A data driven Filtered Wrinkled Flamelet model for premixed hydrogen-air flames

In the next decades, hydrogen is expected to be used as a zero-carbon fuel for a plethora of applications rang- ing from heat generation, transportation and energy dis- tribution. However, the development of hydrogen based combustion devices is often hindered by the lack of re- liable predictive numerical simulations tools. A pecu- liar and key aspect of hydrogen-based flames is the in- trinsic thermal-diffusive (TD) instability of the flame front which is promoted by the elevated mobility of the hydrogen molecule. This happens especially for lean hydrogen-air mixtures when the fuel Lewis number Le decreases below a critical, sub-unity, Lewis number Le0 [1]. The onset of TD instability locally modulate the flame speed along the front, amplifying small amplitude perturbations leading to self-wrinkled, unsteady cellular flames [3]. Such effects are also amplified by the thermal expansion and the ensuing, ubiquitous Darrieus-Landau (DL) instability mechanism as shown in Fig.1. The impact of intrinsic instability, both TD and DL, is currently overlooked by state-of-art models used in LES simulations of turbulent premixed flames therefore motivating this contribution. A first step toward the in- clusion of intrinsic instability has been done in a recent work [5] where a data-driven, laminar, wrinkling factor model has been proposed. In the present contribution, we follow a different strategy [4] which takes advantage of the filtered tabulated chemistry approach and the F- TACLES formalism [2]. The present data driven Filtered Wrinkled Flamelet model, is based on the data driven generation of tables for each unclosed term. The data are collected from a filtered, fully resolved 2D simulation of a self-wrinkling instrinsically-unstable flame, using a fil- ter ∆filt and tabulated as conditional averages with re- spect to two filtered progress variables, φ(Ce1, Ce2; ∆filt) being φ a generic unclosed term. The effectiveness of the model is measured a- posteriori in terms of the capabilities of filtered simula- tions (see Fig.2) to reproduce the flame area and the con- sumption speed of a large-scale flame with L = 400lD, being L the hydrodynamic lengthscale and lD the flame thickeness. The main advantage of this approach is that the tables can be generated using data from a signifi- cantly smaller L ∼ 100lD, and therefore computationally cheaper, self-wrinkling simulation compared to the target large-scale flame.