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SAE TECHNICALPAPER SERIES 2006-01-0243

Spark Ignition Engine Combustion ModelingUsing a Level Set Method with

Detailed Chemistry

Long Liang and Rolf D. ReitzUniversity of Wisconsin – Madison

Reprinted From: Multi-Dimensional Engine Modeling 2006(SP-2011)

Detroit, MichiganApril 3-6, 2006

2006 SAE World Congress

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2006-01-0243

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

Long Liang and Rolf D. Reitz University of Wisconsin-Madison

Copyright © 2006 SAE International

ABSTRACT

A level set method (G-equation)-based combustion model incorporating detailed chemical kinetics has been developed and implemented in KIVA-3V for Spark-Ignition (SI) engine simulations for better predictions of fuel oxidation and pollutant formation. Detailed fuel oxidation mechanisms coupled with a reduced NOX mechanism are used to describe the chemical processes. The flame front in the spark kernel stage is tracked 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 tracked 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 spark kernel flame. To test the model, a homogeneous charge propane SI engine was modeled using a 100-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 spark timing, engine speed and EGR levels. The model was also applied to a stratified charge two-stroke 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 key 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 k-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 [2]. 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 in-cylinder 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 [2,6] subsequently extended this approach to the turbulent flame regime. The turbulent G-equation concept has been successfully applied to SI engine combustion simulations by Dekena 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 kinetic mechanisms. A large amount of work has been done on developing detailed chemical kinetic mechanisms for fuel oxidation and pollutant formation [10]. Further, research on mechanism reduction and parallel computing techniques have made it computationally affordable to incorporate the reduced detailed chemical kinetic mechanisms into multidimensional engine simulations. The objective of the current work is to incorporate detailed chemical

kinetics into the G-equation-based turbulent combustion model which was implemented into the KIVA-3V code by Tan et al. [11,12]. Specifically, for SI engine combustion, detailed fuel oxidation mechanisms coupled with a reduced NOX mechanism are applied behind the mean flame front for modeling post flame combustion and NOX formation. The chemical kinetic 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 [2], 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, 2G′′ , 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, 0

TS . These equations together with the Reynolds averaged Navier-Stokes equations and the turbulence modeling equations, form a complete set to describe premixed turbulent flame front propagation [2]. Considering the Arbitrary Lagrangian-Eulerian (ALE) numerical method used in the KIVA code, Tan [12] modified the convection term of the G transport equation to account for the velocity of the moving vertex, vertexv . Thus, the equation set suitable for KIVA

implementation is:

0( ) | | | |uf vertex T t

G v v G S G D Gt

ρκ

ρ∂

+ − ⋅∇ = ∇ − ∇∂

(1)

22 2

2 2

( ) ( )

2 ( )

uf vertex t

t s

G v v G D Gt

D G c Gk

ρρ

ε

′′∂ ′′ ′′+ − ⋅∇ = ∇ ⋅ ∇∂

′′+ ∇ −

(2)

1 222 2024 3 4 3

4 30 01 1

12 2

T

F FL L F

a b a bS l l u la bb l b lS s l

⎡ ⎤⎛ ⎞ ′⎢ ⎥= − + +⎜ ⎟⎢ ⎥⎝ ⎠⎣ ⎦

(3)

where fv is the fluid velocity vector, tD is the turbulent diffusivity, and 4a , 1b , 3b , and sc are modeling constants from the turbulence model or experiment (cf. Peters [2]). k and ε are the Favre mean turbulence kinetic energy and its dissipation rate from the RNG k - ε model [13]. u′ is the turbulence intensity. 0

LS is the unstretched laminar flame speed, and l and Fl are the turbulence integral length scale and laminar flame thickness, respectively. κ is the mean flame front curvature:

| |GG

κ⎛ ⎞∇

=∇⋅⎜ ⎟∇⎝ ⎠

(4)

The flame thickness, Fl , can be estimated by [14]:

0

0

( / ) |p TF

u L

cl

Sλρ

= (5)

where the / pcλ term is approximated by [15]:

0.74 g/ 2.58 10

cm sec 298KpTcλ − ⎛ ⎞= × ⎜ ⎟− ⎝ ⎠

(6)

In this work the inner layer temperature, 0T , was approximated as 1500K for the propane and iso-octane flames considered.

In the implementations both by Tan [11,12] and Ewald [9], a normal distance constraint | | 1G∇ = is applied beyond the flame front surface. In this case, the turbulent flame brush thickness, ,F tl , can be defined in

terms of 2G′′ as [2]:

0

2 1/ 2, ( ( , )) |F t G Gl G x t =

′′= (7)

It should be noted that Eq. (3) is for the fully developed turbulent flame, and the relation , 2F tl b l= was used in the derivation by Peters [2], where 2 1.78b = is a constant obtained from dimensional reasoning. It was shown by Peters [2] and Ewald [9] that the unsteady solution of ,F tl can be derived from Eq. (2) by assuming that the turbulence quantities tD , k , 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 2G′′ all vanish, and Eq. (2) can be reduced to an ordinary differential equation for the turbulent flame brush thickness (cf. [2]):

, 2 2 22 ,( / )

F ts s F t

dlb c l c l

d t τ= − (8)

where kτ ε= is used as a nondimensionalizing

timescale, and correlations relating tD , k , and ε to u′ , l , and τ have been used. Choosing , 0F tl = as the initial value at spark timing, an algebraic solution results:

1 2, 2 [1 exp( / )]F t sl b l c t τ= − − (9)

Based on Eq. (9), the unsteady turbulent flame speed is,

1 222 2024 3 4 3

4 30 01 1

12 2

TP

F FL L F

a b a bS l l u lI a bb l b lS s l

⎧ ⎫⎡ ⎤⎛ ⎞ ′⎪ ⎪⎢ ⎥= + ⋅ − + +⎨ ⎬⎜ ⎟⎢ ⎥⎝ ⎠⎪ ⎪⎣ ⎦⎩ ⎭

(10)

where 1 2

P [1 exp( / )]sI c t τ= − − (11)

Physically, the additional exponential term, PI , 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 kernel 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 kernel flame by Herweg et al. [16]. According to Peters [2], 2.0sc = 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 kernel 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, 2mC , while keeping the same scaling relation, i.e.,

1 2P 2[1 exp( /( ))]mI t C τ= − − ⋅ (12)

Although 2mC is regarded as tunable for different engines, it is fixed for all spark timing sweeps, rpm sweeps and Exhaust Gas Recirculation (EGR) sweeps for each specific engine in the present work.

Figure 1 Triple flame structure in DISI engines [11].

Although the above G-equation description was originally developed for premixed flames by Peters [2], 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 kinetics.

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:

0 0,

,

uL L ref dil

u ref ref

T PS S FT P

α β⎛ ⎞ ⎛ ⎞

= ⋅⎜ ⎟ ⎜ ⎟⎜ ⎟ ⎜ ⎟⎝ ⎠ ⎝ ⎠

(13)

where the subscript ref means the reference condition of 298K and 1atm. dilF is a factor accounting for the diluent’s effect. The fuel-type independent exponents α and β were correlated as functions of equivalence ratio as:

2.18 0.8( 1)α φ= − − (14)

0.16 0.22( 1)β φ= − + − (15)

The reference flame speed is given as:

0 2, 2 ( )L ref M MS B B φ φ= + − (16)

Values for MB , 2B and Mφ for propane and isooctane are listed in Table 1.

Table 1 Values for MB , 2B and Mφ with Eq. (16) Fuel MB (cm/s) 2B (cm/s) Mφ Propane 34.22 -138.65 1.08 Isooctane 26.32 -84.72 1.13

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 0.6 1.7φ< < , 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.,

( )( )20, expL refS ηωφ ξ φ σ= − − (17)

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 0.65 1.6φ< < . Gülder’s values and the new values are listed in Table 2, and a comparison of isooctane reference flame speeds from the different correlations is shown in Fig. 2. The same treatment can be adopted for other fuel types.

Table 2 Coefficient values in Eq. (17) for isooctane

ω η ξ σGülder [19] 46.58 -0.326 4.48 1.075

Present 26.9 2.2 3.4 0.84

0.0 0.5 1.0 1.5 2.0 2.50

10

20

30

40

50

S L,re

f0 [ c

m/s

ec ]

φ

Metghalchi et al. Gulder Present study

Figure 2 Comparison of laminar flame speed correlations for isooctane under reference conditions (T=298K, P=1atm).

The presence of diluent 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 dilF in Eq. (13). One expression suggested for all fuel

types is [20]:

1dil dilF f Y= − ⋅ (18)

where dilY is the mass fraction of diluent and f is an experimentally determined constant. Ryan et al. [21] suggested that 2.5f = is valid for 0 0.3dilY< < . Metgalchi et al. [20] suggested 2.1f = to be valid for 0 0.2dilY< < . Rhodes et al. [22] proposed another expression based on laminar flame speed measurements of indolene-air-diluent mixtures, viz.,

0.7731 2.06dil dilF X= − ⋅ (19)

where dilX is the mole fraction of the diluent.

In this study, we combined the correlations by Ryan [21] and by Metghalchi et al. [20], i.e., in Eq (18)

2.1 1.33 dilf Y= + ⋅ for 0 0.2dilY< < (20)

2.5f = for 0.2 0.476dilY< < (21)

However, it can be seen that this expression fails beyond 0.476dilY > 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 diluent 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.

0.00 0.05 0.10 0.15 0.20 0.25 0.30 0.35

0.2

0.4

0.6

0.8

1.0

F dil

Ydil

Metgalchi et al. Ryan et al. Present study

Figure 3 Comparison of different diluent 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 [12] suggested a method for calculating the species density change in the cells containing the mean flame front, viz.,

( ) , 4 0, ,

4

f iii u i b T

i

Ad Y Y Sdt Vρ

ρ= − (22)

where ρ is the average density of the mixture in cell, 4i . ,i uY and ,i bY are the mass fractions (i.e., fractions of

the total mass in the cell) of species i in the unburnt and burnt mixtures, respectively. fA is the mean flame front area and V is the cell volume. 4i is the cell index used in KIVA. Tan and Reitz [12] assumed seven species in their study, including fuel, O2, N2, CO2, H2O, CO, H2.

,i bY was also assumed to be the local equilibrium value. One issue associated with Eq. (22) is how to determine

,i uY . By assuming the ,i uY of N2, CO2, H2O, CO, H2 to be constantly equal to their initial values at the time of ignition, the ,i uY of fuel and O2 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 ,i uY 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 uV and a burnt volume bV , 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 tracked 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:

( ) , 4 0, ,

4

f iiu i u i b T

i

Ad Y Y Sdt Vρ

ρ= − (23)

Compared to Eq. (22), the cell averaged density ρ is replaced by the density of the unburnt mixture uρ and now the ,i uY and ,i bY are evaluated with respect to the mass of unburnt and burnt mixture, respectively, viz.,

, , 1i u i bi i

Y Y= =∑ ∑ (24)

Figure 4 Numerical descriptions of the turbulent flame structure and the flame containing cells.

The steps to determine the unburnt species mass fractions ,i uY are as follows:

1. Determine the equilibrium species mass fractions ,i bY and the adiabatic flame temperature b adiaT T= . In

this study, a Fortran code by Pope [23,24] was used for the calculation of the chemical equilibrium. This code is based on the element potential method as in the STANJAN code [25], but an improved numerical algorithm called Gibbs function continuation is adopted for better computational stability and efficiency.

2. Calculate the burnt gas density and the burnt species densities based on the equation of state and the mass fractions ,i bY from step 1.

4 ,i mix bb

u b

P MWR T

ρ⋅

= (25)

, ,i b b i bYρ ρ= ⋅ (26)

where ,mix bMW is the average molecular mass of the burnt mixture, and uR is the universal gas constant.

3. Calculate the unburnt species densities ,i uρ based on species mass conservation.

4 ,,

i i i b bi u

u

V VV

ρ ρρ

−= (27)

4. Finally, determine the unburnt species mass fractions:

,,

,

i ui u

i ui

Yρρ

=∑

(28)

In KIVA, the heat release due to the chemistry source term is directly related to the species conversion [26]. It needs to be noted that the four species associated with the NOX formation mechanism, i.e., NO, NO2, N, and N2O [27], are excluded from the equilibrium calculation due to their relatively short residence time within the flame front, and the relative slow rate of the NOX 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 kinetics-controlled should be answered by further experimental or Direct Numerical Simulation (DNS) investigations. In this study, the computational cells

Vb

Vu

Mean Flame Front

Burnt

Unburnt

behind the flame front are modeled as Well Stirred Reactors (WSR). Detailed hydrocarbon oxidation chemical kinetic 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 H2-O2 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 kinetic timescale. This kinetic timescale can be selected as the conversion timescale of a heat-release-rate-limiting species, such as CO (cf. Kong et al. [28]).

A nine-reaction reduced NOX mechanism was coupled with the hydrocarbon oxidation mechanism for predicting the formation of NO and NO2. The reactions include [27]:

2N NO N O+ ⇔ + (29a)

2N O NO O+ ⇔ + (29b)

2 2N O O NO+ ⇔ (29c)

2 2 2N O OH N HO+ ⇔ + (29d)

2 2( ) ( )N O M N O M+ ⇔ + + (29e)

2 2HO NO NO OH+ ⇔ + (29f)

2NO O M NO M+ + ⇔ + (29g)

2 2NO O NO O+ ⇔ + (29h)

2NO H NO OH+ ⇔ + (29i)

Chemical kinetics based end-gas autoignition modeling

It is generally accepted that engine knock 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 knock is the Livengood-Wu integral [29], 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, Eckert et al. [30] applied the “Shell” autoignition model to simulate the autoignition of the end-gas in SI engines. Research on detailed chemical kinetic 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 makes it possible to accurately describe the location and intensity of the end-gas autoignition in SI engines without tuning any reaction rate constants. In this study, detailed chemical kinetic mechanisms are also applied in each cell in front of the mean flame front. The auto-ignited mixture can be tracked by monitoring certain species that characterize the high temperature heat release, such as the OH radical. Although no knocking modes are considered in the test cases in this paper, this methodology will be followed in our future study of engine knock.

IGNITION KERNEL MODEL

The growth of the ignition kernel is tracked by using the DPIK model by Fan, Tan, and Reitz [11,31]. By assuming a spherical shaped kernel, the flame front position is marked 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 kernel to be uniform, the kernel growth rate is:

( )k uplasma T

k

drS S

dtρρ

= + (30)

where kr is the kernel radius, uρ is the local unburnt gas density, and kρ is the gas density inside the kernel region.

The plasma velocity plasmaS is given as [8]:

24 ( )

spk effplasma

uk u k u

k

QS

r u h P

η

ρπ ρρ

⋅=

⎡ ⎤− +⎢ ⎥

⎣ ⎦

(31)

where spkQ is the electrical energy discharge rate, effη is the electrical energy transfer efficiency due to heat loss to the spark plug. 0.3effη = , as suggested by Heywood [32] is used in this study. uρ and uh are the density and enthalpy of the unburnt mixture. kρ and ku are the density and internal energy of the mixture inside the kernel.

The laminar flame speed 0LS in Eq. (10) was multiplied

by a stretch factor, 0I , which accounts for strain and curvature effects, and the modified correlation is used as the turbulent flame speed, TS , in the kernel stage. 0I follows the suggested expression of Herweg et al. [16]:

3 21 2

0 01 215

uF F

k kL

l luIl rS

ρρ

⎛ ′ ⎞⎛ ⎞= − − ⋅⎜ ⎟⎜ ⎟⎝ ⎠ ⎝ ⎠

(32)

Note that curvature effects are also considered in the present combustion model by the last term of Eq. (1).

The chemistry processes in the kernel 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 kernel particles, thus providing the necessary information for the chemical heat release calculations.

The transition from the kernel model to the turbulent G-equation model follows the same criterion as the one used in the previous work by Tan and Reitz [36],

namely, that the transition is controlled by a comparison of the kernel radius with a critical size which is proportional to the locally averaged turbulence integral length scale, viz.,

3 2

1 1 0.16k m mkr C l Cε

≥ ⋅ = ⋅ (33)

where 1mC is a model constant. Compared with the previous work by Tan [8], where two different turbulent flame speed correlations were applied in the kernel model and in the G-equation combustion model, 1mC is no longer as crucial in the model calibration since the turbulent flame speed correlations used in the kernel 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-stroke Mercury Marine DISI gasoline engine. In the simulations, CHEMKIN II [33] was used for solving the detailed chemical kinetics.

CATPILLAR-CONVERTED PROPANE ENGINE

The experimental data for the homogeneous charge Caterpillar propane engine cover different operating conditions, including a spark 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 100-species, 539-reaction propane mechanism from the Lawrence Livermore National Lab (LLNL) was used in the calculations [10].

Figure 5 shows a 360˚ mesh and a 2D sector mesh of the axially symmetric cylinder. The 2D sector mesh with periodic boundaries was used due to CPU time considerations. The spark plug is located at the center of the cylinder head, and is represented using stationary particles, as implemented by Fan [31]. The initial in-cylinder mixture was assumed to be completely homogeneous. The simulations start from IVC. The initial swirl ratio was set as 0.78 according to experimental measurements. The initial turbulence kinetic energy was assumed to be uniform in the cylinder, with an estimated value equal to the kinetic energy based on the mean piston speed.

360˚ full mesh 2D sector mesh

Figure 5 Computational meshes of Caterpillar converted propane SI engine at -30˚CA ATDC.

Table 4 Caterpillar C3H8 engine specifications.

Engine CAT 3401 SI Gas Retrofit

Bore × Stroke (mm) 137.16 × 165.1 Compression Ratio 10:1 Equivalence Ratio Stoichiometric

Spark Duration (ms) 2 Intake Valve Closure (˚) -147 ATDC

Initial Pressure at IVC (kPa) 51.0 kPa

Table 5 Operational settings and measured initial conditions for the Caterpillar C3H8 engine [34].

Engine Speed/% EGR

Ignition Timing

(˚ATDC)

Residual Fraction

(%)

Temperature at IVC

(K) 1600 (rev/min)

0% EGR -10 -20 -30 -40

14.5

367.8

1600 (rev/min)5% EGR

-10 14.5 361.7

1600 (rev/min)10% EGR

-10 14.5 362.0

1000 (rev/min)0% EGR

-10 17 339.4

1900 (rev/min)0% EGR

-10 13 346.9

The model constants 1 2.0mC = and 2 1.0mC = were used in all simulated cases for this engine. As mentioned earlier, 2mC is the only crucial constant to be calibrated.

Figure 6 shows comparisons of measured and predicted in-cylinder pressure and engine-out NOX for different spark timings (two groups of repeatedly measured NOX 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 NOX emissions also decrease with increased EGR due to the reduction of peak 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 NOX 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 NOX in the 1000rpm case may

-100 -80 -60 -40 -20 0 20 40 60 80 1000.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

- 10O ATDC

- 20O ATDC

- 30O ATDC

- 40O ATDC Measured Predicted

Pre

ssur

e [

MP

a ]

Crank Angle [ O ATDC ]

-50 -40 -30 -20 -10 00

500

1000

1500

2000

2500

3000

3500

4000

NO

X ( p

pm )

Spark Timing ( OCA ATDC )

Measured Data1 Measured Data2 Predicted

(6a) (6b)

Figure 6 In-cylinder pressure curves (6a) and engine-out NOX (6b) for the spark timing sweep. (EGR=0%, engine speed=1600 rev/min, residual fraction=14.5%).

-100 -80 -60 -40 -20 0 20 40 60 80 1000.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

10 % EGR

5 % EGR

0 % EGR

Pre

ssur

e [ M

Pa

]

Crank Angle [ O ATDC ]

Measured Predicted

0 2 4 6 8 100

500

1000

1500

2000

2500

3000

3500

4000

NO

X [ p

pm ]

EGR [ % ]

Measured Predicted

(7a) (7b)

Figure 7 In-cylinder pressure curves (7a) and engine-out NOX (7b) for the EGR level sweep. (Engine speed=1600 rev/min, spark timing=-40˚ ATDC, residual fraction=14.5%).

-100 -80 -60 -40 -20 0 20 40 60 80 100

0.0

0.5

1.0

1.5

2.0

2.5

3.0

1900 rpm

1600 rpm

1000 rpm

Pre

ssur

e [ M

Pa

]

Crank Angle [ O ATDC]

Measured Predicted

1000 1200 1400 1600 1800 20000

400

800

1200

1600

2000

2400

NO

X [ p

pm ]

Engine Speed [ RPM ]

Measured Predicted

(8a) (8b)

Figure 8 In-cylinder pressure curves (8a) and engine-out NOX (8b) for the engine speed sweep.(Spark timing=-10˚ ATDC, EGR=0%).

be due to the under-predicted peak pressure (and therefore peak temperature) compared to the experimental pressure.

Figure 9 shows the simulated in-cylinder temperature profiles as the flame propagates out from the spark plug, where the black contour line denotes the locations of the mean flame front ( 0G = iso-surface). As can be seen, the temperature of the mixture immediately behind the turbulent flame brush is above 2500K, which is approximately equal to the local equilibrium temperature.

Figure 10 shows the predicted in-cylinder species mass fractions of C3H8, CO2, CO, OH, NO and NO2 at -6˚ CA ATDC for the spark timing=-30˚ 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 H2-O2 system reactions and the NOX formation mechanism. The mass fraction of NO reaches its peak value in the highest temperature region, as expected. Most of the NO2 is generated right ahead of the mean flame front. This is because NO2 formation is favored under relatively low temperature combustion conditions. Considering that the peak mass fraction of NO2 is two orders of magnitude less than that of NO, the NO2 emission is essentially negligible in this case.

Figure 9 In-cylinder temperature contours at different crank angles (Spark timing=-30˚ ATDC). Solid black line indicates the flame front location.

Figure 10 Species mass fractions at CA=-6˚ ATDC (Spark timing=-30˚ ATDC).

MERCURY MARINE TWO-STROKE GDI ENGINE

To further test the applicability of the models to partially premixed flames, a two-stroke 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 in-cylinder tumble flow transports the injected fuel to the spark plug that is located on the exhaust port side. A stratified mixture is formed around the spark gap at the time of the spark.

The simulations start from exhaust port open (-262˚ ATDC) and cover a full two-stroke engine cycle. The initial swirl ratio was set as 0 because all the ports were still closed at this crank angle. The initial cell turbulence kinetic energy density in the cylinder and all the ports was assumed to be uniform and estimated to be equal to the kinetic 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 crank case pressures were specified versus crank angles. The outlet of the exhaust port was set as an open boundary, where the measured exhaust pressures were specified versus crank angles. The scavenging and mixture formation processes have been studied by Tan and Reitz [36] in previous work, and we focus only on the combustion phase in this study.

Figure 11 Computational mesh of the Mercury Marine two-stroke gasoline direct injection engine.

Table 6 Mercury Marine two-stroke GDI engine specifications and experimental conditions [35].

Bore × Stroke (mm) 85.8 × 67.3 Compression Ratio 7.4:1

Exhaust Port Timing (˚ ATDC) 95 Boost Port Timing (˚ ATDC) -243

Transfer Port Timing (˚ ATDC) -243 Injection Timing (˚ ATDC) -85 Engine Speed (rev/min) 2000 Spark Timing (˚ ATDC) -41, -31, -21, -16

Total Sprayed Fuel Mass (g) 7.29e-3

To simulate the chemical kinetics of gasoline combustion, a 21-species, 42-reaction isooctane (iC8H18) mechanism was used. This mechanism is extracted from the reduced Primary Reference Fuel (PRF) mechanism of Tanaka et al. [37] by excluding the n-heptane (nC7H16) related species and reactions. Four cases were simulated with a spark timing sweep. The simulated pressure traces and engine-out NOX were compared with the measured data. In the simulations of this engine, the model constants 1 2.0mC = and

2 3.0mC = were fixed and no case-by-case adjustment was made.

Figure 12a shows the comparison of in-cylinder pressures. The matching between the measured [35] and predicted peak pressures and combustion phasing is reasonably good considering the complicated spray and flow conditions in this two-stroke configuration. The predicted NOX data are compared with the measured data in Fig. 12b. Although there are discrepancies in the absolute values, the general trends match pretty well.

-100 -50 0 50 1000.0

0.5

1.0

1.5

2.0

2.5

3.0

-16 OATDC

-21 OATDC

-31 OATDC

-41 OATDC Measured Predicted

Pre

ssur

e (M

Pa)

Crank Angle (O ATDC)

(12a)

-45 -40 -35 -30 -25 -20 -150

100

200

300

400

500

600

700

800

NO

X (p

pm)

Spark Timing (OCA ATDC)

Measured Predicted

(12b)

Figure 12 In-cylinder pressure curves (12a) and engine-out NOX (12b) of Mercury Marine engine for spark timing sweep (Engine speed=2000 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 known that isooctane/air mixtures leaner than

0.65φ = are able to be ignited. In contrast, the predicted results of Eq. (17) look 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.

Boost Port

Transfer Port

Exhaust Port

Location of

Spark Plug

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)).

Figure 14 Species mass fractions and flow velocities at 35˚ ATDC (spark timing=-31˚ ATDC).

Figure 14 shows the species mass fractions of iC8H18, O2, CO, OH, NO and velocity contours on a clip plane through the cylinder diameter at 35˚ ATDC (spark timing=-31˚ ATDC). As in Fig. 9, the black lines represent the mean flame font location. At this time, the fuel within the burnt region has all broken down to smaller species. Most of the CO is generated behind the left branch of the flame font because some fuel and O2 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.

CONCLUSION

Detailed chemical kinetics 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 in-cylinder pressure traces and engine-out NOX 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.

Previously proposed turbulent flame speed correlations were restudied and updated in the present model for a better description of the ignition kernel flame evolution. The laminar flame speed correlations were modified to account for very lean and very rich mixtures under partially premixed combustion conditions. The diluent 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 post-flame heat release and pollutant formation calculations, and for end-gas autoignition predictions were also introduced. More emphasis will be placed on them in future work.

ACKNOWLEDGMENTS

Ford Motor Company is greatly acknowledged for the financial support of this project. The authors also thank Dr. Youngchul Ra at the Engine Research Center for helpful discussions.

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CONTACT

Long Liang Engine Research Center University of Wisconsin-Madison 1500 Engineering Drive, Madison WI 53706, USA lliang@wisc.edu

ABBREVIATIONS

ATDC After Top Dead Center CTC Characteristic Timescale Combustion (Model) DISI Direct Injection Spark Ignition DPIK Discrete Particle Ignition Kernel GDI Gasoline Direct Injection EGR Exhaust Gas Recirculation IVC Intake Valve Closure PDF Probability Density Function PRF Primary Reference Fuel SI Spark Ignition