A novel treatment for radiative absorption in flamelet modelling

Flamelet models are widely used in combustion analysis, yet their integration of radiative re-absorption effects remains inadequately explored. This study introduces a novel Lagrangian radiative absorption flamelet model, which maps the radiative absorption term from physical space to the mixture fraction space, ensuring enhanced consistency in the radiative absorption between the Computational Fluid Dynamics (CFD) level and the flamelet level. For comparison, three Eulerian approaches from the existing literature are also examined: two employing steady flamelet solutions and one utilising unsteady flamelet equations under the effect of radiative emission. The performance of these four models is evaluated against fully resolved simulations that solve the full transport equations for all species (FTE) in a laminar methane–air diffusion flame, where a numerical experiment is conducted by introducing different radiation levels. While the Eulerian models align with FTE results at lower radiation levels, they exhibit increased deviations as radiation intensifies. However, these Eulerian models still achieve reasonably satisfactory predictions over a wide range of optical thicknesses, provided the flame does not undergo extinction. Compared to the steady Eulerian flamelet methods, the unsteady Eulerian flamelet model is more sensitive to enhanced radiation levels; its suboptimal performance in optically thick flames is justified by a timescale analysis showing its inability to adapt to changes in mixing in flames with strong radiation. Moreover, none of the Eulerian models is able to capture radiative extinction or account for potential heat gain from strong radiative absorption in optically thick flames. In contrast, the proposed Lagrangian model demonstrates robust accuracy in predicting temperature and species across all radiation levels. This study underscores the superior modelling accuracy of the proposed Lagrangian approach at elevated radiation levels and highlights the constraints of the studied Eulerian flamelet models under such conditions.