Experimentally Closing the Balance of Progress of Reaction in Premixed Turbulent Combustion in the Thin Flame Regime

We investigate the possibility of determining the local turbulent flame speed by measuring the individual terms in the balance of a mean progress of reaction variable for the case of a low turbulence methane-air Bunsen flame in the thin flame regime. Velocity distributions and flame edge positions were measured by particle image velocimetry techniques at 3 kHz for a flame stabilized by a surrounding pilot of the same stoichiometry, for a turbulent Reynolds number around 66 and Karlovitz numbers of the order of 4. The conservation equation for mean progress variable was analyzed along different streamlines as a balance of terms expressed as velocities, including terms for convection, turbulent diffusion, mean reaction, and turbulent and molecular diffusion. Each term was estimated from local velocities and flame locations using a thin flame approximation, and their uncertainty was evaluated based on propagation of experimentally measured statistical correlations. The largest terms were the convective and reaction terms, as expected, with smaller roles for turbulent and molecular diffusion across the flame brush. Countergradient diffusion and transition to gradient diffusion were observed across the flame brush. Closure of the balance of terms in the conservation equations using independently measured terms was not consistently achieved across the flame brush within the reckoned uncertainties, arriving at a balance within 20–30% of the absolute value. Testable hypotheses are offered for the possible reasons for the mismatch, including the role of spatial filtering and 3D effects on the reaction rate term. Finally, the experiments identify the inaccuracies in measuring a true local turbulent flame speed, and suggest a consistent methodology to reduce errors in such estimations. This is the first time such a detailed experimental closure is attempted for any configuration. The results suggest that the significant improvements in spatial resolution are necessary for a full closure.