Statistics conditioned to isoscalar surfaces in highly turbulent premixed reacting systems

The paper aims at clarifying some issues associated with evaluation of surface-averaged quantities in Direct Numerical Simulation (DNS) of a turbulent reacting flow. For a quantity phi(t, x) averaged over an isosurface c(t, x) =(c) over cap of a reaction progress variable c, there exist at least two different definitions of surface averages; an area-weighted surface average (s)vertical bar((c) over cap ,t) and an unweighted surface average (v)vertical bar((c) over cap ,t) These two fine-grained averages can also be extended to coarse-grained surface averages (s)vertical bar((c) over cap,epsilon,t) and (v)vertical bar((c) over cap,epsilon,t) over an interval of (c) over cap <= c(t, x) <= (c) over cap + epsilon. In a highly turbulent medium, the difference (s) - (v) between the area-weighted and unweighted surface averages can be significant for most quantities phi of basic interest. The sign of this difference depends on the sign of the correlation between phi and vertical bar del c vertical bar, can be opposite for different phi or even for different isosurfaces of the same scalar field phi. For a quantity phi that can become singular in the zero-gradient points vertical bar del c vertical bar (t, x) = 0, its unweighted or area-weighted surface averages can still be bounded. The difference between area-weighted and unweighted surface averages of 1/vertical bar del c vertical bar or vertical bar del c vertical bar is relevant to explaining the well-known, but still challenging controversy between available data on the influence of turbulence on the local flame thickness. (C) 2019 Elsevier Ltd. All rights reserved.