Combustion research currently aims to reduce emissions, whilst improving the fuel economy. Burning fuel in excess of air, or lean-burn combustion, is a promising alternative to conventional combustion, and can achieve these requirements simultaneously. However, lean-burn combustion poses new challenges, especially for internal combustion (IC) engines. Therefore, models used to predict such combustion have to be reliable, accurate and robust.

In this work, the flamelet approach in the Reynolds-Averaged Navier- Stokes framework, is used to simulate flames relevant to spark-ignition IC engines. A central quantity in the current modelling approach is the scalar dissipation rate, which represents coupling between reaction and diffusion, as well as the flame front dynamics.

In the first part of this thesis, the predictive ability of two reaction rate closures, viz. strained and unstrained flamelet models, are assessed through a series of experimental test cases. These cases are: spherically propagating methane- and hydrogen-air flames and combustion in a closed vessel. In addition to these models, simpler algebraic closures are also used for comparison.

It is shown that the strained flamelet model can predict unconfined, spherically propagating methane-air flames reasonably well. By comparing spherical flame results with planar flames, under identical thermochemical and turbulence conditions, it is shown that the turbulent flame speed of spherical flames are 10 to 20% higher than that of planar flames, whilst the mean reaction rates are less influenced by the flame geometry.

Growth of the flame brush thickness in unsteady spherical flames have been attributed to turbulent diffusion in past studies. However, the present analyses revealed that the dominant cause for this increase is the heat-release induced convective effects, which is a novel observation.

Unlike methane-air flames, hydrogen-air flames have non-unity Lewis numbers. Hence, a novel two degrees of freedom approach, using two progress variables, is used to describe the thermochemistry of hydrogen-air flames. Again, it is shown that the strained flamelet model is able to predict the experimental flame growth for stoichiometric hydrogen-air flames. However, none of the models used in this work were able to predict lean hydrogen-air flames. This is because these flames are thermo-diffusively unstable and the current approach is inadequate to represent them.

When combustion takes place inside a closed vessel, the compression of the end gases by the propagating flame causes the pressure to rise. This is more representative of real IC engines, where intermittent combustion takes place. The combustion models are implemented in a commercial computational fluid dynamics (CFD) code, STAR-CD, and it is shown that both strained and unstrained flamelet models are able to predict the experimental pressure rise in a closed vessel.

In the final part of this work, a spark-ignition engine is simulated in STAR-CD using the flamelet model verified for simpler geometries. It is shown that this model, together with a skeletal mechanism for iso-octane, compares reasonably well with experimental cylinder pressure rise. Results obtained from this model are compared with two models available in STAR- CD. These models require some level of tuning to match the experiments, whereas the modelling approach used in this work does not involve any tunable parameters.