A fast RANS method for methane-air non-premixed combustion is proposed, using a k-ω SST model for turbulence, a transport species model for chemistry and eddy dissipation model for turbulence-chemistry interaction. The method is validated with experimental data from Sydney Swirl Flow and Flame Database. The same method is then used to simulate a two-dimensional axisymmetric combustor liner geometry, and finally a Design Exploration is proposed to optimize the Pattern Factor at the combustor outlet, obtaining the response surface for the entry variables, namely the Swirl Number and mass flows for each row of holes. An optimal combustor configuration is chosen. The results are then discussed and compared to similar works, showing the viability of the simplified CFD simulation and DoE optimization methodology.