Surface density function in premixed turbulent combustion modeling, similarities between probability density function and flame surface approaches

To characterize the dynamics and the physical properties of isoconcentration surfaces of a random reactive scalar field, an instantaneous isosurface quantity and its transport equation are introduced. For turbulent flows, the mean area of isoconcentration surface per unit volume is studied through its transport equation derived by using the probability density function (pdf) formalism. This approach allows the value of the reactive scalar used to define the level surface to be treated as an independent variable. It also leads to the definition of a surface density function. The developed formalism is applied to premixed turbulent combustion and a bridge is built between modeling approaches based on pdf, and others based on the flame surface concept.