Evolution and scaling of the peak flame surface density in spherical turbulent premixed flames subjected to decaying isotropic turbulence

The peak flame surface density within the turbulent flame brush is central to turbulent premixed combustion models in the flamelet regime. This work investigates the evolution of the peak surface density in spherically expanding turbulent premixed flames with the help of direct numerical simulations at various values of the Reynolds and Karlovitz number. The flames propagate in decaying isotropic turbulence inside a closed vessel. The effects of turbulent transport, transport due to mean velocity gradient, and flame stretch on the peak surface density are identified and characterized with an analysis based on the transport equation for the flame surface density function. The three mechanisms are governed by distinct flow time scales; turbulent transport by the eddy turnover time, mean transport by a time scale related to the pressure rise in the closed chamber, and flame stretch by the Kolmogorov time scale. Appropriate scaling of the terms is proposed and shown to collapse the data despite variations in the dimensionless groups. Overall, the transport terms lead to a reduction in the peak value of the surface density, while flame stretch has the opposite effect. In the present configuration, a small imbalance between the two leads to an exponential decay of the peak surface density in time. The dimensionless decay rate is found to be consistent with the evolution of the wrinkling scale as defined in the Bray-Moss-Libby model.