Numerical simulations of combustion efficiency were performed for buoyancy-driven turbulent diffusion flames with a controlled air-nitrogen co-flow, including conditions that lead to full flame extinction. Numerical simulations of combustion efficiency are performed for a laboratory flame. The numerical simulations used FireFOAM and a flame extinction model based on the concept of a critical flame Damköhler number and a flame reignition model based on the concept of a critical gas temperature. The numerical simulations use a flame extinction model and a flame reignition model. The numerical simulations were shown to reproduce the experimentally observed abrupt transition from a strong flame with a global combustion efficiency close to one to a suppressed flame with a global combustion efficiency close to zero.The numerical simulations show an abrupt transition from burning to extinction. The experimental extinction limit was Xo2=12.2%Xo2=12.2%; the numerical extinction limit was Xo2=11%Xo2=11%. The experimental oxygen limit is XO2 = 12.2%; the numerical limit is XO2 = 11%.