  Reported in the paper are results of unsteady three-dimensional direct
numerical simulations of laminar and turbulent, lean hydrogen-air,
complex-chemistry flames propagating in forced turbulence in a box. To explore
the eventual influence of thermo-diffusive instability of laminar flames on
turbulent burning velocity, (i) a critical length scale {\Lambda}n that bounds
regimes of unstable and stable laminar combustion is numerically determined by
gradually decreasing the width {\Lambda} of computational domain until a stable
laminar flame is obtained and (ii) simulations of turbulent flames are
performed by varying the width from {\Lambda} < {\Lambda}n (in this case, the
instability is suppressed) to {\Lambda} > {\Lambda}n (in this case, the
instability may grow). Moreover, simulations are performed either using
mixture-averaged transport properties (low Lewis number flames) or setting
diffusivities of all species equal to heat diffusivity of the mixture
(equidiffusive flames), with all other things being equal. Obtained results
show a significant increase in turbulent burning velocity UT when the boundary
{\Lambda} = {\Lambda}n is crossed in weak turbulence, but almost equal values
of UT are computed at {\Lambda} < {\Lambda}n and {\Lambda} > {\Lambda}n in
moderately turbulent flames characterized by Karlovitz number equal to 3.4 or
larger. These results imply that thermo-diffusive instability of laminar
premixed flames substantially affects burning velocity in weak turbulence only,
in line with a simple criterion proposed by Chomiak and Lipatnikov (Phys. Rev.
E 107, 015102, 2023).
