PDF methods for turbulent reactive flows

The aim of the methods described is to calculate the properties of turbulent reactive flow fields. At each point in the flow field, a complete statistical description of the state of the fluid is provided by the velocity-composition joint pdf. This is the joint probability density function (pdf) of the three components of velocity and of the composition variables (species mass fractions and enthalpy). The principal method described is to solve a modelled transport equation for the velocity-composition joint pdf. For a variable-density flow with arbitrarily complex and nonlinear reactions, it is remarkable that in this equation the effects of convection, reaction, body forces and the mean pressure gradient appear exactly and so do not have to be modelled. Even though the joint pdf is a function of many independent variables, its transport equation can be solved by a Monte Carlo method for the inhomogeneous flows of practical interest. A second method that is described briefly is to solve a modelled transport equation for the composition joint pdf. The objective of the paper is to provide a coomprehensive and understandable account of the theoretical foundations of the pdf approach.