Assessment of Bray Moss Libby formulation for premixed flame-wall interaction within turbulent boundary layers: Influence of flow configuration

Abstract

Three-dimensional direct numerical simulations (DNS) of two different flow configurations have been performed for premixed flames interacting with chemically inert isothermal walls at the unburned gas temperature in fully developed turbulent boundary layers. The first configuration is an oblique flame-wall interaction (FWI) of a V-flame in a turbulent channel flow and the second configuration is a head-on quenching planar flame in a turbulent boundary layer. These simulations are representative of stoichiometric methane-air mixture at unity Lewis number under atmospheric conditions. The turbulence in the non-reacting conditions for these simulations is representative of the friction velocity based Reynolds number of Reτ=110. Differences in the statistical behaviours of the mean values of progress variable, temperature, and density during the FWI process have been reported for the two configurations. It is found that the mean flame brush thickens in the near wall region leading to significant departures from the strict Bray Moss Libby (BML) formulation limit during the FWI process and that is reflected in the probability density function (PDF) distributions of c for both flame configurations. The closures from the BML formulation for Reynolds averaged progress variable c¯ and the Favre averaged variance of the progress variable c′′2˜ have also been investigated and it is found that these closures need to be modified to account for the FWI process even when the flame away from the wall represents high Damköhler number premixed turbulent combustion. Furthermore, the statistical behaviours of the quantities required for Flame Surface Density (FSD) based mean reaction rate closure including the flame orientation factor σy, the flamelet length scale Ly and the flame stretch factor I0 have been interrogated from the DNS data for the two flame configurations. The flamelet length scale and the stretch factor extracted from the DNS data are compared with the closures for these quantities proposed in the literature. It is found that σy exhibits significant spatial variation for both cases. The existing closures for Ly and I0 which exhibit the best quantitative agreement with DNS data have been identified. It has been found that the models for Ly and I0 have scopes for further improvement to enable satisfactory predictions of these quantities during the FWI process within turbulent boundary layers.