Experimental investigation of scalar-scalar-dissipation filtered joint density function and its transport equation

Abstract

The filtered joint density function (FJDF) of a conserved scalar and its dissipation rate and the FJDF transport equation are studied experimentally in the fully developed region of a turbulent jet with a jet Reynolds number Rej=UjDj/ν of 40 000. Filtered variables are obtained by a two-dimensional box filter having a size of 90 scalar dissipation scales, realized by using three discrete sensors aligned in the cross-stream direction and by invoking Taylor’s hypothesis. One-dimensional filters are also used to examine the effects of filter scales. The results show that for small and large subgrid-scale (SGS) scalar variance the FJDF and its dynamics have qualitatively different characteristics. The conditional mean FJDF for small SGS variance is generally unimodal and the dependence of the dissipation on the SGS scalar is moderate. The dissipation rate is diffused toward its conditional mean and its production rate is generally smaller than its destruction rate. These characteristics are similar to those of scalar-scalar-dissipation joint probability density functions in a fully developed turbulent flow. On the other hand, the conditional FJDF for large SGS variance is bimodal and the dissipation shows strong dependence on the SGS scalar. Diffusion of the dissipation toward values much larger than its conditional mean is observed. The production of the dissipation generally exceeds its destruction, indicating nonequilibrium scalar dissipation. These characteristics are found to be associated with diffusion-layer-like structure in the SGS scalar for large SGS variance. In addition to the SGS scalar variance, the time scale of the SGS scalar also affects the FJDF. A current assumed FJDF model is also examined. The results provide new fundamental understanding of the structure of the small-scale scalar, which is important for improving large eddy simulation of nonpremixed turbulent combustion as well as for studying local extinction and reignition phenomena.