Extracting global reaction rate and turbulent flame speed from reconstructed 3D spherically expanding flames

We analyse a recent set of experiments on turbulent premixed spherically expanding flames (SEFs) using fast 3D scanning measurements of hydrogen and methane/air mixtures. The flame reconstruction using Mie scattering allows for the determination of the volume burned, flame surface location and volume growth rate of mixtures of lean methane and hydrogen at different pressures and temperatures. A balance of progress of reaction unambiguously defines the reaction, convection and accumulation (engulfment) terms within the flame brush. The terms are extracted from 3D and 2D reconstructions of the flame, as a function of the surface location in terms of progress of reaction across the flame brush. We show that the accumulation/engulfment term is of leading order, except at selected locations in the flame, and that it cannot be neglected. Further, we show that measurements of turbulent flame speed in the literature based on the popular approximation $s_T=\frac{{\rho }_b}{{\rho }_u}\frac{d{R}_v}{dt}$ may be in error by a systematic factor of up to 1.5$\sim$2.0 for the present mixtures. Recommendations are made regarding the analysis of future 3D and 2D measurements, and how one may be able to robustly extract accurate measurements of displacement and reaction speeds from high frequency 2D turbulent SEF interface reconstructions.

Novelty and significance statement

The balance of mean progress of reaction is first analysed in an integrated form in spherical expanding flames reconstructed from 3D scanning results. The evolution of the progress of reaction and total volume of burned gas in spherical expanding flames is analysed for the first time in full 3D flame surfaces. Different flame speed terms in the balance equation for the mean progress of reaction are extracted from 3D and 2D reconstructions of the flame surfaces and a new understanding of how to estimate reaction rates and turbulent flame speeds is proposed compared with a popular approximation. Rates of burning, and flame surface density in 2D vs 3D are compared for the first time. The systematic error in the conventional approximation of turbulent flame speeds in spherical expanding flames is quantitatively estimated. A suggested procedure for estimating turbulent flame speeds from the rate of growth of from centreline 2D or full 3D measurements is proposed.