Numerical studies of turbulent swirling reacting flows are performed using unsteady Reynolds-averaged Navier-Stokes (URANS) and large-eddy simulation (LES) approaches. Aiming at the reduction of computational costs, the present research assesses the feasibility of URANS for the computations of turbulent reacting flows. The conserved scalar-mixture fraction-based thermo-chemical variables are described using the steady laminar flamelet model. The Favre-filtered scalars are obtained from the presumed beta probability density function (β–PDF) approach. The flow field exhibits upstream recirculation zone due to the bluff body and a downstream vortex breakdown region induced by the swirling flow. The study reveals that the strength of the vortex decays with the increase of distance from the injection region. The temperature exhibits high values in the region surrounding the flame. The present research shows that in spite of its low computational cost, the URANS approach is quite dissipative when compared with LES. Therefore, LES is a more appropriate approach for the numerical simulation of turbulent combustion, when the solution accuracy is of concern.