Bounds for the propagation speed of combustion flames

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.…”

“…Under these assumptions and neglecting mass diffusion, advection, radiative heat losses and conductive heat losses through the boundaries, the model reduces to the following balance equations of energy and fuel density ρ F [32] …”

“…Equation (80) corresponds to the consumption of fuel, and prevents the temperature from increasing without bound. The last term within the second parentheses in equations (79) and (80) is the so-called 'cold boundary layer' heat loss term, and it ensures steadiness ( ∂θ ∂t = 0 and ∂ρ ∂t = 0) if all points of the system are at room temperature (θ = θ 0 ) [32,82].…”

“…For this purpose, the main requirement is that both thermal and mass gradients reach non-zero values only in the narrow region where the front arises. This leads to the following equations, that have been tested by numerical integrations of the system (79) and (80) [32],…”

“…For example, combustion flames are a very active area of research [30][31][32][33][34]. 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].…”