a b s t r a c tA presumed probability density function (PDF) model for temperature fluctuation is proposed and formulated in this paper. It incorporates the four-step reaction mechanism of methane combustion. A set of analytical expressions is derived for the time-averaged four-step reaction rates. The model is employed to numerically simulate methane turbulent swirling flame in the TECFLAM combustor. The calculated gas axial, radial and tangential velocities, species mass fractions, temperature, and temperature fluctuation are compared with the measured test data. Agreement is achieved between the calculation and the measurement.