The analytical result concerning the Markstein number of adiabatic flames was obtained in 1982 with the one-step Arrhenius model in the limit of a large activation energy. This result is not relevant for real flames. The form of the law expressing the flame velocity in terms of the total stretch rate of the flame front through a single Markstein length is not conserved when the location of the front (surface of zero thickness) changes within the flame thickness. It is shown in this paper that two different Markstein numbers ${\mathscr{M}}_{I} \not = {\mathscr{M}}_{II} $ characterize usual wrinkled flames sustained by a multiple-step chemical network, ${\mathscr{M}}_{I} $ for the modification of the flame velocity due to the curvature of the front and ${\mathscr{M}}_{II} $ for the effect of the flow strain rate. In contrast to ${\mathscr{M}}_{I} $, ${\mathscr{M}}_{II} $ depends on the location of the flame surface within the flame thickness, in such a way that the final result for the flame dynamics is not depending on this choice. The first part of the paper is devoted to present a general method of solution, valid for any multiple-step chemical network. The two Markstein numbers for two-step chain-branching models representing rich hydrogen–air flames and lean hydrocarbon–air flames are then computed analytically in the second part.

This paper reports an experimental investigation of premixed propane and methaneair flames propagating freely in tubes 1.5 m long and with diameters ranging from 26 to 141 mm. The thermo-acoustic instability was eliminated by means of a novel acoustic absorber placed at the closed end of the tube. We first remark that the flame can adopt different shapes either quasi-axisymmetric and normal to the mean direction of propagation, or inclined with a larger propagation speed because of the increase in flame surface area. The

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Thermal protection systems (TPS) are used to protect spacecraft payloads during the extreme conditions of atmospheric entry. The backbone of the composite TPS material used in the NASA Stardust Sample Return Capsule and the Mars 2020 mission is carbon fiber, which oxidizes at these temperatures and atmospheric conditions. This study presents the direct observation of carbon oxidation using in situ Scanning Transmission Electron Microscopy (STEM). A thin section of a commercially-available carbon fiber material containing multiple carbon structures was examined by STEM in a closed-environmental cell in which temperature was raised from 25 to 1050°C under a steady flow of air. Results show that the random polycrystalline carbon structure oxidized more uniformly and rapidly than the single crystallite region, which oxidized more anisotropically. These findings are the first to directly observe the structural dependence of carbon oxidation rates at these length-scales while also giving important insight into the onset of pitting at various active surface sites, important pieces in fundamentally understanding of carbon oxidation.