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 ($θ_{\mathrm{s}}$) 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 ($θ_{\mathrm{u}}$), 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 $φ=0.35$ to 0.8--0.9 at $φ=0.40$, consistent with theoretical predictions. Additional numerical simulations in a reduced two-dimensional representation reproduce the same transition behaviour and yield qualitatively consistent results.

Figures (7)

• Figure 1: Cross section of the test rig with imaging FOV.
• Figure 2: Selected single shots (left panels) and averages (right panels) for all equivalence ratios. The horizontal dashed red lines indicate the mean onset location of TDIs. An example of the calculated fit segments is given for the equivalence ratio of $\phi=0.36$. The fit of the stable section is indicated by the blue dashed line, the fit of the unstable section by the orange dashed line.
• Figure 3: Schematic of the numerical setup. The dimensions of the computational domain are given in mm. Note that the figure is rotated by 90$^\circ$ relative to the experimental setup.
• Figure 4: Selected instantaneous snapshots from the simulations (left panels) and the corresponding temporally averaged fields (right panels) of the recomputed OH-LIF signal for all simulated equivalence ratios. Note that the subfigure labels (a), (c), and (f) are chosen to be consistent with the experimental cases shown in Fig. \ref{['fig:AllOPs']}.
• Figure 5: Selected instantaneous snapshots from the simulations (left panels) and the corresponding temporally averaged fields (right panels) of $Y_{\mathrm{c}}$ for all simulated equivalence ratios. In the right panels, the regions used to determine the stable branch (blue) and unstable branch (red) are highlighted. In addition, the corresponding linear fits to the mean flame front in these regions are indicated by blue and red lines, respectively. In the left panels, the flame front of the unstable branch is exemplarily highlighted for one instantaneous snapshot.