Hybrid presumed pdf and flame surface density approaches for Large-Eddy Simulation of premixed turbulent combustion. Part 2: Early flame development after sparking

This paper is the second part of a work addressing the coupling of presumed probability density function (pdf) with flame surface density (FSD) for the premixed flame modeling in a Large-Eddy Simulation (LES) framework. The main objective of this work is to propose approaches able to correctly describe local flame speed as well as detailed chemistry. Models based on the tabulation of flamelet structures, like Presumed Conditional Moments-Flame Prolongation of Intrinsic Low Dimensional Manifolds (PCM-FPI), appear as good candidates to account for complex chemistry. However, it was shown in the first part that the β-shape of the pdf provides reliable propagating velocities only in a restricted operating range. On the other hand, FSD models, like Extended Coherent Flame Model for LES (ECFM-LES), based on a transport equation for the filtered FSD, naturally enable to control the flame speed but generally rely on a simplified description of chemical kinetics. Hybrid models coupling FSD and presumed-pdf, called PCM-CFM (I and II), were then proposed in the previous part (Lecocq et al. [Combust. Flame 158 (6) (2011) 1201–1214]) to combine the strengths of these two approaches. In many industrial devices, such as spark–ignition engines or gas turbines, a premixed flame is initiated through the electrical discharge of a spark plug. The early flame development that follows is of major importance for the history of the flame front propagation and should then be precisely reproduced. The aim of this second paper is thus to propose modelings of spark–ignition that can be coupled to PCM-CFM models. Such a modeling is also investigated for PCM-FPI in order to understand if its operating range determined in the first part of this work can be extended to highly unsteady configurations such as flame kernel development. The sub-model AKTIM-Euler is then chosen among the models of the literature to treat spark–ignition, as it can include many physical features, notably the electrical circuit characteristics. Couplings are proposed between AKTIM-Euler and PCM-FPI as well as PCM-CFM I and II, thus providing full models accounting for detailed chemistry effects for gas composition. Canonical test cases of spherical flames expanding in a frozen turbulence are first performed to validate the functionality of these models. Notably, several strategies linking AKTIM-Euler and PCM-FPI, in terms of transition timing and Sub-Grid Scale scalar dissipation rate closure are tested, allowing to retain two different options. The experiment of Renou et al. [Combust. Flame 123 (2000) 507–521], for which the flame kernel was tracked at several equivalence ratios and moderate turbulent intensities, is then used for quantitative comparisons with the various models proposed. While PCM-CFM approaches coupled to AKTIM-Euler work well in all conditions, PCM-FPI does not allow the burned gases pocket transmitted by the ignition model to grow. This result can be explained by the lack of prediction capabilities of β-presumed pdf in weakly turbulent flow with a coarse mesh resolution, as shown in the first part of this work. Consequently, synthetic tests are carried out in higher turbulent conditions, more representative of those found in industrial configurations. The PCM-FPI response looks better, close to the one brought by the hybrid models, especially when using a Bi-Modal-Limit closure of scalar dissipation rate. Nevertheless, close quantitative comparisons show discrepancies between this version of PCM-FPI and the PCM-CFM approaches in terms of characteristic wrinkling of the flame front.