Advances in the Analysis and Prediction of Turbulent Viscoelastic Flows

It has been well-known for over six decades that the addition of minute amounts of long polymer chains to organic solvents, or water, can lead to significant turbulent drag reduction. This discovery has had many practical applications such as in pipeline fluid transport, oil well operations, vehicle design and submersible vehicle projectiles, and more recently arteriosclerosis treatment. However, it has only been the last twenty-five years that the full utilization of direct numerical simulation of such turbulent viscoelastic flows has been achieved. The unique characteristics of viscoelastic fluid flow are dictated by the nonlinear differential relationship between the flow strain rate field and the extra-stress induced by the additive polymer. A primary motivation for the analysis of these turbulent fluid flows is the understanding of the effect on the dynamic transfer of energy in the turbulent flow due to the presence of the extra-stress field induced by the presence of the viscoelastic polymer chain. Such analyses now utilize direct numerical simulation data of fully developed channel flow for the FENE-P (Finite Extendable Nonlinear Elastic – Peterlin) fluid model. Such multi-scale dynamics suggests an analysis of the transfer of energy between the various component motions that include the turbulent kinetic energy, and the mean polymeric and elastic potential energies. It is shown that the primary effect of the interaction between the turbulent and polymeric fields is to transfer energy from the turbulence to the polymer.