Efficient modeling of the complex dynamics between flow physics and chemical kinetics during flame propagation is crucial for understanding combustion mechanisms in real-world applications such as propulsion, energy conversion, and emission control. A two-dimensional, high-order, compact finite difference computational fluid dynamics (CFD) code in cylindrical coordinates has been developed to investigate the interaction between flow and chemistry in a laminar non-premixed flame. The numerical framework (implemented in Fortran) employs a fifth-order scheme for convective terms and a fourth-order scheme for viscous terms to enhance the resolution of steep gradients characteristic of reacting flows. Conversely, a fourth-order Runge–Kutta (RK4) time integration scheme improves solution stability and reduces the convergence error by approximately 20% compared to the simpler Euler-forward (EF) method. To accurately capture the intricate coupling between flow and chemistry, the steady flamelet model (SFM) with detailed kinetics is incorporated into the CFD framework, enabling a reduced yet robust representation of chemical kinetics. The model is validated against benchmark experimental and numerical datasets, demonstrating strong agreement and predictive capability, with 60% and 15% lower Root Mean Squared Error (RMSE) for temperature and H2O mole fraction, compared to the species-transport-based numerical results. A systematic parametric study was conducted using a canonical co-flow laminar methane–air diffusion flame configuration. The effects of varying Reynolds number, fuel-to-air velocity ratio, and combustor geometry are analyzed in detail. The study reveals that increasing the combustor length leads to more anchored and spatially confined flame structures. Additionally, the study demonstrates that increasing the inner diameter enhances radial diffusion, resulting in more dispersed flame fronts. These findings underscore the role of combustor geometry in optimizing designs for both efficiency and emissions control. Furthermore, the proposed higher-order scheme advances reactive flow modeling by offering a validated and computationally efficient tool for high-resolution simulations of chemically reacting flows.
Haque et al. (Fri,) studied this question.