Statistics conditioned to isoscalar surfaces in highly turbulent premixed reacting systems

Journal article, 2019

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 ϕ(t, x) averaged over an isosurface c(t,x)=c^ of a reaction progress variable c, there exist at least two different definitions of surface averages; an area-weighted surface average 〈ϕ〉 s | c^,t and an unweighted surface average 〈ϕ〉 v | c^,t . These two fine-grained averages can also be extended to coarse-grained surface averages 〈ϕ〉 S | c^,ϵ,t and 〈ϕ〉 V | c^,ϵ,t over an interval of c^≤c(t,x)≤c^+ϵ. In a highly turbulent medium, the difference 〈ϕ〉 s −〈ϕ〉 v between the area-weighted and unweighted surface averages can be significant for most quantities ϕ of basic interest. The sign of this difference depends on the sign of the correlation between ϕ and |∇c|, can be opposite for different ϕ or even for different isosurfaces of the same scalar field ϕ. For a quantity ϕ that can become singular in the zero-gradient points |∇c|(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/|∇c| or |∇c| is relevant to explaining the well-known, but still challenging controversy between available data on the influence of turbulence on the local flame thickness.