Scaling and collapse of conditional velocity structure functions in turbulent premixed flames

Abstract

A new scale-sensitive physical-space conditional analysis is outlined and used to examine the scaling and collapse of velocity structure functions in turbulent premixed flames. The conditioning is based on local instantaneous temperatures in the premixed flame, and structure function scaling and collapse are examined using Kolmogorov-type dimensional arguments and scaling relations. Both longitudinal and lateral structure functions are computed using the local flame normal and tangent as reference directions. The analysis is based on data from direct numerical simulations of unconfined statistically-planar flames at three different intensities of turbulence in the premixed reactants. The analysis shows that as the turbulence intensity increases and for locations near the unburnt reactants, conditional structure functions approach the rN/3 inertial range scaling predicted by Kolmogorov, where N is the structure function order. Using conditionally-calculated scaling variables, it is further shown that structure functions throughout the flame increasingly collapse as the turbulence intensity increases, with a more complete collapse observed for longitudinal structure functions and for small r within the analytic (or dissipative) range. These results suggest that, at sufficiently high intensities, Kolmogorov-type scaling laws and dimensional arguments may retain some validity in premixed flames, provided that scaling variables are computed on a conditional basis for different temperatures.