The present paper describes a mathematical model for turbulent methane-air jet diffusion flames. The mathematical model solves density-weighted governing equations for momentum, mass continuity, turbulent kinetic energy and its dissipation rate. The combustion model solves density-weighted transport equations for the mixture fraction “f”, its variance “g” and its skewness “s”. These variables are used to compute one part of the probability density function (PDF) in mixture fraction domain. The second part of the PDF is computed from the numerical solutions of the mixture fraction dissipation rate “χ” and its variance χ˜″2. The resulting two-dimensional PDF is defined in the mixture-fraction-scalar-dissipation-rate 2D space. The flamelet combustion sub-model is used to compute the mean flame temperature, density and species mass fractions. The flamelet model provides instantaneous state relationships for the stretched flamelets up to the extinction limit. The mean flame properties are computed through the integration of the stretched flamelet state relationships over the two-dimensional PDF. The present 2D probability density function model can predict rim-attached flames as well as unstable lifted flames. This is because the flamelet model provides information on the flame instability arising from the stretching effects of highspeed flowing gases. The new two-dimensional probability density function is used to predict the flame properties of a free jet methane-air flame for which experimental data exists.
Mathematical model for the irradiance probability density function of a laser beam propagating through turbulent media
