### Turbulence for Non-Newtonian Fluid Flows

Fundamental research on turbulent flows of non-Newtonian fluids, especially those that exhibit elastic effects, including turbulence models development, especially for large eddy simulation. Our research on turbulence started with the FENE-P constitutive equation, but has now extended to consider also models such as Oldroyd-B, PTT and Giesekus amongst others, and uses DNS data for understanding the mechanisms of turbulence as well as for a priori and a-posteriori turbulent model development. Over the last six years we extended our in-depth investigation of the physics of forced homogeneous isotropic turbulence (HIT) of viscoelastic fluids to inhomogeneous flows, such as wall-free flows, namely the planar jet and the planar wake. In addition to an in-depth understanding of the physics of such flows, which includes the development of scaling laws for the characteristic quantities required to obtain self-similarity of such quantities such as the conformation tensor fields, we have also extended the Dynamic Similarity model (DSIM) for the closure of the sub-grid scale contribution to the polymer stretching in the evolution equation for the filtered conformation tensor, thus allowing large eddy simulations of viscoelastic inhomogeneous flows, where the inertial sub-grid scale stresses are modelled by a dynamic Smagorinski closure as for Newtonian fluids. Our current research on this topic is aimed at extending the DSIM model to channel flow, assessing the sensitivity of DSIM to other rheological constitutive equations and also performing DNS of turbulent flows of FENE-P fluids with separation for an understanding of its physics and further extension of the turbulent closures.

Research on this topic is now carried out in collaboration with Prof. Carlos Bettencourt da Silva at Instituto Superior Técnico.