Turbulent Drag Reduction in Polymer Solutions: Studies of the Interaction of Viscoelasticity and Exact Coherent States

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ABSTRACTPROPOSAL NO.: CTS-0328325PRINCIPAL INVESTIGATORS: MICHAEL D. GRAHAMINSTITUTION: UNIVERSITY OF WISCONSINTURBULENT DRAG REDUCTION IN POLYMER SOLUTIONS: STUDIES OF THE INTERACTION OF VISCOELASTICITY AND EXACT COHERENT STATESThe energy required to rapidly pump a liquid can be dramatically reduced by addition of a small quantity of very large polymer molecules. This "rheological drag reduction" phenomenon has found widespread application in reduction of energy losses in pipelines, has spurred research into reducing drag over ships and has recently gained attention for its potential to dramatically improve efficiency of so-called district heating and cooling systems, in which chilled or heated water is generated at a central location and pumped to buildings in the surrounding area. Despite its widespread current and potential applications, however, the fundamental mechanisms underlying this phenomenon remain unclear. This study builds on the recent discovery of "exact coherent states" -- traveling wave flow patterns that underlie the organized fluid motions of turbulence near solid surfaces. These organized motions, or "coherent structures" are closely associated with the energy consumed by the flow, so the exact coherent states provide a natural starting point for better understanding rheological drag reduction. Using computations with molecularly based mathematical models of the flow of polymer solutions, the effect of polymer on these states will be elucidated and compared with those observed experimentally. Of particular interest is the origin of the so-called "maximum drag reduction asymptote", the experimentally observed upper limit on the amount of drag reduction that can be achieved with polymer additives. This study will provide educational opportunities at a number of levels. The graduate students involved will gain a unique multidisciplinary perspective, combining polymer physics, rheology, fluid dynamics and nonlinear dynamics. Undergraduate students will participate in a project involving practical issues of implementing drag-reducing fluids in a large-scale flow system. The knowledge gained under this study will lead to principles for rational design of both fluids and flow systems to best take advantage of drag-reducing additives. More broadly, the study will enable development of energy saving flow control strategies by contributing to a firm understanding of the coherent structures of turbulence.