Turbulent auto-igniting diffusion flames are common in combustion systems, where the mixing of the fuel jet with the outer oxidant flow is the fundamental mechanism for the flame ignition and development. The paper presents a critical analysis on the Reynolds-Averaged-Navier-Stokes (RANS) simulation of a methane-air flame, done with a two equations turbulence model, in comparison with detailed experimental data. In the first part, the non-reactive jet is simulated with the standard ?? ? ?? model and a modified version, obtained with motivated changes of the ??m and ??k constants. In the second part the reactive jet is simulated, introducing a consistent modification of the ??c constant, in the eddy dissipation concept (EDC) model. The comparison with experimental data confirms the validity of the proposed model and highlights the effect of the proper turbulent jet development on the mechanisms of the diffusive flame ignition and propagation.