Determination of laminar flame speeds using stagnation and spherically expanding flames: Molecular transport and radiation effects

The uncertainties associated with the extraction of laminar flame speeds through extrapolations from directly measured experimental data were assessed using one-dimensional direct numerical simulations with focus on the effects of molecular transport and thermal radiation loss. The simulations were carried out for counterflow and spherically expanding flames given that both configurations are used extensively for the determination of laminar flame speeds. The spherically expanding flames were modeled by performing high fidelity time integration of the mass, species, and energy conservation equations. The simulation results were treated as “data” for stretch rate ranges that are encountered in experiments and were used to perform extrapolations using formulas that have been derived based on asymptotic analyses. The extrapolation results were compared then against the known answers of the direct numerical simulations. The fuel diffusivity was varied in order to evaluate the flame response to stretch and to address reactant differential diffusion effects that cannot be captured based on Lewis number considerations. It was found that for large molecular weight hydrocarbons at fuel-rich conditions, the flame behavior is controlled by differential diffusion and that the extrapolation formulas can result in notable errors. Analysis of the computed flame structures revealed that differential diffusion modifies the fluxes of fuel and oxygen inside the flame and thus affect the reactivity as stretch increases. Radiation loss was found to affect notably the extracted laminar flame speed from spherically expanding flame experiments especially for slower flames, in agreement with recent similar studies. The effect of radiation could be eliminated however, by determining the displacement speed relative to the unburned gas. This can be achieved in experiments using high-speed particle image velocimetry to determine the flow velocity field within the few milliseconds duration of the experiment. In general, extrapolations were found to be unreliable under certain conditions, and it is proposed that the raw experimental data in either flame configurations are compared against results of direct numerical simulations in order to avoid potential falsifications of rate constants upon validation.