A 0-D flame wrinkling equation to describe the turbulent flame surface evolution in SI engines

The current development of reciprocating engines relies increasingly on system simulation for both design activities and conception of algorithms for engine control. These numerical simulation tools require high computational efficiencies, as calculations have to be performed in times close to real-time. Then, they are today mainly based on simple empirical laws to describe the combustion processes in the cylinders. However, with the rapid evolution of emission regulations and fuel formulation, more and more physics is expected in combustion models. A solution consists in reducing 3-D combustion models to build 0-dimensional models that are both CPU-efficient and based on physical quantities. This approach has been used in a previous work to reduce the 3-D ECFM (Extended Coherent Flame Model), leading to the so-called CFM1D. A key feature of the latter is to be based on a 0-D equation for the flame wrinkling derived from the 3-D equation for the flame surface density. The objective of this paper is to present in details the theoretical derivation of the wrinkling equation and the underlying modeling assumptions as well. Academic validations are performed against experimental data for several turbulence intensities and fuels. Finally, the proposed model is applied to engine simulations for a wide range of operating conditions. Comparisons are successfully conducted between in-cylinder measurements and the model predictions, highlighting the interest of reducing 3-D CFD models for calculations performed in the context of system simulation.