Study of random particle interactions for analysis of diffusion lengths in turbulent combustion modelling

Abstract

Turbulent combustion is commonly modelled using probability density function (PDF) methods; to close these methods, micro-mixing models are required: these are most commonly based on stochastic particle interactions. While it is standard practice for the turbulent diffusion coefficient to be used to specify the amount of mixing, few models account for the corresponding diffusion length scale that defines interacting particle separation. This study investigates ensemble averages of the minimum, mean and maximum inter-particle distances for random realisations as a precursor to comparing with the diffusion length in real simulations. It was found that the ensemble of results for each type of inter-particle distance (minimum, mean or maximum) had a normal distribution. For 1 to 1000 dimensions, the minimum inter-particle distances for 100 particles were 0.0051 to 12.3406 and the average distances were 0.3297 to 12.7776.