  NO$_{\rm x}$ formation in lean premixed and highly-strained pure hydrogen-air
flamelets is investigated numerically. Lean conditions are established at an
equivalence ratio of 0.7. Detailed-chemistry, one-dimensional simulations are
performed on a reactants-to-products counter-flow configuration with an applied
strain rate ranging from $a=100 \, {\rm s}^{-1}$ to $a=10000 \, {\rm s}^{-1}$
and the \texttt{GRI3.0} mechanism. Following a similar setup, two-dimensional
direct numerical simulations are also conducted for representative strain rates
of $2000 \, {\rm s}^{-1}$ and $5000 \, {\rm s}^{-1}$. Both solutions show a
decreasing NO$_{\rm x}$ trend as the applied strain rate is increased. This
decreasing emission outcome is highlighted for the first time in this study for
lean pure-hydrogen flamelets. A deep analysis of the 2D solution underlines
that there is no production of NO$_{\rm x}$ in the second dimension, thus
proving that the emission trend is not a result of a setup preconditioning, but
is instead a direct physical effect of stretch on the flame. Furthermore, a
detailed analysis of the NO$_{\rm x}$ formation pathways at $a=2000 \, {\rm
s}^{-1}$ and $a=5000 \, {\rm s}^{-1}$ is performed. Thermal NO$_{\rm x}$ and
NNH pathways are shown to both contribute significantly to the total NO$_{\rm
x}$ production. While the NNH route contribution is roughly constant at
different strain rates, a significant decrease is observed along the thermal
NO$_{\rm x}$ route. Overall, results show that lean and highly-strained
hydrogen flames experience a significant decrease of NO$_{\rm x}$. This
property is discussed and analysed in the paper.
