Large eddy simulation of a growing turbulent premixed flame kernel using a dynamic flame surface density model

The relevant description of a flame kernel growth in homogeneous isotropic turbulence environment is a key ingredient for the simulation of combustion in spark-ignited internal combustion engine. A small flame kernel burns at an increasing rate as it grows and becomes progressively more and more wrinkled by the prevailing turbulence. Large eddy simulation (LES) models based on algebraic expressions for the turbulent flame speed, the flame surface density or the flame wrinkling factor cannot reproduce such a situation because they assume an equilibrium between turbulence and flame wrinkling which is generally not reached during the simulation as the flame is laminar at early stages. A possible solution is to solve an additional balance equation for the flame surface density or for the wrinkling factor but a promising alternative is to implement a dynamic model where the wrinkling factor, measuring the subgrid scale flame surface, is automatically determined along the computation from the known instantaneous resolved flame front. A Germano-like identity expresses the conservation of the total flame surface at filter and test filter scales to automatically adjust the parameter of a fractal-like wrinkling factor model from the instantaneous resolved flame front characteristics. This model is tested against the experimental data of Renou et al. (2000) [33] to reproduce the temporal evolution of the flame kernel growth. For a range of ignition parameters, preliminary results are in good agreements with experimental data and show that the model parameter evolves with time and depends on operating conditions, validating the dynamic procedure.