Swirl combustion is one of the most efficient approach to efficient combustion processes and therefore, it has received great interest particularly from aerospace industry. Swirl combustion has been studied in the past both experimentally and computationally. However, in spite of the extended studies, the swirl combustion is still not well understood and therefore, further studies are required. One of the open questions in the swirl combustion is the effect of the swirl number on the combustion efficiency and instabilities. Over decades, extensive experimental and computational studies of swirl combustion have been performed. The experimental studies of swirl combustion are quite challenging due to the unsteady nature of the combustion process. To overcome these challenges, computational studies have been used in the study of turbulent combustion. The present study concerns the effect of the swirl number on the combustion efficiency and flame stability. The combustion efficiency is assessed based on the temperature developed inside the combustion chamber and NOx levels. The effect of air/fuel blowing ratio on the combustion efficiency and instability is also investigated in this research. The computations are carried out using the large-eddy simulation (LES) approach along with the flamelet combustion model. The analysis reveals the unsteady nature of the flame and thus, its departure from the core of the combustor. The analysis also reveals the presence of a region of high level of temperature, NO and CO2, inside the combustor.