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

TL;DR

This paper presents a new experimental method using OH-PLIF imaging to directly measure the stretch factor in laminar premixed hydrogen flames, capturing the transition from stable to thermodiffusively unstable regimes and analyzing the effects of instabilities.

Contribution

It introduces a novel experimental setup and three complementary methods to measure the stretch factor and flame surface area changes during thermodiffusive instability transitions.

Findings

The stretch factor decreases with increasing equivalence ratio.

Thermodiffusive instabilities increase flame surface area.

Numerical simulations qualitatively agree with experimental results.

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.