Macroscopic View of Reynolds Scaling and Stretch Effects in Spherical Turbulent Premixed Flames

Abstract

The burning rate in a spherically expanding turbulent premixed flame is explored using direct numerical simulations, and a model of ordinary differential equations is proposed. The numerical dataset, from a previous work, is obtained from direct numerical simulations of confined spherical flames in isotropic turbulence over a range of Reynolds numbers. We begin the derivation of the model with an equation for the burning rate for the domain under consideration, and using a thin flame assumption and a two-fluid approach, we find the normalized turbulent burning rate to be controlled by the increase in flame surface area due to turbulent wrinkling, and correction factor that is observed to be consistently less than unity. A Reynolds scaling hypothesis for the flame turbulent wrinkling from a previous work using the same numerical dataset is used to model the term controlling the increase in flame surface area. The correction factor is hypothesized to reflect flame stretch effects, and hence this factor is modeled using Markstein theory applied to global averaged quantities. The ordinary differential equations are rewritten to reflect easily observable quantities such as the chamber pressure and mean flame radius, and then expressed in dimensionless form to assess dependence on various dimensionless parameters. The model predictions are found to be in good agreement with the numerical data within expected variances. Additionally, Markstein theory is found to be sufficient in describing the effects of flame stretch in the turbulent premixed flames under consideration.