  A series of Direct Numerical Simulations (DNS) of lean methane/air flames was
conducted in order to investigate the enhancement of the turbulent flame speed
and modifications to the reaction layer structure associated with the
systematic increase of the integral scale of turbulence $l$ while the Karlovitz
number and the Kolmogorov scale are kept constant. Four turbulent slot jet
flames are simulated at increasing Reynolds number and up to $Re \approx
22000$, defined based on the bulk velocity, slot width, and the reactants'
properties. The turbulent flame speed $S_T$ is evaluated locally at select
streamwise locations and it is observed to increase both in the streamwise
direction for each flame and across flames for increasing Reynolds number, in
line with a corresponding increase of the turbulent integral scale. In
particular, the turbulent flame speed $S_T$ increases exponentially with the
integral scale for $l$ up to about 6 laminar flame thicknesses, while the
scaling becomes a power-law for larger values of $l$. These trends cannot be
ascribed completely to the increase in the flame surface, since the turbulent
flame speed looses its proportionality to the flame area as the integral scale
increases; in particular, it is found that the ratio of turbulent flame speed
to area attains a power-law scaling $l^{0.2}$. This is caused by an overall
broadening of the reaction layer for increasing integral scale, which is not
associated with a corresponding decrease of the reaction rate, causing a net
enhancement of the overall burning rate. This observation is significant since
it suggests that a continuous increase in the size of the largest scales of
turbulence might be responsible for progressively stronger modifications of the
flame's inner layers even if the smallest scales, i.e., the Karlovitz number,
are kept constant.
