Conditionally Statistical Description of Turbulent Scalar Mixing at Subgrid-Scales

Abstract

Conditionally filtered passive scalar density function (FDF), dissipation (CFD), diffusion (CFDIF) and conditionally filtered velocity (CFV) are studied by using direct numerical simulation (DNS) data of homogeneous isotropic turbulent mixing with an imposed mean scalar gradient. The velocity and scalar fields are statistically stationary and have a Taylor micro-scale Reynolds number of 209. A three-dimensional box filter with a filter width of 21 scalar dissipation scales is employed to obtain filtered variables. The PDFs of conditioning variables, filtered scalar ($\left \langle \phi \right \rangle _L$), and subgrid-scale (SGS) scalar variance ($\left \langle \phi ^{\prime \prime 2} \right \rangle _L$), are shown and are in reasonably good agreement with the experimental results of a one-dimensional filter. Since the three-dimensional filter has been used, the PDF of the filtered scalar exhibits perfect symmetry, and this significantly affects the symmetry of succeeding conditionally filtered statistics on $\left \langle \phi \right \rangle _L$ such as FDF, CFD, and CFDIF. The FDF, CFD, and CFDIF also show visible dependence on $\left \langle \phi ^{\prime \prime 2} \right \rangle _L$. When $\left \langle \phi ^{\prime \prime 2} \right \rangle _L$ varies from large to small, CFD varies from bell-shaped to U-shaped curves, and CFDIF varies from an inverse-S curve to a linear line; these are in accordance with the evolution of the FDF varying from bimodal to Gaussian. It suggests that the SGS mixing could be compared with global binary mixing in the view of the conditional description and this also suggests that it would reveal the non-equilibrium characteristics of the SGS scalar mixing; this SGS scalar mixing is supposed to be caused by diffusion-layer-like structures. In addition, the CFV remains linear regardless of the value of $\left \langle \phi ^{\prime \prime 2} \right \rangle _L$. These results numerically confirm two distinct regimes of SGS mixing observed in previous experimental studies and extend the experimental results into isotropic turbulence, which suggests that the characteristics of the SGS scalar are intrinsic behavior of SGS mixing, independent of flow types.