A-priori and a-posteriori studies of finite-rate chemistry based combustion models for turbulent spherical lean premixed hydrogen/air flames

Lean hydrogen combustion has emerged as a promising pathway to achieve high efficiency and low emissions in various energy and propulsion systems. However, the development of accurate turbulent combustion models for lean premixed hydrogen flames remains a significant challenge due to the complicated interplay between thermodiffusive instabilities and turbulence. In this study, the spherically expanding flame of a lean H${}_2$/air mixture is simulated in a homogeneous isotropic turbulence environment at engine-relevant conditions using both direct numerical simulation (DNS) and large-eddy simulation (LES). These simulations enable both a-priori and a-posteriori evaluations of finite-rate chemistry (FRC) based turbulent combustion models within the LES framework, with the focus on their abilities to predict turbulent burning velocity ($S_T$). Two combustion models are investigated in particular: the well-stirred reactor (WSR) model and the thickened flame model (TFM). A-priori evaluation is first carried out for the WSR model based on DNS results. It is found that WSR tends to over-predict $S_T$, which can be reproduced from a 1-D twin-premixed stretched laminar flame at high stretch rates. This indicates that such over-prediction is resulted from the response of local reaction rates to the LES filtering operation, rather than turbulence. In contrast, the a-posteriori test through LES shows that $S_T$ is significantly under-predicted by the WSR model. This is because the interactions between flame instabilities and turbulence are not sufficiently captured in LES/WSR, which leads to reduced flame wrinkling and stretching factors. The performance of the TFM model is also evaluated a-posteriori in LES. Results show that with flame thickening, the local flame reactivity is enhanced, while the flame wrinkling is reduced, resulting in limited improvement on the prediction of $S_T$ by LES/TFM. By introducing a proper correction factor to the efficiency function, the prediction by TFM can be largely improved, but the instantaneous $S_T$ is still not well reproduced. These findings highlight that caution needs to be taken when interpreting the a-priori analysis results for FRC-based turbulent combustion models. Results from this study further provide novel insights into potential pathways to improve turbulent combustion models such as TFM, especially in the context of turbulent lean premixed hydrogen flames.