Enhancing the fidelity of steady flamelet-based LES of turbulent non-premixed flames using high-order compact finite difference schemes

Non-premixed turbulent combustion is central to many practical energy conversion systems, where turbulence drives the mixing of the fuel and oxidizer at the molecular scale in high-Reynolds number flows. In this study, high-order compact finite-difference schemes are studied as a means of enhancing the numerical fidelity of steady flamelet-based large eddy simulation (LES) for turbulent non-premixed flames. A Fortran-based LES model employing high-order compact finite-difference discretization is developed within a steady flamelet framework to solve the filtered compressible Navier–Stokes equations with an implicit Smagorinsky–Lilly subgrid-scale model in cylindrical coordinates. Spatial discretization is performed using fifth- and fourth-order compact schemes for the convective and viscous terms, respectively, while temporal integration is carried out using a fourth-order Runge–Kutta method. The computational framework is validated using benchmark turbulent pipe-flow data, along with detailed experimental measurements from the Sandia piloted Flame D benchmark flame. The proposed LES framework provides statistically converged predictions of velocity, mixture fraction, temperature, and major species (H2O and CO2). Moderate discrepancies are observed for carbon monoxide (CO), which are attributed to the steady-state chemistry assumption and its inability to fully represent finite-rate oxidation processes in post-flame regions. Predictions of nitric oxide (NO) show a marked improvement compared to results obtained using a conventional flamelet/progress-variable (FPV) formulation, highlighting the benefit of enhanced numerical fidelity in reducing numerical dissipation within a steady flamelet framework. Comparisons with FPV formulations that incorporate a separate transport equation for NO suggest that explicitly accounting for the transient evolution of NO remains important for accurately capturing the behavior of slow-forming species. The results suggest that the use of high-order compact finite-difference schemes presents coherent numerical formulation with enhanced accuracy compared to traditional FPV formulation in the simulation of turbulent flames and pollutant formation.