Statistics conditioned to iso-scalar 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)=cˆ of a reaction progress variable c, there exist at least two different definitions of surface averages; an area-weighted surface average φs and an unweighted surface average φv . These two fine-grained averages can also be extended to coarse-grained surface averages φS and φV over an interval of cˆ≤c(t,x)≤cˆ+e. In a highly turbulent medium, the difference φs−φv 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.
Turbulent reacting flow DNS Conditioned statistics