A Novel Approach for Direct Measurement of the Stretch Factor in Laminar Premixed Hydrogen-Air Flames Affected by Thermodiffusive Instabilities

Abstract

This study introduces a novel experimental configuration using OH-PLIF imaging to directly determine the stretch factor ($I_0$) in laminar premixed hydrogen flames transitioning from a quasi-stable to a thermodiffusively unstable regime. A rod-anchored V-flame is stabilised in a laminar premixed reactant flow. Near the anchoring rod, the mildly strained flame remains quasi-stable, exhibiting a smooth surface and a well-defined inclination angle ($\theta_{\mathrm{s}}$) to the main flow. This stable branch is associated with a burning rate $S_{\mathrm{s}}$. Farther downstream, the flame abruptly transitions to a regime dominated by thermodiffusive (TD) instabilities, characterised by cellular structures and a wrinkled surface. The distance between this transition and the anchor decreases with increasing equivalence ratio. This TD-unstable branch exhibits a larger mean flame-surface angle ($\theta_{\mathrm{u}}$), enabling direct determination of the flame-speed increase, $S_{\mathrm{u}}/S_{\mathrm{s}}$. It is assumed that this ratio represents the normalised flame consumption speed, $S_{\mathrm{c}}/S_{\mathrm{L}}$. Determination of $I_0$ additionally requires the increase in flame-surface area caused by the thermodiffusive instabilities. Three complementary methods are therefore used to evaluate the surface area of the TD-unstable branch ($A$) relative to a smooth reference area ($A_0$), yielding consistent trends in $A/A_0$ over the investigated equivalence-ratio range. The resulting $I_0$ values, with the main uncertainty arising from $A$, decrease monotonically with increasing equivalence ratio, from about 1.1--1.3 at $\phi=0.35$ to 0.8--0.9 at $\phi=0.40$, consistent with theoretical predictions. Additional numerical simulations in a reduced two-dimensional representation reproduce the same transition behaviour and yield qualitatively consistent results.