Numerical Simulations and Validation of Engine Performance Parameters Using Chemical Kinetics

Abstract

Use of detailed chemistry augments the combustion model of a three-dimensional unsteady compressible turbulent Navier–Stokes solver with liquid spray injection when coupled with fluid mechanics solution with detailed kinetic reactions. Reduced chemical reaction mechanisms help in the reducing the simulations time to study of the engine performance parameters, such as, in-cylinder pressure in spark ignition engines. Sensitivity analysis must be performed to reduce the reaction mechanism for the compression and power strokes utilizing computational singular perturbation (CSP) method. To study a suitable well-established surrogate fuel, an interface between fluid dynamics and chemical kinetics codes must be used. A mesh independent study must be followed to validate results obtained from numerical simulations against the experimental data. To obtain comprehensive results, a detailed study should be performed for all ranges of equivalence ratios as well as stoichiometric condition. This gives rise to the development of a reduced mechanism that has the capability to validate engine performance parameters from stoichiometric to rich mixtures in a spark ignition engine. The above-mentioned detailed methodology was developed and implemented in the present study for premixed and direct injection spark ignition engines which resulted in a single reduced reaction mechanism that validated the engine performance parameters for both engine configurations.

1. Introduction

In Computational Fluid Dynamics (CFD), many simplifications and assumptions are made to the mathematical models to make them computationally affordable. The rapid development and progress in the field of computer processors and enhancement of computer memory has enabled scientists and engineers to review and revisit some of the assumptions. This has helped to improve and enhance the predictive capabilities of computer modeling. This approach has also been implemented in engine simulation codes and tools. The objective of this study and research is to identify the reactions that govern the chemical kinetics of fuel oxidization and move from multi-step global reactions to a reduced number of elementary reactions that can better model the combustion and engine performance parameters [1].

For the development of future fuels and the optimization of automotive engines, computer modeling and simulation has proved itself as an inseparable tool alongside experimental study. Due to computational limitations, the traditional approach has been to utilize simplified global reactions to simulate and evaluate the combustion and performance parameters in internal combustion engines. Due to increased interest in various advanced engine configurations with various combustion modes and injection strategies, this approach could reduce credibility of the predictions for advanced concepts since it depends on arbitrary adjustment of model parameters.

Oxidation of hydrocarbons is shown by detailed chemical kinetic mechanisms. These detailed mechanisms are very large and comprised of a large number of species and reactions. As the size of the hydrocarbon increases, the length (number of species and reactions) of the mechanism increases along with it. Due to the construction from smaller hydrocarbons (HC) progressing to larger HC and intermediate radicals, detailed mechanisms of large hydrocarbons consist of many species and reactions that are redundant. Those species do not have significant impact on simulating ignition and combustion phenomenon and needlessly raise the computational and memory requirements. These reactions and species can be identified and eliminated from the detailed reaction mechanism without compromising the accuracy and integrity of the detailed reaction mechanism. The detailed and large mechanisms cannot be employed in present solvers because they are time expensive. For example, gasoline and diesel fuels consist of thousands of reactions and hundreds of hydrocarbons [2].

Fuels, such has gasoline and diesel, are composed of hundreds of hydrocarbons. These hydrocarbons include alkanes, alkenes, aromatics and naphthenes. Surrogate fuel mechanisms that contain limited number of hydrocarbons from all the above-mentioned hydrocarbon types are important in this regard. There is a necessity to use reduction techniques to produce reduced order mechanisms that can replicate the predictions of detailed mechanisms [3]. The reduction techniques decrease the number of species and reactions.

Redundant reactions were identified by two methods [1, 2, 3]:

1. reaction rates analysis and,

2. sensitivity analysis

In a reaction mechanism, there are two subsets of reactions; slow reactions and fast reactions. The reaction rates analysis divides a reaction mechanism into above-mentioned two subsets of slow and fast reactions. The sensitivity analysis is performed to divide the reaction mechanism into two subsets of rate limiting and non-rate limiting reactions. When combined, both analyses identify redundant reactions. The redundant reactions identified by this method are non-rate limiting slow reactions. As the redundant reactions are eliminated, the species taking part in those reactions gets automatically eliminated, hence, a reduced mechanism is obtained [1, 2, 3]. Sensitivity analysis is discussed further in detail in the next section with detailed references.

Using the computational singular perturbation (CSP) technique [4, 5], reduction of iso-octane/n-heptane reaction mechanism by Soyhan et al. [4] and Valorani et al. [5] has been performed that has resulted in reduced and skeletal mechanisms.

Using various computational codes [6, 7, 8, 9, 10, 11, 12, 13, 14, 15] and experimental tools, various researchers performed multiple studies to review surrogate fuel mixtures [8], reduced PRF mechanisms [9], with variable intake parameters including an operating range of equivalence ratios, intake pressures and temperatures while considering various engine performance parameters such as heat release rate (HRR) analysis, in-cylinder pressure data [10] and emissions on various engine geometries operating at various operational ranges [11, 12]. Using a mixture of iso-octane, n-heptane and toluene as gasoline surrogate fuel predicts engine performance parameters correctly, especially in HCCI and SI engines. Further addition of di-isobutylene and methylcyclohexane is also recommended. Under stoichiometric and lean conditions, significant number of small particulate formation occurs while large particulate formation shows existence with increasing equivalence ratio. Decrease in the peak in-cylinder pressure can be achieved by mass and temperature reduction. This phenomenon occurs due to heat loss to the chamber walls [13].

A reaction mechanism reduction through sensitivity analysis of a skeletal reaction mechanism for the compression and power strokes by utilizing computational singular perturbation (CSP) method and using the low temperature reaction pathway analysis leads to a reaction mechanism that predicts accurate results for computational studies. Detailed chemistry in conjunction with fluid dynamics enhances the ability of a computational code to correctly predict the engine performance parameters. This is proven in benchmarking the global and quasi-global mechanisms [1] which provided necessary data and confidence in the use of detailed chemistry to correctly predict the engine performance parameters. Also, using 90% iso-octane and 10% n-heptane as surrogate fuel for gasoline helps in correct prediction and best modeling the engine performance parameters. Along with a correct reduced mechanism, mesh independent study is a key to correctly predict and validate the engine performance parameters against the experimental data for a range of equivalence ratios in premixed spark ignition engines.

2. Materials and methods

KIVA-3 V [7] is a code developed by Los Alamos National Laboratory for numerical calculation of transient, two- and three-dimensional chemically reactive fluid flows with sprays [1]. It is used to perform numerical simulations which were then used to compare and investigate the variation against the experimental data for a premixed case in a spark ignition engine. To perform the studies, iso-octane is used as a gasoline surrogate.

CHEMKIN [16] has many modules; one of which is SENKIN [17] that performs sensitivity analysis and subsequent reduction of skeletal reaction mechanism. Extraction of the sensitivity data using SENKIN leads to the next step of performing mechanism reduction using KINALC [18] which uses the computational singular perturbation (CSP) method. Sensitivity analysis for spark ignition (SI) engines is performed for both the compression and power strokes since combustion occurs in some portion of each stroke. CSP analysis utilizes to set the size of the time criterion for the characteristic chemical reaction in such a way that fast reactions are discarded from the reduced chemical reaction mechanism while rate limiting reactions are included into the reduced reaction mechanism since the slower reactions are the rate-controlling reactions [19]. On the other hand, fast reactions cause magnification of the inaccuracies which makes the numerical methods to be unstable. The best way to set the time criterion for CSP is such that it encompasses the combustion process to the end of power stroke. This in effect creates a reduced mechanism that encompasses for the full duration of combustion process, therefore, the selected reactions selected are sensitive and important to the whole combustion process in the engine. For performing the numerical simulation using the reduced reaction mechanism, a mixture of 90% iso-octane and 10% n-heptane is recommended to be used as a gasoline surrogate.

The comprehensive analysis discussed above, helps in construction of a reduced reaction mechanism which mitigates experimental results as well as promotes a greater understanding of the chemical kinetics. Experimental results obtained from [20, 21] for premixed case, at equivalence ratio of 0.98 and 1.3 are mitigated to prove the accuracy of the above-mentioned process. For this, an engine geometry used 85.96 mm bore, 94.6 mm stroke, compression ratio of 11.97 running at 2100 rpm. Engine performance parameters of in-cylinder pressure and heat release rate showed a comparative analysis.

Due to chemical stiffness and large size of reaction mechanisms, computations based on detailed reaction mechanisms are complex. Therefore, it is required to reduce chemical mechanisms. This can be performed using the two levels of reductions mentioned below. As a result, the reduced mechanism is extracted which is a subset of the detailed reaction mechanism.

Level I - Skeletal Reduction: Methods used to eliminate unimportant species and reactions: Directed relation graph (DRG), DRG with error propagation (DRGEP), path flux analysis (PFA), revised DRG (DRGMAX), and computational singular perturbation (CSP) [22].

Level II – Global Reduction Methods: Methods used for analysis of timescale impact on reaction mechanism: Computational singular perturbation (CSP), and quasi-steady-state approximation (QSSA) [22].

The first step to reduce the detailed reaction mechanism to a skeletal reaction mechanism is the elimination of unimportant species using the DRG method which identifies the species closely coupled with major species, such as fuel and oxidizer [19]. This is achieved from a sensitivity analysis that uses Jacobian matrix or sensitivity matrix that can be normalized. The Jacobian matrix is the matrix of all first-order partial derivatives of a vector valued function [19]. This method is important for reduction of a large reaction mechanism. The reduced skeletal mechanisms obtained from DRG are not minimal in size due to assumption of the upper-bound error propagation. A more straightforward definition of DRG is,

$${\mathit{r}}_{\mathit{A},\mathit{B}}=\frac{{\sum }_{\mathit{j}=\mathbf{1},\mathit{I}}\mid {\mathrm{\nu }}_{\mathit{A},\mathit{i}}{\mathit{\omega }}_{\mathit{i}}{\mathit{\delta }}_{\mathit{Bi}}\mid }{{\sum }_{\mathit{j}=\mathbf{1},\mathit{I}}\mid {\mathrm{\nu }}_{\mathit{A},\mathit{i}}{\mathit{\omega }}_{\mathit{i}}\mid }$$E1

where, ${\mathrm{\delta }}_{\mathrm{Bi}}=1$, if the ith elementary reaction involves species B, otherwise, 0; r_AB is the relative error induced to species A by elimination of B, subscript ‘i’ represents the ith elementary reaction and ‘j’ represents the jth species, ν_A is the net stoichiometric coefficient of species A, ${\mathrm{\omega }}_{\mathrm{i}}={\mathrm{\omega }}_{\mathrm{f},\mathrm{i}}-{\mathrm{\omega }}_{\mathrm{b},\mathrm{i}}$ where ω_f,i, ω_b,i and ω_i is the forward, backward and net reaction rates respectively, that can be calculated from the already given coefficients and activation energy in the CHEMKIN input file. If r_A,B < ϵ for all species, then the relation between B and A is considered to be negligible. Species B is selected when r_A,B ≥ ϵ. Here ϵ is a user-defined small threshold value. In most cases, ϵ = 0.1 is used [23, 24]. Since ϵ is a user-defined small threshold value, it depends on the application and user experience.

The second step is to further reduce the skeletal mechanism by using the technique called directed relation graph-aided sensitivity analysis (DRGASA). This method further reduces the species set by performing the sensitivity analysis on the already obtained species data from the previous DRG method. The parameters that are focused for the DRGASA method are ignition delays, extinction times, and laminar flame speeds. The reduction with this method is carried out using for a range of pressure, temperature and equivalence ratio. These two steps provide the researchers with a skeletal mechanism.

Skeletal mechanisms are still too large to be used in the computational work and it is important to reduce the skeletal mechanism into a reduced mechanism. A major advancement in the CSP technique has been introduction of a new concept of using a vector G that represents the rate of change of species mass fraction (Y) and temperature (T). Numerical computations are used to monitor any contributions to vector G. Identification of various terms becomes straightforward with this method as it can help identify the reactions that are controlling the reaction, constant terms and chemical species that have depleted [24]. The ODEs given for a reactive system,

$$\mathit{G}=\frac{\mathit{dy}}{\mathit{dt}}={\mathrm{S}}_{\mathrm{r}}{\mathrm{F}}_{\mathrm{r}}\mathrm{,}\mathrm{\text{where}}\mathrm{y}\mathrm{=}{\mathrm{y}}_{\mathrm{i}}\mathrm{\text{and}}{\mathrm{y}}_{\mathrm{i}}\mathrm{=}{\mathrm{Y}}_{\mathrm{i}}\mathrm{\text{or}}\mathrm{T}$$E2

where, S_r is the stoichiometric vector and F_r is the reaction rate of rth reaction [25].

$$\mathit{G}=\frac{\mathit{dy}}{\mathit{dt}}={\mathrm{S}}_{\mathrm{r}}{\mathrm{F}}_{\mathrm{r}}={\mathrm{\nu }}_{\mathrm{r}}{\mathrm{q}}_{\mathrm{r}}$$E3

$${\mathrm{\nu }}_r={\left[{\mathrm{\nu }}_1{\mathrm{\nu }}_2\dots \dots \dots {\mathrm{\nu }}_n\right]}^T$$E4

where, r = 1, ….., N and n = 1, …, s. Here ‘r’ is number of reactions and ‘n’ is number of species.

All the reactions in the reactive system form the vector G.

$$\frac{\mathit{dG}}{\mathit{dt}}=\mathrm{J}.G,\mathrm{J}=\frac{\mathit{dG}}{\mathit{dy}}$$E5

where, J is a Jacobian. G is divided into fast and slow subspace. The following steps are performed to solve a CSP problem [25]:

1. Identify S_r and F_r (or alternatively ν_r and q_r respectively, both symbols are synonymous here) from a given G(y)

2. Find Jacobian

3. Find eigenvalues, λ

4. An eigenvalue is considered large if, $\mid \mathrm{\lambda }\mathrm{\Delta t}\mid >1.0$, where Δt is the time step.

5. Determine the total number of large eigenvalues (m) from step 4.

6. Since, reaction mechanism is composed of fast and slow reactions, therefore, $\mathrm{G}\left(\mathrm{y}\right)={\mathrm{G}}_{\text{fast}}+{\mathrm{G}}_{\text{slow}}$. To determine G_fast and G_slow, first find the characteristic chemical timescale of each reaction by taking the negative reciprocal of the eigenvalues determined in Step 3, i.e. $-1/\mathrm{\lambda }=\mathrm{\tau }$. This timescale calculation will show the magnitude of fast and slow reactions.

7. Eliminate fast reactions. If step 4 satisfies, fast reactions can be eliminated.

Using the CSP method, a term is only discarded or eliminated when it becomes numerically too small that it does not make any difference. This is determined by the importance index Eq. (6). CSP, as a reduction method, has been used by other researchers successfully [19, 26, 27].

Lu and Law [19] developed the CSP method for the removal of the unimportant reactions. The method used an importance index that eliminates the unimportant species. For the above-mentioned method, the importance index of the reaction is defined as

$${\mathit{I}}_{\mathit{A},\mathit{i}}=\frac{\mid {\mathrm{\nu }}_{\mathit{A},\mathit{i}}{\mathit{q}}_{\mathit{i}}\mid }{{\sum }_{\mathit{j}=\mathbf{1},{\mathit{N}}_{\mathit{R}}}\mid {\mathrm{\nu }}_{\mathit{A},\mathit{j}}{\mathit{q}}_{\mathit{j}}\mid }$$E6

where, ‘A’ is species, ‘i’ is reaction and ‘q’ is overall reaction rate of the ith reaction. Also, ν_A,j is the stoichiometric coefficient of species A in the jth reaction. It must be noted that a reversible reaction must be treated as a single reaction [19].

If I_A,I < ϵ_Reac for all species, then the reaction is an unimportant reaction where ϵ_Reac is a user-defined small threshold.

The parameter ϵ_Reac is a dimensionless parameter and can be defined as [26]:

$${ϵ}_{\mathit{\text{Reac}}}=\mid \frac{{\mathrm{\tau }}_{\mathit{\text{fast}}}}{{\mathrm{\tau }}_{\mathit{\text{slow}}}}\mid$$E7

|τ_fast| is the slowest relevant time scale for the fast reaction group and |τ_slow| is the fastest relevant time scale for the slow reaction group [25]. τ is defined as the characteristic chemical time scale. The characteristic time scales are negative reciprocals of the diagonal elements of the problem’s Jacobian [27].

Simplification of detailed model is achieved by eliminating the following [5]:

1. Species having weakly coupled chemical kinetics with the species of interest and,

2. the reactions deemed unimportant to the species that are retained.

The above procedure results in a smaller kinetic mechanism. This smaller mechanism is formed from the detailed mechanism and is a subset of the detailed mechanism. The accuracy of the skeletal mechanism is defined with respect to the species that are declared of interest for the problem and the domain of applicability defined for the problem. The domain of applicability is defined on the following criterion [5]:

1. the type of problem defined, for example, various types of reactors, ignition, flame speed and structure, etc., and

2. the defined range of initial conditions and mixture concentration. Reference problems would be solved for a specified range of initial conditions such as pressure, initial temperature, and mixture concentration specified by equivalence ratio.

Reaction flow analysis can prove to be very helpful with complex reactions. If the reaction rate satisfies the following condition for all times t, then the reaction rate is unimportant [25]:

$$\mid {\mathit{RR}}_{t,r,s}\mid <\mathrm{\epsilon }\left|{\mathit{Max}}_{r=1,2,\dots .M}{\mathit{RR}}_{t,r,s}\right|s=1,2,\dots \mathit{Nt}=0,\dots ,t_{\mathit{\text{total}}}$$E8

where, ε is a very small value which is arbitrarily specified, ‘r’ is elementary reaction number, and ‘s’ is number of species.

The physics of the process of reaction of complex hydrocarbons follows the three basic reaction steps: chain-initiating reactions, chain-branching/carrying reactions and chain-terminating reactions. Chain-initiating reactions are those elementary reactions that produce free radicals. Similarly, free radicals are destroyed in chain-terminating reactions. Chain-propagating reactions or chain-carrying reactions are defined as the elementary reactions where the ratio of free radicals in products to the free radicals in reactants is equal to 1. If this ratio is greater than 1, then the reactions are called chain-branching reactions [28]. Concentrations of free radicals are treated as constant as they remain essentially constant throughout the reaction, except for the short initial and final periods which is minimal as compared to the entire reaction period.

High temperature oxidation of paraffins (C_nH_2n + 2) that are larger and more complex than the methane is much more complicated as they include many complex hydrocarbons in the mixture. Over the years, the evolution of combustion science has developed detailed combustion mechanisms for those smaller hydrocarbons that are now part of various combustion libraries. Therefore, it is possible to develop a general framework for the complex combustion process [28].

The first step in the combustion process of larger paraffins (C_nH_2n + 2) is that rather than directly breaking into CH₃, it first breaks down into hydrocarbon radicals of lower order, C_nH_2n + 1. The hydrocarbon radicals of higher order are highly unstable and are further broken down to CH₃ and a lower order olefinic compound, C_n-1H_2n-2. For hydrocarbons larger than C₃H₈, the process of fission takes place between the olefinic compound and a lower order radical. Further reactions of those radicals include intermediate steps that eventually form the methyl (CH₃) radical. Also, formaldehyde formed during the reactions is rapidly attacked in flames by the O, H, and OH atoms. Therefore, formaldehyde in found only in trace amounts in flames. The situation is more complex for fuel rich hydrocarbon flames [28].

Hydrocarbons follow a similar set of steps for combustion and oxidation. The difference between various hydrocarbons requires further intermediate steps but they go through the same oxidation procedure. The process of complex hydrocarbon oxidation occurs in the following manner [29]:

1. Carbon▬carbon (C▬C) bond is broken: The C▬C bonds are primarily broken over H▬C bond because C▬C bonds are much weaker than H▬C bonds.

2. H-atom abstraction: Resulting hydrocarbon radicals further break down into olefins (hydrocarbons with double carbon bonds, C〓C) and H-atoms.

3. Radical formation: Creation of H-atoms forms a pool of radicals.

4. Formation of radicals gives pathways for fuel molecules to attack O, OH and H atoms.

5. Hydrocarbon radicals again decay via H-atom abstraction.

6. Formyl radical (HCO) and Formaldehyde (CH₂O) are formed.

7. Radical reacts with O-atoms that result in the formation of carbon monoxide (CO).

8. Carbon monoxide (CO) oxidation occurs and results in the formation of carbon dioxide (CO₂).

A skeletal mechanism [9] was selected and used for further reduction. The skeletal mechanism was enhanced with extended Zeldovich mechanism for the formation of NO_x emissions which resulted in 299 reactions and 75 species. Reduction was performed using the CSP technique to achieve 53 reactions and 44 species in the reduced mechanism.

The reduced mechanism was used in the KIVA-CHEMKIN interface to make it part of the KIVA input file. Simulations were performed for the same conditions performed in the engine study for premixed engine [20, 21]. This reaction mechanism has proved to predict and validate the results for both stoichiometric and fuel-rich conditions. Sensitivity analysis using SENKIN was performed for both compression and power stroke as the combustion takes place during some part of both strokes.

2.1 Premixed case

Experimental results obtained from [20, 21] for premixed case, at equivalence ratio of 0.98 and 1.3 show validation and improved prediction of the engine performance parameters of in-cylinder pressure and heat release rate (HRR). Figure 1 and Table 1 show the pentroof engine geometry with no moving valves.

Figure 1.

Pentroof engine geometry [1, 30] – isometric view and mesh.

Dimension	Unit	Value
Compression Ratio	[−]	11.97
Bore	[mm]	85.96
Stroke	[mm]	94.6
Connecting Rod Length	[mm]	152.4
Clearance Volume	[cm^3]	50.0
Displacement	[cm^3]	549.0
Engine Speed	[rpm]	2100

Table 1.

Engine geometry [1, 20, 21].

A mesh independent study performed for the reduced mechanism utilized three meshes shown in Table 2. Validation studies are performed to compare the general trend of the engine performance parameters. Figure 1 shows the isometric view of mesh # 3.

	Mesh # 1	Mesh #2	Mesh # 3
Number of cells	100,000	178,000	230,000

Table 2.

mesh independent study.

2.2 Direct-injection case

Similar analysis was performed for injection case [31, 32] for the engine geometry shown in Table 3, where validation of peak in-cylinder pressure was performed against the experimental data. In this case, mass fractions were calculated based on equivalence ratio of 1.

Dimension	Unit	Value
Compression Ratio	[−]	9.4
Bore	[mm]	89.0
Stroke	[mm]	81.4
Displacement	[cm^3]	0.51 L
Engine Speed	[rpm]	1500

Table 3.

Engine geometry – direct injection.

The mixture is injected at 30^o BTDC for 1.75 ms or an equivalent of 15.75^o. The mixture is ignited at 14^o BTDC. The initial temperature is 302 K and the pressure is 76 ± 1 kPa [31, 32]. The cylinder wall temperature, cylinder fire deck temperature, and the piston temperature are set at 400 K. Mass fractions for fuel and oxidizer are calculated. The fuel is 90% iso-octane and 10% n-heptane [33] given the complexity of a multi-component detailed chemistry model.

The analysis results again showed better agreement of in-cylinder pressure data with the reduced reaction mechanism for the direct injection case (Figure 2).

Figure 2.

Pentroof engine geometry [1, 30] – isometric view with mesh.

3. Results and discussion

To better predict the engine performance parameters of in-cylinder pressure and heat release rate (HRR), detailed chemistry is incorporated into the CFD model. To achieve this, KIVA-CHEMKIN interface is used to extract reaction rates and reaction constants for the reaction data and, heat of formation and molecular weights for the species data, that is used for input into KIVA simulations. The reduced reaction mechanism has 53 reactions and 44 species.

3.1 Premixed case

3.1.1 In-cylinder pressure and heat release rate, Φ = 0.98

For a mixture of 90% iso-octane (iC₈H₁₈) and 10% n-heptane (nC₇H₁₆) at ϕ = 0.98, numerical simulations were performed for comparison and validation are performed for in-cylinder pressure at the ignition timing of 20^o BTDC. Figure 3 shows the validation results showing a good agreement and prediction of in-cylinder pressure against the experimental data.

Figure 3.

In-cylinder pressure; 100,000, 178,000 & 230,000 cells.

Figure 4 shows a good agreement of predicted heat release rate (HRR) obtained from the numerical solution from the reduced mechanism using KIVA-CHEMKIN interface against the experimental data. HRR is the ratio of difference in heat release values and corresponding crank angle values. These values are obtained from KIVA output file. This also shows that detailed chemistry is very important to capture the correct trend of engine performance parameters. The reduced mechanism achieved from this research has given a confident deduction that the numerical simulations for ϕ = 0.98 has successfully modeled the engine performance parameters of in-cylinder pressure and heat release rate (HRR). It is recommended to build a library of reduced mechanisms for all the fuels that are used in the internal combustion engines so that the correct prediction of experimental results can be recorded and achieved.

Figure 4.

Heat release rate (HRR); 100,000 cells.

3.1.2 In-cylinder pressure and heat release rate, Φ = 1.3

Numerical simulations and comparison is performed below for a mixture of 90% iso-octane (iC₈H₁₈) and 10% n-heptane (nC₇H₁₆) at ϕ = 1.3 using the reduced mechanism.

Good prediction of in-cylinder pressure for ϕ = 1.3 is achieved using the reduced mechanism and is shown in Figure 5.

Figure 5.

In-cylinder pressure; 100,000, 178,000 & 230,000 cells.

Figure 6 shows the heat release rate (HRR) for ϕ = 1.3. The results for Heat release rate (HRR) obtained from the numerical solution from the reduced mechanism using KIVA-CHEMKIN interface again shows a good prediction. This also shows that detailed chemistry is very important to capture the correct trend of engine performance parameters.

Figure 6.

Heat release rate (HRR); 100,000, 178,000 & 230,000 cells.

3.1.3 Emissions

Apart from validating the engine performance parameters of in-cylinder pressure and heat release rate (HRR), this study also validated the emission results with the experimental data [21]. The engine-out exhaust emission data is shown in Figure 7 for the exhaust species of H₂, CO₂ and CO. The results show a good agreement between the numerical and experimental results for the equivalence ratio of ϕ = 0.98 and ϕ = 1.3, where the predicted values of exhaust species of H₂, CO₂ and CO obtained through combustion-CFD simulations exactly match the experimental data at the equivalence ratio of ϕ = 0.98. At ϕ = 1.3, H₂ and CO values obtained through numerical simulations exactly match and overlap the experimental value while CO₂ values also show a good agreement. The results obtained from Figure 7 shows that the reduced mechanism developed was able to validate the engine performance parameters as well as the emissions which makes this reduced model reliable in predicting performance parameters for premixed spark ignition engines.

Figure 7.

Emissions.

3.2 Direct-injection case

Numerical simulations are performed for the direct-injection case at equivalence ratio of 1.0. The pentroof engine geometry and mesh is shown in Figure 2 and specification are mentioned in Table 3. There are no moving valves in the geometry.

Results shown in Figure 8 and Table 4 represent the importance of using the detailed chemistry in the CFD solvers where detailed chemistry has improved and better predicted the engine performance parameters.

Figure 8.

Maximum or peak in-cylinder pressure (breakup model on).

	Experimental Value [31], MPa	Global Mech, MPa	Quasi-Global Mech, MPa	Reduced Mech, MPa
Numerical Simulation	2.51	2.61	2.58	2.51
Deviation	—	3.98%	2.78%	0%

Table 4.

Maximum or peak in-cylinder pressure at stoichiometric conditions for direct-injection case.

To test the effect of the breakup model, numerical simulations were performed for global mechanism, quasi-global mechanism and, reduced mechanism obtained through this research, with breakup model turned off. The global reaction mechanism still over predicted the results of in-cylinder pressure while the quasi-global mechanism under predicted the results. Summary of results is given in Table 5.

	No Residual		With Residual
Mechanism	Breakup ON	Breakup OFF	Breakup ON	Breakup OFF
Global	2.62	2.55	3.04	2.75
Quasi-Global	1.78	1.82	2.09	1.72
Reduced	—	—	2.51	2.35

Table 5.

Summary of results for breakup model analysis.

4. Conclusions

Development of a single reduced mechanism was performed for SI engine geometries and configurations which required performing sensitivity analysis and reduction of the skeletal reaction mechanism using SENKIN, a sensitivity analysis module of CHEMKIN. The extraction of the sensitivity data from SENKIN using KINALC was then performed and a mechanism reduction was completed using the computational singular perturbation (CSP) method. This helped in minimizing the computational time by using fewer required reactions and species. A reduced mechanism was then constructed that validated engine performance and combustion parameters of in-cylinder pressure, heat release rate, and emissions for a range of equivalence ratios utilizing the low temperature pathway analysis.

A well-established surrogate, such as iso-octane, was selected for study as gasoline is a complex mixture of various compounds and hydrocarbons. The fundamental research provided the data and mechanistic understanding needed for the development of a library for detailed mechanisms that can be used to correctly predict engine performance parameters.

Understanding of the reduction techniques, and a practical reduced reaction mechanism for spark-ignition engines and combustion has been achieved through the above-mentioned methodology. Also, it has shown the need for using detailed chemistry in reactive flow problems which can help predict the combustion and engine performance parameters more accurately. To gain the necessary data and confidence for use of detailed chemistry, benchmarking was performed using the global and quasi-global mechanisms in a previous study.