Bounds for the speed of combustion flames: The effect of mass diffusion

Progress in front propagation research

“…In contrast, the application of some levels of simplification to the governing equations leads to simple models from which estimates for the propagation speed of the flame are obtained by employing a variety of techniques [77][78][79]. Here we review some recent developments in this field [29][30][31][32][33][34], which provide good estimates for the front propagation speed in some combustion processes.…”

“…where T is the absolute temperature, r is the radial coordinate, t is the time, Q is the heat produced by the combustion reaction per unit mass of fuel, c p is the specific heat of the mixture at constant pressure, ρ is the density of the mixture (which is constant, since here we neglect convection; see [33]) and D ≡ λ/(c p ρ) is the heat diffusivity, where λ is the thermal conductivity (assumed constant in this section). Equation (80) corresponds to the consumption of fuel, and prevents the temperature from increasing without bound.…”

“…Here we extend the model to include (1) advection, (2) mass diffusion and (3) the dependence of transport coefficients on temperature [33].…”

“…They have been recently described using a single, reduced variable, which makes it possible to derive analytical lower and upper bounds on the propagation speed [32]. We review these results for flame propagation, as well as their extensions to encompass the effects of mass diffusion, heat convection and temperature-dependent parameters of heat and mass transport [33,34].…”

“…In figure 1 we present the speed predicted by equation (17) as a function of the random walk bias β (see equation (33)). The HRD speed (18), which corresponds to the non-biased limit (β = 0), is also shown.…”