PDF of distance function for level-set flamelet library modelling

The difference between a presumed distribution of flamelet position and a numerically simulated distribution of distance function (a signed distance to flamelet) is investigated. It is shown that even if the distribution of flamelet position is symmetrical and close to Gaussian, the distribution of distance function away from the mean flame position is skewed towards the mean position and the mean of the distance function is also different from the distance to the mean position. The difference depends on the distance to the mean flame and the flame wrinkling amplitude. An extension method for the variance of the distance function and an upwind scheme for solving the re-initialization equation are presented. A numerical simulation of a premixed turbulent flame is compared to experimental data.