Measurements of conserved scalar filtered density function in a turbulent jet

Abstract

Conserved scalar (temperature) filtered density function (FDF) is studied experimentally in the fully developed region of a turbulent jet with Taylor-microscale Reynolds numbers of 293 and 190. We obtain the FDFs using one-dimensional box filters of widths Δ ranging from 30 to 248 scalar dissipation scales (ηφ) as well as a two-dimensional box filter (Δ/ηφ=90) which consists of three discrete sensors. Taylor’s hypothesis is used to perform streamwise filtering operations. The mean conserved scalar FDF conditioned on the resolvable-scale scalar fluctuations 〈φ〉L and the subgrid scale (SGS) variance 〈φ″2〉L (log-normally distributed) is found to be bimodal when 〈φ″2〉L/〈φ″2〉 is large, indicating that the conditional SGS mixing is nearly binary. For small 〈φ″2〉L/〈φ″2〉 (<1) the conditional FDF is approximately Gaussian. The kurtosis of the conditional FDF decreases with increasing SGS variance and is independent of the filter widths for large SGS variance. The bimodal distribution can be symmetric or asymmetric depending on the curvature of the resolvable-scale scalar. As the SGS variance increases, the conditional scalar differences for separations comparable to the filter widths also change from Gaussian to bimodal distributions. At the same time the conditional SGS scalar changes from approximately isotropic to strongly anisotropic. The results show that the contributions to the bimodal distributions come primarily from the SGS scales comparable to the filter width. It is remarkable that similarities exist between the bimodal conditional FDFs obtained here in a fully developed jet and bimodal probability density functions observed in the early stages of binary scalar mixing. The present study provides a physical basis for the assumed FDF method for conserved scalars used in large-eddy simulation of turbulent combustion.