b 1, b 3, and c s are modeling constants from the turbulence model or experiment (cf. Peters []). and ε are the Favre mean turbulence inetic energy and its dissipation rate from the RNG - ε model [13]. u is the turbulence intensity. S L is the unstretched laminar flame speed, and l and l F are the turbulence integral length scale and laminar flame thicness, respectively. κ is the mean flame front curvature: G κ = G The flame thicness, l F, can be estimated by [14]: l F p T us L (4) ( λ / c ) = (5) where the λ / cp term is approximated by [15]: 4 g T λ / cp =.58 1 cm sec 98K In this wor the inner layer temperature, T, was approximated as 15K for the propane and iso-octane flames considered. In the implementations both by Tan [11,1] and Ewald [9], a normal distance constraint G = 1 is applied beyond the flame front surface. In this case, the turbulent flame brush thicness, l F, t, can be defined in terms of G as []: 1/ lft, = ( G ( x, t )) = G G It should be noted that Eq. (3) is for the fully developed turbulent flame, and the relation lf, t = bl was used in the derivation by Peters [], where b = 1.78 is a constant obtained from dimensional reasoning. It was shown by Peters [] and Ewald [9] that the unsteady solution of l F, t can be derived from Eq. () by assuming that the turbulence quantities D t,, and ε are constant, and by assuming a uniform turbulence profile. Based on these assumptions, the convection and diffusion terms which include the gradient of G all vanish, and Eq. () can be reduced to an ordinary differential equation for the turbulent flame brush thicness (cf. []):.7 (6) (7)

5 dlf, t = b csl cslf, t (8) d( t / τ ) where τ = ε is used as a nondimensionalizing timescale, and correlations relating D t,, and ε to u, l, and τ have been used. Choosing l Ft, = as the initial value at spar timing, an algebraic solution results: l b l c t τ 1 Ft, = [1 exp( s / )] (9) Based on Eq. (9), the unsteady turbulent flame speed is, ST ab 4 3 l ab 4 3 l ul = 1+ I P + + a4b3 SL b1 lf b1 lf sll F 1 (1) where 1 IP = [1 exp( c t/ τ )] (11) s Physically, the additional exponential term, I P, can be interpreted as a progress variable which accounts for the increasing disturbing effect of the surrounding eddies on the flame front surface as the ignition ernel grows from the laminar flame stage into the fully developed turbulent stage. Similar terms also appear in the turbulent flame speed correlation for an ignition ernel flame by Herweg et al. [16]. According to Peters [], c s =. is a constant derived from spectral closure. However, in practical engine simulations, uncertainties associated with other sub-models including chemistry mechanisms or even mesh resolution during the ernel growth could result in difficulties in matching experimental data. Therefore, this progress variable was selected to be tunable in the present study by introducing a model constant, C m, while eeping the same scaling relation, i.e., I t C τ 1 P = [1 exp( /( m ))] (1) Although C m is regarded as tunable for different engines, it is fixed for all spar timing sweeps, rpm sweeps and Exhaust Gas Recirculation (EGR) sweeps for each specific engine in the present wor. Although the above G-equation description was originally developed for premixed flames by Peters [], it is also applied to partially premixed flames in Direct Injection SI (DISI) engines in this study. This scenario features the so-called triple flame structure, as shown in Fig. 1. The premixed flame branches are described using the G-equation, while the secondary heat release and pollutant formation within the diffusion flames behind the flame front are modeled by detailed chemical inetics. The prediction of the turbulent burning velocity plays a crucial role in the modeling of SI engine combustion. The laminar flame speed is one of the most important scaling factors in most of the published correlations for the turbulent flame speed. Metgalchi et al. [17] found that the experimentally measured laminar flame speed can be correlated as a function of equivalence ratio, temperature and pressure by: α β T u P L = Lref, T uref, P ref S S F (13) where the subscript ref means the reference condition of 98K and 1atm. F is a factor accounting for the uent s effect. The fuel-type independent exponents α and β were correlated as functions of equivalence ratio as: α =.18.8( φ 1) (14) β =.16 +.( φ 1) (15) The reference flame speed is given as: S ( ) Lref, = BM + B φ φm (16) Values for B M, B and φ M for propane and isooctane are listed in Table 1. Table 1 Values for B M, B and φ M with Eq. (16) Fuel B (cm/s) M B (cm/s) φ M Propane Isooctane Figure 1 Triple flame structure in DISI engines [11]. Unfortunately, Eq. (16) predicts negative flame speeds for very lean or very rich mixtures. For example, the flammability range of isooctane is generally quoted as.6 < φ < 1.7, which is acceptable for simulations of premixed flames near stoichiometric conditions, but is not applicable to stratified charge combustion in DISI engines. As suggested by Deur et al. [18], one practical solution is to follow the expression proposed by Gülder [19] in which the flame speed will never be driven negative, viz.,

6 S Lref ( ( ) ) η, = ωφ exp ξ φ σ (17) F.773 = 1.6 X (19) where ω, η, ξ, and σ are data fitting coefficients. However, the reference flame speeds based on the values of the coefficients originally suggested by Gülder [19] show a relatively large discrepancy with published experimental data in the literature [17]. For isooctane, following the idea of Deur [18], in the present study, a group of new values of the coefficients in Eq. (17) was obtained by correlating the data of Metgalchi et al. [17] within the range.65 < φ < 1.6. Gülder s values and the new values are listed in Table, and a comparison of isooctane reference flame speeds from the different correlations is shown in Fig.. The same treatment can be adopted for other fuel types. Table Coefficient values in Eq. (17) for isooctane ω η ξ σ Gülder [19] Present where X is the mole fraction of the uent. In this study, we combined the correlations by Ryan [1] and by Metghalchi et al. [], i.e., in Eq (18) f = Y for < Y <. () f =.5 for. < <.476 (1) However, it can be seen that this expression fails beyond Y >.476 because the flame speed becomes negative outside this range. However, the new correlation gives good results in engine simulations as will be shown later. The different mass fraction-based uent factors are compared in Fig. 3. In comparison, the mole fraction-based Eq. (19) results in more reduction effect compared to all the mass fraction-based correlations presented here. Y 5 4 Metghalchi et al. Gulder Present study 1..8 Metgalchi et al. Ryan et al. Present study [ cm/sec ] S L,ref 3 F φ Figure Comparison of laminar flame speed correlations for isooctane under reference conditions (T=98K, P=1atm). The presence of uent due to internal residual and/or EGR has a significant effect on the laminar flame speed. This effect is usually accounted for by a term such as F in Eq. (13). One expression suggested for all fuel types is []: F = 1 f Y (18) where Y is the mass fraction of uent and f is an experimentally determined constant. Ryan et al. [1] suggested that f =.5 is valid for < Y <.3. Metgalchi et al. [] suggested f =.1 to be valid for < Y <.. Rhodes et al. [] proposed another expression based on laminar flame speed measurements of indolene-air-uent mixtures, viz., Figure 3 Comparison of different uent factors. Primary heat release within the turbulent flame brush In the present implementation of the G-equation model, it is assumed that after the flame front has passed, the mixture within the mean flame brush tends to the local and instantaneous thermodynamic equilibrium. The species conversion rate and the associated primary heat release at the flame front are calculated based on this assumption. Tan and Reitz [1] suggested a method for calculating the species density change in the cells containing the mean flame front, viz., d A i = ( Y, Y, ) S () dt f,4 i iu ib T Vi 4 where is the average density of the mixture in cell, Y i 4. Y and Y ib, are the mass fractions (i.e., fractions of

7 the total mass in the cell) of species i in the unburnt and burnt mixtures, respectively. A f is the mean flame front area and V is the cell volume. i 4 is the cell index used in KIVA. Tan and Reitz [1] assumed seven species in their study, including fuel, O, N, CO, H O, CO, H. Y ib, was also assumed to be the local equilibrium value. One issue associated with Eq. () is how to determine Y. By assuming the Y of N, CO, H O, CO, H to be constantly equal to their initial values at the time of ignition, the Y of fuel and O can be estimated from the C, H and O element conservation relations (cf. Tan [8]). However, when a large number of intermediate species are included, and detailed chemistry is considered as in the present study, the above method is no longer able to give the predicted Y for all the species. This is because the number of elements and therefore the available conservation equations is limited. Therefore, a new method is suggested that is based on the sub-grid scale unburnt/burnt volumes of the flame-containing cells. In this method, it is assumed that the mean flame front surface cuts every flame-containing cell into two parts, an unburnt volume V u and a burnt volume V b, as shown in Fig. 4. As the mean flame front sweeps forward, the mixture within the sweeping volume tends to local equilibrium following a constant pressure, constant enthalpy process. The pressure is assumed to be homogeneous across the flame in the cell, consistent with deflagration wave theory. The sub-grid scale volumes are traced for every time step based on the coordinate information of the cell vertices and the flame surface piercing points. The species density conversion rate then becomes: d A i = (,, ) (3) dt f,4 i u Yi u Yi b ST Vi 4 Compared to Eq. (), the cell averaged density is replaced by the density of the unburnt mixture u and now the Y and Y ib, are evaluated with respect to the mass of unburnt and burnt mixture, respectively, viz., Y (4) i = Yib, = 1 i Unburnt Burnt Figure 4 Numerical descriptions of the turbulent flame structure and the flame containing cells. V u V b Mean Flame Front The steps to determine the unburnt species mass fractions Y are as follows: 1. Determine the equilibrium species mass fractions Y ib, and the adiabatic flame temperature T b = T adia. In this study, a Fortran code by Pope [3,4] was used for the calculation of the chemical equilibrium. This code is based on the element potential method as in the STANJAN code [5], but an improved numerical algorithm called Gibbs function continuation is adopted for better computational stability and efficiency.. Calculate the burnt gas density and the burnt species densities based on the equation of state and the mass fractions Y ib, from step 1. P MW i4 mix, b b = (5) RT u b = Y (6) ib, b ib, where MW mix, b is the average molecular mass of the burnt mixture, and R u is the universal gas constant. 3. Calculate the unburnt species densities based on species mass conservation. V V i i4 i, b b = (7) Vu 4. Finally, determine the unburnt species mass fractions: Y = (8) iu, i In KIVA, the heat release due to the chemistry source term is directly related to the species conversion [6]. It needs to be noted that the four species associated with the NO X formation mechanism, i.e., NO, NO, N, and N O [7], are excluded from the equilibrium calculation due to their relatively short residence time within the flame front, and the relative slow rate of the NO X chemical reactions. Post-flame heat release and pollutant formation Fundamental understanding of the chemical processes occurring behind the turbulent flame brush in SI engines is still incomplete, especially for partially premixed combustion. Whether the species conversion in this region is turbulence mixing-controlled or chemical inetics-controlled should be answered by further experimental or Direct Numerical Simulation (DNS) investigations. In this study, the computational cells

8 behind the flame front are modeled as Well Stirred Reactors (WSR). Detailed hydrocarbon oxidation chemical inetic mechanisms are applied to account for the further oxidation of CO and other intermediate species, such as small hydrocarbon molecules and the species in the H -O system. To consider the effects of turbulent mixing, the reaction rates can be adjusted by considering the eddy turnover time as a turbulent timescale, and by combining this timescale with a inetic timescale. This inetic timescale can be selected as the conversion timescale of a heat-release-rate-limiting species, such as CO (cf. Kong et al. [8]). A nine-reaction reduced NO X mechanism was coupled with the hydrocarbon oxidation mechanism for predicting the formation of NO and NO. The reactions include [7]: N + NO N + O (9a) N + O NO+ O (9b) NO+ O NO (9c) NO+ OH N + HO (9d) NO( + M) N + O( + M) (9e) HO + NO NO + OH (9f) NO + O + M NO + M (9g) NO + O NO + O (9h) NO + H NO + OH (9i) Chemical inetics based end-gas autoignition modeling It is generally accepted that engine noc is caused by the autoignition of a portion of the end-gas prior to the flame arrival. A simple but widely used approach to predict engine noc is the Livengood-Wu integral [9], which essentially uses a one-step reaction to approximate the autoignition mechanism. Recently, researchers have proposed using more detailed mechanisms to predict the autoignition time more accurately. For example, Ecert et al. [3] applied the Shell autoignition model to simulate the autoignition of the end-gas in SI engines. Research on detailed chemical inetic mechanisms for the autoignition of fuel/air mixtures has achieved much more accurate predictions of the autoignition delay time and the related thermo-chemical parameters. This maes it possible to accurately describe the location and intensity of the endgas autoignition in SI engines without tuning any reaction rate constants. In this study, detailed chemical inetic mechanisms are also applied in each cell in front of the mean flame front. The auto-ignited mixture can be traced by monitoring certain species that characterize the high temperature heat release, such as the OH radical. Although no nocing modes are considered in the test cases in this paper, this methodology will be followed in our future study of engine noc. IGNITION KERNEL MODEL The growth of the ignition ernel is traced by using the DPIK model by Fan, Tan, and Reitz [11,31]. By assuming a spherical shaped ernel, the flame front position is mared by Lagrangian particles, and the flame surface density is obtained from the number density of particles in each computational cell. Assuming the temperature inside the ernel to be uniform, the ernel growth rate is: dr dt u = ( S plasma + ST ) (3) where r is the ernel radius, u is the local unburnt gas density, and is the gas density inside the ernel region. The plasma velocity S plasma = 4 π u( u) S plasma is given as [8]: Q sp η eff u r u h + P (31) where Q sp is the electrical energy discharge rate, η eff is the electrical energy transfer efficiency due to heat loss to the spar plug. η eff =.3, as suggested by Heywood [3] is used in this study. u and h u are the density and enthalpy of the unburnt mixture. and u are the density and internal energy of the mixture inside the ernel. The laminar flame speed S L in Eq. (1) was multiplied by a stretch factor, I, which accounts for strain and curvature effects, and the modified correlation is used as the turbulent flame speed, S T, in the ernel stage. I follows the suggested expression of Herweg et al. [16]: I 1 lf u 15l S L 3 l = 1 r F u (3) Note that curvature effects are also considered in the present combustion model by the last term of Eq. (1). The chemistry processes in the ernel growth stage are treated in the same way as in the G-equation combustion model. Although the transport equation of G is not solved here, the G field is constructed based on the positions of the ernel particles, thus providing the necessary information for the chemical heat release calculations. The transition from the ernel model to the turbulent G- equation model follows the same criterion as the one used in the previous wor by Tan and Reitz [36],

9 namely, that the transition is controlled by a comparison of the ernel radius with a critical size which is proportional to the locally averaged turbulence integral length scale, viz., 3 r Cm1 l = Cm1.16 (33) ε where C m1 is a model constant. Compared with the previous wor by Tan [8], where two different turbulent flame speed correlations were applied in the ernel model and in the G-equation combustion model, C m1 is no longer as crucial in the model calibration since the turbulent flame speed correlations used in the ernel model and the G-equation combustion model are essentially consistent. ENGINE SIMULATION RESULTS Two SI engines were modeled as test cases for the present combustion model. One is a homogeneous charge Caterpillar converted propane-fueled engine; the other is a two-stroe Mercury Marine DISI gasoline engine. In the simulations, CHEMKIN II [33] was used for solving the detailed chemical inetics. CATPILLAR-CONVERTED PROPANE ENGINE The experimental data for the homogeneous charge Caterpillar propane engine cover different operating conditions, including a spar timing sweep, an EGR level sweep and an engine speed sweep [34]. The engine specifications and operating conditions are listed in Table 4 and Table 5. A 1-species, 539-reaction propane mechanism from the Lawrence Livermore National Lab (LLNL) was used in the calculations [1]. Figure 5 shows a 36 mesh and a D sector mesh of the axially symmetric cylinder. The D sector mesh with periodic boundaries was used due to CPU time considerations. The spar plug is located at the center of the cylinder head, and is represented using stationary particles, as implemented by Fan [31]. The initial incylinder mixture was assumed to be completely homogeneous. The simulations start from IVC. The initial swirl ratio was set as.78 according to experimental measurements. The initial turbulence inetic energy was assumed to be uniform in the cylinder, with an estimated value equal to the inetic energy based on the mean piston speed. 36 full mesh D sector mesh Figure 5 Computational meshes of Caterpillar converted propane SI engine at -3 CA ATDC. Table 4 Caterpillar C 3 H 8 engine specifications. Engine CAT 341 SI Gas Retrofit Bore Stroe (mm) Compression Ratio 1:1 Equivalence Ratio Stoichiometric Spar Duration (ms) Intae Valve Closure ( ) -147 ATDC Initial Pressure at IVC (Pa) 51. Pa Table 5 Operational settings and measured initial conditions for the Caterpillar C 3 H 8 engine [34]. Engine Speed/ % EGR 16 (rev/min) % EGR 16 (rev/min) 5% EGR 16 (rev/min) 1% EGR 1 (rev/min) % EGR 19 (rev/min) % EGR Ignition Timing ( ATDC) Residual Fraction (%) Temperature at IVC (K) The model constants C m 1 =. and C m = 1. were used in all simulated cases for this engine. As mentioned earlier, C m is the only crucial constant to be calibrated. Figure 6 shows comparisons of measured and predicted in-cylinder pressure and engine-out NO X for different spar timings (two groups of repeatedly measured NO X data are shown in 6b). As seen, the predicted results match the measured data reasonably well. The effect of EGR level on the combustion is shown in Fig. 7. An increase of EGR ratio slows down the combustion by reducing both the laminar and turbulent flame speeds (cf. Eq. (13)). The NO X emissions also decrease with increased EGR due to the reduction of pea temperature. The model captures the general trends very well, as shown by the good matching between the measured and predicted data. It needs to be noted that the total residual fraction in Eq. (18) includes both the EGR and the estimated internal residual (14.5%). Figure 8 shows the pressure traces and NO X data for different engine speeds. The predicted pressure curves generally match the experimental pressures reasonably well. The relatively large discrepancy between the measured and predicted NO X in the 1rpm case may

10 Measured - 4 O ATDC - 3 O ATDC 35 3 Pressure [ MPa ] O ATDC - 1 O ATDC NO X ( ppm ) Measured Data1 Measured Data Cran Angle [ O ATDC ] Spar Timing ( O CA ATDC ) (6a) (6b) Figure 6 In-cylinder pressure curves (6a) and engine-out NO X (6b) for the spar timing sweep. (EGR=%, engine speed=16 rev/min, residual fraction=14.5%) Measured % EGR % EGR 3 Pressure [ MPa ] % EGR Cran Angle [ O ATDC ] NO X [ ppm ] Measured EGR [ % ] (7a) (7b) Figure 7 In-cylinder pressure curves (7a) and engine-out NO X (7b) for the EGR level sweep. (Engine speed=16 rev/min, spar timing=-4 ATDC, residual fraction=14.5%) Pressure [ MPa ] Measured 1 rpm 16 rpm 19 rpm NO X [ ppm ] Measured Cran Angle [ O ATDC] Engine Speed [ RPM ] (8a) (8b) Figure 8 In-cylinder pressure curves (8a) and engine-out NO X (8b) for the engine speed sweep.(spar timing=-1 ATDC, EGR=%).

11 be due to the under-predicted pea pressure (and therefore pea temperature) compared to the experimental pressure. Figure 9 shows the simulated in-cylinder temperature profiles as the flame propagates out from the spar plug, where the blac contour line denotes the locations of the mean flame front ( G = iso-surface). As can be seen, the temperature of the mixture immediately behind the turbulent flame brush is above 5K, which is approximately equal to the local equilibrium temperature. Figure 1 shows the predicted in-cylinder species mass fractions of C 3 H 8, CO, CO, OH, NO and NO at -6 CA ATDC for the spar timing=-3 ATDC case. After the flame front passes, the parent fuel molecules are consumed. The subsequent chemistry process behind the flame brush is governed by the CO oxidation reactions, the H -O system reactions and the NO X formation mechanism. The mass fraction of NO reaches its pea value in the highest temperature region, as expected. Most of the NO is generated right ahead of the mean flame front. This is because NO formation is favored under relatively low temperature combustion conditions. Considering that the pea mass fraction of NO is two orders of magnitude less than that of NO, the NO emission is essentially negligible in this case. Figure 1 Species mass fractions at CA=-6 ATDC (Spar timing=-3 ATDC). MERCURY MARINE TWO-STROKE GDI ENGINE To further test the applicability of the models to partially premixed flames, a two-stroe marine gasoline DISI engine was also modeled. The specifications and tested conditions are listed in Table 6 [35]. The computing mesh at -77 ATDC is shown in Fig. 11. The direct injection combustion system of this engine employs an air-guided scheme. The engine has a flat-top piston and a high-pressure swirl-type injector that is centrally mounted in the dome-shaped cylinder head. The incylinder tumble flow transports the injected fuel to the spar plug that is located on the exhaust port side. A stratified mixture is formed around the spar gap at the time of the spar. Figure 9 In-cylinder temperature contours at different cran angles (Spar timing=-3 ATDC). Solid blac line indicates the flame front location. The simulations start from exhaust port open (-6 ATDC) and cover a full two-stroe engine cycle. The initial swirl ratio was set as because all the ports were still closed at this cran angle. The initial cell turbulence inetic energy density in the cylinder and all the ports was assumed to be uniform and estimated to be equal to the inetic energy density based on the mean piston speed. An inflow boundary condition was specified at the inlet of the boost port, where the experimentally measured cran case pressures were specified versus cran angles. The outlet of the exhaust port was set as an open boundary, where the measured exhaust pressures were specified versus cran angles. The scavenging and mixture formation processes have been studied by Tan and Reitz [36] in previous wor, and we focus only on the combustion phase in this study.

12 Boost Port Location of Spar Plug Exhaust Port Transfer Port Figure 11 Computational mesh of the Mercury Marine two-stroe gasoline direct injection engine. Pressure (MPa) Measured -41 O ATDC -31 O ATDC -1 O ATDC -16 O ATDC Cran Angle ( O ATDC) (1a) Table 6 Mercury Marine two-stroe GDI engine specifications and experimental conditions [35]. Bore Stroe (mm) Compression Ratio 7.4:1 Exhaust Port Timing ( ATDC) 95 Boost Port Timing ( ATDC) -43 Transfer Port Timing ( ATDC) -43 Injection Timing ( ATDC) -85 Engine Speed (rev/min) Spar Timing ( ATDC) -41, -31, -1, -16 Total Sprayed Fuel Mass (g) 7.9e-3 NO X (ppm) Measured Spar Timing ( O CA ATDC) (1b) To simulate the chemical inetics of gasoline combustion, a 1-species, 4-reaction isooctane (ic 8 H 18 ) mechanism was used. This mechanism is extracted from the reduced Primary Reference Fuel (PRF) mechanism of Tanaa et al. [37] by excluding the n-heptane (nc 7 H 16 ) related species and reactions. Four cases were simulated with a spar timing sweep. The simulated pressure traces and engine-out NO X were compared with the measured data. In the simulations of this engine, the model constants C m1 =. and C m = 3. were fixed and no case-by-case adjustment was made. Figure 1a shows the comparison of in-cylinder pressures. The matching between the measured [35] and predicted pea pressures and combustion phasing is reasonably good considering the complicated spray and flow conditions in this two-stroe configuration. The predicted NO X data are compared with the measured data in Fig. 1b. Although there are discrepancies in the absolute values, the general trends match pretty well. Figure 1 In-cylinder pressure curves (1a) and engineout NO X (1b) of Mercury Marine engine for spar timing sweep (Engine speed= rev/min). The development of the simulated flame front surface based on the updated laminar flame speed correlation (Eq. (17)) was also compared with the results using the previous correlation, Eq. (16), as shown in Fig. 13. It can be seen that the left side of the flame front becomes nearly stagnant after around 33 ATDC in the pictures in the left column. This is because the equivalence ratios of the mixture to the left side of this flame front branch are beyond the flammability limits predicted by Eq. (16). Physically, this prediction is not reasonable because it is well nown that isooctane/air mixtures leaner than φ =.65 are able to be ignited. In contrast, the predicted results of Eq. (17) loo more realistic. Although more fundamental study needs to be done for more accurate correlations of the flame speed of lean/rich mixtures, the improvement of Eq. (17) over Eq. (16) is considered to be necessary and considerable.

13 CONCLUSION Detailed chemical inetics was coupled with a G- equation combustion model for better predictions of fuel oxidation, pollutant formation. The integrated model was implemented into the KIVA-3V CFD code to simulate both homogeneous charge and stratified charge combustion in SI engines. A Caterpillar-converted homogeneous charge propane SI engine and a Mercury Marine GDI engine were modeled. The predicted incylinder pressure traces and engine-out NO X were compared with the measured data and good agreement was achieved for a wide range of operating conditions. The in-cylinder temperature and species mass fraction contours of selected cases were also shown and explained. Figure 13 Temperature contour evolution in the Mercury Marine engine showing the influence of the laminar flame speed correlations (Left column: predicted using Eq. (16); Right column: predicted using Eq. (17)). Previously proposed turbulent flame speed correlations were restudied and updated in the present model for a better description of the ignition ernel flame evolution. The laminar flame speed correlations were modified to account for very lean and very rich mixtures under partially premixed combustion conditions. The uent effect on the flame speed was also reconsidered for better matching with the experimental data. A new method based on the sub-grid scale unburnt/burnt volumes was suggested for the species conversion and primary heat release calculations within the turbulent flame brush. In this method, a numerically improved code based on the element potential method was used for the equilibrium calculations. This method proved to be effective of dealing with the consideration of large number of species. Methodologies of using detailed chemistry for the postflame heat release and pollutant formation calculations, and for end-gas autoignition predictions were also introduced. More emphasis will be placed on them in future wor. ACKNOWLEDGMENTS Figure 14 Species mass fractions and flow velocities at 35 ATDC (spar timing=-31 ATDC). Figure 14 shows the species mass fractions of ic 8 H 18, O, CO, OH, NO and velocity contours on a clip plane through the cylinder diameter at 35 ATDC (spar timing=-31 ATDC). As in Fig. 9, the blac lines represent the mean flame font location. At this time, the fuel within the burnt region has all broen down to smaller species. Most of the CO is generated behind the left branch of the flame font because some fuel and O are convected across the flame front from the left side by the in-cylinder flow, which can be seen from the velocity contours. Most of the OH and NO occur within the high temperature burnt region. Ford Motor Company is greatly acnowledged for the financial support of this project. The authors also than Dr. Youngchul Ra at the Engine Research Center for helpful discussions. REFERENCES 1. Abraham, J., Bracco, F. V., and Reitz, R. D., Comparisons of Computed and Measured Premixed Charge Engine, Combustion and Flame, 6: 39-3, Peters, N., Turbulent Combustion, Cambridge University Press,. 3. Bray, K. N. C., Libby, P. A., Recent Developments in the BML Model of Premixed Turbulent Combustion, Turbulent Reacting Flow, Academic Press, London, 1994.

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15 Pacage for the Analyses of Gas Phase Chemical Kinetics, Sandia Report, SAND 89-89, Hampson, G. J., A Theoretical and Experimental Study of Emission Modeling for Diesel Engines with Comparison to In-cylinder Imaging, Ph.D. Thesis, University of Wisconsin-Madison, Huda, E., Time-Resolved Exhaust Measurements of a Two-Stoe Direct-Injection Engine, Master Thesis, University of Wisconsin-Madison, Tan, Z., Fan, L. and Reitz, R. D., Modeling Ignition, Multi-component Fuel Vaporization and Spray Breaup in a DISI Engine, ILASS Americas, 14 th Annual Conference on Liquid Atomization and Spray System, Dearborn, MI, May, Tanaa, S., Ayala, F., and Kec, J. C., A Reduced Chemical Kinetic Model for HCCI Combustion of Primary Reference Fuels in a Rapid Compression Machine, Combustion and Flame, 133: , 3. CONTACT Long Liang Engine Research Center University of Wisconsin-Madison 15 Engineering Drive, Madison WI 5376, USA lliang@wisc.edu ABBREVIATIONS ATDC CTC DISI DPIK GDI EGR IVC PDF PRF SI After Top Dead Center Characteristic Timescale Combustion (Model) Direct Injection Spar Ignition Discrete Particle Ignition Kernel Gasoline Direct Injection Exhaust Gas Recirculation Intae Valve Closure Probability Density Function Primary Reference Fuel Spar Ignition