A multi-scale approach to the propagation of non-adiabatic premixed flames

Flame propagation involves physico-chemical processes that occur over a range of temporal and spatial scales. By use of a multi-scale analysis it is shown that diffusion processes occurring on relatively small scales can be resolved analytically when the overall activation energy of the chemical reactions is large, thus providing, by asymptotic matching, explicit conditions for the state of the gas and for the flow field across the flame zone. The mathematical formulation on the larger hydrodynamic scale reduces to a free-boundary problem, with the free surface being the flame front. The front propagates into the fresh unburned gas at a rate that depends on both the local strain that it experiences and the local curvature, with coefficients that depend on the diffusion rates of heat and mass, the equivalence ratio of the mixture and the chemical kinetic parameters. The simplified model, properly termed a hydrodynamic model, involves the solution of the Navier Stokes equations with different densities and viscosities for the burned and unburned gas. The present work extends earlier studies by including volumetric heat loss, such as radiative loss, which affects the dynamics and may lead to flame extinction.