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A series of Direct Numerical Simulations (DNS) of lean methane/air flames was conducted 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 ≈ 22 , 000 , defined with the bulk velocity, slot width, and the reactants' properties. The turbulent flame speed S T is evaluated locally at selected 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 * Corresponding author.

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We examine finite Reynolds number contributions to the inertial range solution of the third order structure functions D 3,0 and D 1,2 stemming from the unsteady and viscous terms. Under the assumption that the second order correlations f and g are self-similar under a coordinate change, we are able to rewrite the exact second order equations as a function of a normalized scale r only. We close the resulting system of equations using a power law and an eddy-viscosity ansatz. If we further assume K41 scaling, we find the same Reynolds number dependence as previously in the literature. We proceed to extrapolate towards higher Reynolds numbers to examine the unsteady and viscous terms in more detail. We find that the intersection between the two terms, where their contribution to the solution of the structure function equations is relatively small, scales with the Taylor scale λ.

We examine balances of structure function equations up to the seventh order N = 7 for longitudinal, mixed and transverse components. Similarly, we examine the traces of the structure function equations, which are of interest because they contain invariant scaling parameters. The trace equations are found to be qualitatively similar to the individual component's equations. In the even-order equations, the source terms proportional to the correlation between velocity increments and the pseudo-dissipation tensor are significant, while for odd N, source terms proportional to the correlation of velocity increments and pressure gradients are dominant. Regarding the component equations, one finds under the inertial range assumptions as many equations as unknown structure functions for even N, i.e. can solve for them as function of the source terms. On the other hand, there are more structure functions than equations for odd N under the inertial range assumptions. Similarly, there are not enough linearly independent equations in the viscous range r → 0 for orders N > 3.