Conditional scalar dissipation statistics in a turbulent counterflow

Abstract

Cold-wire measurements of a scalar, temperature, its fluctuations and the axial and radial components of the scalar dissipation between two opposed turbulent jet flows, where one jet was slightly heated, show that the residence times of the scalar in the mixing layer were short, that the scalar fluctuations and their dissipation were strongly correlated and that the probability distributions of the conditional scalar dissipation components were log-normal at values of the dissipation larger than the mean. The first finding is consistent with the fact that the scalar turbulence was ‘young’, in the sense that residence times were shorter than the large-eddy turn-over time, so that the results are likely to be representative of scalar turbulence when scalar mixing first takes place between two streams, for example close to the stabilization region of turbulent diffusion flames. The second implies that the mean scalar dissipation, conditional on the stoichiometric mixture fraction, is larger than the unconditional mean by up to an order of magnitude. Dependence of the distributions of the mean and r.m.s. conditional scalar dissipation on the shape of the scalar p.d.f. was demonstrated by relating the largest conditional dissipation values to the rarest scalar fluctuations and it was found that this dependence was also valid in other flows where scalar dissipation has been measured. The third finding implies that the use of a log-normal distribution to describe the p.d.f. of the conditional scalar dissipation, in the context of flame extinction modelling, will be in error by only 15% provided that the mean and the r.m.s. conditional scalar dissipation are accurately known.