On the occurrence of negative propagation speeds and negative divergence in turbulent premixed flames

Based on the analysis of data from recent Direct Numerical Simulation of turbulent premixed flames, at moderate values of the Reynolds number, we find that the propagation speed of reactive fronts in turbulent premixed flames takes instantaneous values that are negative in sign and large in absolute value. The ensuing probability density function (PDF) of the propagation speed is complex: the PDF has a positive mean, is bimodal with two local maxima – one at positive and one at negative values for sufficiently high values of the Reynolds number, is skew-positive, and has a large kurtosis indicating extreme events. Further, negative displacement speeds correlate strongly with negative values of the velocity divergence and large values of the most compressive eigenvalue of the rate of strain tensor. Despite strong similarities to isothermal turbulence, we also find an unmistakable dependence of the statistics of the rate of strain tensor on the Karlovitz number (at least for those values considered in our preliminary analysis), whereby as the Karlovitz number decreases, the probability that all strain eigenvalues are positive increases for small values of strain. The statistics of the propagation speed that we observe from DNS data are fundamentally inconsistent with existing theory that explains changes to propagation speed with the effect of stretch. Instead, the statistics of the propagation speed appear to be closely related to classical mechanisms of scalar mixing in isothermal turbulence with important Reynolds number effects pertaining to small-scale intermittency.