  Hydrogen-enrichment of conventional natural gas mixtures is an
actively-explored strategy for reducing pollutant emissions from combustion.
This study investigates the effect of hydrogen enrichment on the unsteady flame
response to perturbations, with a view to understanding the implications for
thermoacoustic stability. The Level Set Approach for kinematically tracking the
flame front was applied to a laminar conical premixed methane / hydrogen / air
flame subjected to 2D incompressible velocity perturbations. For hydrogen
enrichment levels ranging from 0% to 80% by volume, the resulting unsteady heat
release rate of the flame was used to generate the Flame Describing Functions
(FDFs). This was performed across a range of perturbation frequencies and
levels at ambient pressure. The mean heat release rate of the flame was fixed
at $\overline{\dot{Q}} = 2.69\ \textrm{kW}$ and the equivalence ratio was set
to $\varphi=1.08$ for all hydrogen enrichment levels. Hydrogen-enrichment was
found to shift the FDF gain drop-off to higher frequencies, which will increase
propensity to thermoacoustic instability. It also reduced the effective flame
time delay. Sensitivity analyses at $\varphi = 0.8$ revealed that the changes
in FDF were driven predominantly by the flame burning speed, and were
insensitive to changes in Markstein length.
