Scalar Mixing in Homogeneous Isotropic Turbulence: a Numerical Study

Abstract:

The prediction of turbulent dispersion is of primary importance in estimating the mixing processes involved in a variety of events playing a significant role in our daily life. This motivates research on the characterisation of statistics and the complex temporal evolution of passive scalars in turbulent flows. A key aspect of these studies is the modelling of the probability density function (PDF) of the passive scalar concentration and the identification of its link with the mixing properties. In order to investigate the dynamics of passive scalars, as observed in nature and in laboratory experiments, we perform direct numerical simulations (DNS) of a passive tracer injected in the stationary phase of homogeneous isotropic turbulence (HIT) flows, in a setup mimicking the evolution of a fluid volume in the reference frame of the mean flow. In particular, we show how the gamma distribution proves to be a suitable model for the PDF of the passive scalar concentration and its temporal evolution in a turbulent flow throughout the different phases of the mixing process. Notably, gamma distributions allow for a reliable prediction of the decay of the concentration fluctuations intensity as governed by a mixing time scale, the latter reflecting the dynamics of small scale turbulence. The results proposed here show a remarkable agreement agreement between the gamma distribution model predictions at subsequent times and the statistics based on both DNS and wind tunnel runs.