Gradient, counter-gradient transport and their transition in turbulent premixed flames

We theoretically and numerically analyse the phenomenon of counter-gradient transport in turbulent premixed flames with pressure distribution across the flame brush mainly controlled by heat release. The focus is on the transition from counter-gradient to gradient transport obtained when increasing the turbulence intensity/laminar flame speed ratio, a phenomenon recently found in open laboratory flame experiments by Frank et al (1999 Combust. Flame 116 220). The analysis is based on the turbulent flame closure combustion model for the simulation of turbulent premixed flames at strong turbulence (u' much greater than S-L). In this case, earlier work suggests that turbulent premixed flames have non-equilibrium increasing flame brush width controlled in the model only by turbulence and independent from the counter-gradient transport phenomenon which has gasdynamic nature, and equilibrium turbulent flame speed which quickly adapts to the local turbulence. Flames of this type have been called intermediate steady propagation flames. According to the present analysis, transport in turbulent premixed flames is composed of two contributions: real physical gradient turbulent diffusion, which is responsible for the growth of flame brush thickness, and counter-gradient pressure-driven convective transport related to the different acceleration of burnt and unburnt gases subject to the average pressure variation across the turbulent flame. The original gasdynamics model for the pressure-driven transport which is developed here shows that the overall transport may be of gradient or counter-gradient nature according to which of these two contributions is dominant, and that along the flame a transformation from gradient to counter-gradient transport takes place. Reasonable agreement with the mentioned laboratory experimental data strongly support the validity of the present modelling ideas. Finally, we explain why this phenomenon is also highly probable in large-scale industrial burners at much larger turbulent Reynolds numbers.