Numerical simulation and vortex analysis of flow turbulence in viscoelastic fluids

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Dissolving a minute amount of polymers into a viscous solvent can introduce elasticity to the fluid. Turbulent flow of such viscoelastic fluids can show substantial reduction in its friction drag compared with that of a purely viscous fluid -- up to 80% under certain conditions. With increasing elasticity, drag reduction (DR) behaviors undergo several stages of transitions. Over the past few years, I have established a vibrant research program focusing on the fundamental understanding of the multistage transitions in viscoelastic turbulence using direct numerical simulation (DNS). As we push the boundaries of knowledge in this field, innovative research methods are also being developed along the way. Our specific goals for the next five years are fourfold. The first goal (G1) is an in-depth analysis of the turbulence self-sustaining cycles (SSCs) at the high-elasticity and high-DR limit. This limit has attracted most attention because of the maximum drag reduction (MDR) phenomenon -- existence of a universal upper limit of DR by polymers. Our recent contribution overturned a long-standing fundamental presumption that at MDR turbulent dynamics converges to an invariant "ultimate state". It pointed to an entirely different direction than the past 50 years of MDR research. The proposed work will reveal the nature of this non-convergent dynamics. G2 is to settle a decades-long debate about whether DR is fundamentally attributed to the high extensional viscosity (viscous theory) or elasticity (elastic theory) of polymer solutions. G3 builds on our recently developed VATIP (vortex axis tracking by iterative propagation) method, which allows for fully automated and unbiased turbulent vortex analysis. It will remove a key constraint in the current VATIP algorithm and generalize it for studying all vortex types. G4 is to develop a toolbox around the core VATIP program, including statistical classification of vortices and direct extraction of their life-time dynamics, for application in fundamental turbulence research. These goals build on our recent breakthroughs in both fundamental inquiry and methodology development and are designed to maximize the impact of those advances. G1 and G2 will address the most significant fundamental questions in the field. Physical understanding of those questions will guide the design and selection of drag-reducing polymers for applications in fluid transport and oil drilling and recovery. Methodology development from G3 and G4 will not only support our fundamental inquiry into viscoelastic turbulence, it will also catalyze a paradigm change in turbulence research at large, by shifting the focus from anecdotal observations of flow images to systematic and statistical analysis of vortex dynamics.