S.I. engine modelling

Multi-dimensional CFD models

Multidimensional modelling has been adopted as a powerful tool to investigate and analyse phenomena occurring in internal combustion engines, particularly with the rapid increase of computer power in recent years. Theoretically, a full-scale integration of CFD model of fine grid design with detailed chemical kinetics model provides unrivalled simulation accuracy and details of in-cylinder flow and combustion behaviours. However, a model at this numeric scale requires substantial CPU computing speed, large-scale storage and robust and fast numerical algorithm. Even with today’s advanced high performance computers, the simulation time of such models is still measured in weeks or months.

Several solutions have been proposed trying to find the balance between the computational costs and the simulation accuracy. Reitz et al. (2006) adopted a 7-species chemical equilibrium model into his multi-dimensional engine model. The turbulent flame location, local temperature and pressure and the heat release rate are computed using KIVA-3V CFD codes with a mesh size in the range of 2-5mm. Burnt products are assumed to reach thermodynamic and chemical equilibrium states immediately behind the flame brush.

Other researchers proposed cost-reduction solution methods that either adopted a global or reduced chemical kinetics mechanism (Li et al. 2003; Kong & Reitz 1993; Ali et al. 2003) or a reduced CFD mesh to one- or two-dimensional (Iida et al. 2003;

Iwashiro et al. 2002). These methods suffer from either degraded simulation accuracy or computational costs that are still relatively high.

Aceves et al. (2000) was among the first researchers who presented hybrid approach that formed a segregated sequential CFD multi-zone thermo-kinetic model. In the

16

model, a detailed chemical kinetics model is implemented into a KIVA-2.1 CFD solver and a multi-zone thermodynamics model. The CFD model is responsible for solving the temperature and mixture formation process in the compression stroke until the ignition timing. The multi-zone model takes over from the ignition and simulates the combustion and expansion processes. These zones are defined by mass distribution and mixing between adjacent zones is disallowed. The model was validated against experimental results and showed good capability of predicting cylinder pressure and burn rate. The model also successfully reduced the computation time scale from weeks or months to hours or days. However, the model failed on the prediction of HC and CO emissions which are critical in modern engine design.

Quasi-dimensional multi-zone models

Quasi-dimensional models are used to simulate the ‘closed’ part of the S.I. engine cycle as they cannot properly predict the intake and exhaust strokes due to their dimensionless nature (Verhelst & Sheppard 2009). Quasi-dimensional models are distinguished from zero-dimensional models by the inclusion of certain geometrical parameters in the basic thermodynamic approach. This usually includes the radius of a thin flame front that separates the burnt and unburnt zones, creating a two-zone formation.

One advantage of these zero-dimensional models is the avoidance of the modelling of the in-cylinder process. Instead of considering the intake, mixture preparation, combustion and exhaust processes, a zero-dimensional model uses a pre-defined mass burning rate, also known as the Wiebe function (Liu & Chen 2009), to describe the combustion process. When the engine operating point stays the same Wiebe functions provide unrivalled simulation accuracy as it, in fact, works back from known experimental results. However as each Wiebe function is empirically defined as a specific engine operating point, extrapolation to other operating points is problematic.

17

Most quasi-dimensional S.I. engine models adopt a two-zone formation, assuming that the flame is a ultimately thin transition layer that transport mass and energy between the burnt and unburnt zones (Liu & Chen 2009). Additionally, the flame is assumed to be adiabatic and in chemical and thermodynamic equilibrium. The unburnt mass entrained into the flame is assumed to be consumed and transferred into burnt mass instantaneously. The burnt mixture composition is calculated using chemical equilibrium at a pre-defined combustion temperature and pressure. Typically, up to 12 species are considered in the equilibrium calculation: H₂O, H₂, OH, H, N₂, NO, N, CO₂, CO, O₂, O and Ar (Verhelst & Sheppard 2009). The actual number of species considered varies when the interests of the simulation shifts from just the combustion process. Reitz et al. (2006) used a 7-species chemical equilibrium system to determine the burnt mixture composition but an additional 10-species and 9-reaction kinetics model was adopted to predict the formation of NO and NO₂. Liu et al. (2009) proposed an zero-dimensional two-zone model to study the knock in S.I.

engine. A chemical equilibrium containing 32 species was used in Liu’s model. The larger equilibrium system was chosen in order to keep accordance to the number of species included in the reduced chemical kinetics mechanism used to predict end gas autoignition.

In additional to the two-zone layout, some researchers developed a thermal boundary layer between the unburnt zone and the cylinder wall (Fiveland & Assanis 2001;

Puzinauskas & Borgnakke 1991; Borgnakke et al. 1980), as shown in Fig. 2-2. The addition of the boundary layer aids the fundamental understanding of the heat transfer process inside the cylinder.

18

Fig. 2-2 Illustration of the interactions between the adiabatic core and the thermal boundary layer in a two-zone HCCI engine combustion model (Fiveland

& Assanis 2001).