Advances in particle representation modeling of homogeneous turbulence. From the linear PRM version to the interacting viscoelastic IPRM

Abstract

In simple flows with mild mean deformation rates the Reynolds stresses are determined by the strain rate. On the other hand, when the mean deformation is very rapid, the turbulent structure takes some time to respond and the Reynolds stresses are determined by the amount of total strain. A good turbulence model should exhibit this viscoelastic character of turbulence, matching the two limiting behaviors and providing a reasonable blend in between. We show that in order to achieve this goal one needs to include structure information in the tensorial base used in the model, because non-equilibrium turbulence is inadequately characterized by the turbulent stresses themselves. We also argue that the greater challenge in achieving visco-elasticity in a turbulence model is posed by matching Rapid Distortion Theory (RDT). In this direction, we present the linear Particle Representation Model (PRM), and its extension in order to account for non-linear interactions. The key idea in the linear PRM version, is to evaluate the one-point statistics of an evolving turbulence field by following an ensemble of hypothetical “particles” with properties governed by equations chosen so that the statistical results for an ensemble of particles are exactly the same as in linear RDT. The non-linear extension of the PRM, the Interacting Particle Representation model (IPRM), incorporates a relatively simple model for the non-linear turbulence-turbulence interactions, and is able to handle quite successfully a wide range of different flows.