Investigation of scalar–scalar-gradient filtered joint density function for large eddy simulation of turbulent combustion

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The scalar–scalar-gradient filtered joint density function (FJDF) and its transport equation for large eddy simulation of turbulent combustion are studied experimentally. Measurements are performed in the fully developed region of an axisymmetric turbulent jet (with jet Reynolds number UjDj/ν=40 000) using an array consisting of three X-wires and three resistance-wire temperature probes. Filtering in the cross-stream and streamwise directions is realized by using the array and by invoking Taylor's hypothesis, respectively. The FJDF and the terms in the transport equation are analyzed using their means conditional on the filtered scalar and the subgrid-scale (SGS) scalar variance. The FJDF is unimodal when the SGS scalar variance is small compared to its mean value. The scalar gradient depends weakly on the SGS scalar. For large SGS variance, the FJDF is bimodal and the gradient depends strongly on the SGS scalar; therefore, the often-invoked independence assumption is not valid. The SGS scalar under such a condition contains a diffusion layer structure and the SGS mixing is similar to the early stages of binary mixing. The isoscalar surface in the diffusion layer has a lower surface-to-volume ratio than that in a well-mixed scalar. The conditionally filtered diffusion of the scalar gradient has an S-shaped dependence on the scalar gradient, which is expected to be qualitatively different from that of a reactive scalar under fast chemistry conditions. However, because modeling is performed at a higher level and because the scalar–scalar-gradient FJDF contains the information about the scalar dissipation and the surface-to-volume ratio, the FJDF approach is expected to be more accurate than scalar filtered density function approaches and has the potential to model turbulent combustion over a wide range of Damköhler numbers.