THURSDAY, March 29, 2007
Time: 7:30 PM
OCNPS 200

Title: Recent Advances in Direct Numerical Simulations of Turbulent Viscoelastic Channel Flows: Towards a better Understanding of Polymer-Induced Drag Reduction

Antony N. Beris
Department of Chemical Engineering
University of Delaware

The phenomenon of polymer-induced drag reduction describes the effect that even minute quantities of a high molecular weight polymer can have, as small as of the order of ppm by weight, when added to a low molecular weight solvent, such as water or crude oil, in reducing considerably the turbulent drag. Despite a voluminous amount of research from its original discovery in the late 40s by Mysels and Tomms, unresolved issues still remain. Here I will describe the recent progress achieved thanks to Direct Numerical Simulations (DNS) of the turbulent channel flow of a dilute polymer solution modeled from first principles with a kinetic-theory-based (FENE-P) or network-based (Giesekus) constitutive equation.

The main effect of viscoelasticity is shown to be the strengthening of the largest size turbulent structures which become much more coherent with a dynamics that changes at an appreciably lower rate than for the equivalent Newtonian structures. Our parametric study strongly suggests that this feature develops due to an enhanced resistance to extensional deformation induced due to viscoelasticity and it results to a lower energy transfer from the wall to the turbulent core, thus explaining the drag reduction. The numerical results provide thus evidence and in depth analysis to a mechanism proposed first in the 60s by Lumley and Metzner based on experimental observations: As the polymer elasticity increases, so does the resistance offered to extensional deformation. That, in turn, changes the structure of the most energy-containing turbulent eddies (they become wider, more well correlated, and weaker in intensity) so that they become less efficient in transferring momentum, thus leading to drag reduction.

More recent analysis of the coherent structures using principal orhtogonal decomposition (POD) allows to further substantiate the evidence in support of the above-mentioned drag reduction mechanism. It also underscores the tremendous difficulty underling any effort towards a low-dimensional modeling of turbulent flows, gievn the large extent of scales of length and time characterizing turbulent dynamics. The POD analysis helps to elucidate the role of the larger scales and demonstrates the complicated interplay between the various coherent structures a key effect of intermittence and chaos characterising all turbulent flows.