Probability density function approach to non-premixed turbulent flames

The turbulent non-premixed flames are of interest in practical applications such as jet engines, diesel engines, steam boilers and furnaces. The understanding of non-premixed flames is obtained by flow computation based on mathematical models. The flow field of a non-premixed turbulent flame has been modelled using the steady conservation equations of mass, axial momentum, mean mixture fraction, turbulent kinetic energy, turbulent energy dissipation rate and square of mixture fraction fluctuations in axisymmetric coordinates. The computations of state relationships involve conventional adiabatic mixing calculations, with the local state of the mixture specified by the mixture fraction, f, the fraction of the material at a point which originated at the injector.; Consistent with the assumption of equal exchange coefficients, the instantaneous properties may be treated as a function only of mixture fraction. This facilitates the determination of all scalar properties (temperature, composition and density), as a function of mixture fraction. Mean scalar properties such as density and temperature are computed using various probability density functions based on periodic and non-periodic random distributions. The case study considered for validation is a combusting propane gas jet. The predictions show that the maximum mean temperatures are reached away from the axis of the jet. All these temperatures are below the adiabatic flame temperature for stoichiometric combustion (2270K). These lower values are due to turbulent "unmixedness", which is represented in the calculations by the rectangular, triangular, clipped-Gaussian and beta distributions. The temperature distributions are predicted reasonably well throughout the flow region by both clipped-Gaussian and beta distributions, whereas, the rectangular and triangular distributions predicted well the near centerline regions of the jet indicating their limitation to compute the flow at the edges of the jet flame.