Designing a combustion chamber for gas turbines is considered both a science and an art. This study presents a comprehensive methodology for designing an annular combustion chamber tailored to the operating conditions of a CFM-56 engine, a widely used high bypass ratio turbofan engine. The design process involved calculating the basic criteria and dimensions for the casing, liner, diffuser, and swirl, followed by an analysis of the cooling sections of the liner. Numerical simulations using NUMECA software and the HEXPRESS meshing tool were conducted to predict the combustion chamber’s behavior and performance, employing the κ-ε turbulence model and the Flamelet combustion model. Methane was used as the fuel, and simulations were performed for three fuel injection angles: axial, 45°, and 60°. Results demonstrate that the combustion chamber is properly dimensioned and achieves complete combustion for all configurations. The pressure ratio is 0.96, exceeding the minimum design criteria. Additionally, the emissions of unburned hydrocarbons are zero, while nitrogen oxides and carbon monoxide levels are below regulatory limits. These findings validate the proposed design methodology, ensuring efficient and environmentally compliant combustion chamber performance.