Numerical simulation and vortex analysis of flow turbulence in viscoelastic fluids

将微量聚合物溶解到粘性溶剂中可以为流体引入弹性。与纯粘性流体相比，这种粘弹性流体的湍流可以显示出其摩擦阻力的显著减小-在某些条件下高达80%。随着弹性的增加，减阻（DR）行为经历了几个阶段的过渡。在过去的几年里，我已经建立了一个充满活力的研究计划，专注于使用直接数值模拟（DNS）的粘弹性湍流的多级转换的基本理解。当我们在这一领域推动知识的边界时，创新的研究方法也在沿着发展。我们今后五年的具体目标有四个方面。第一个目标（G1）是在高弹性和高DR极限的湍流自持循环（SSC）的深入分析。由于聚合物的最大减阻（MDR）现象--聚合物的最大减阻存在一个普遍的上限，这一限制引起了人们的极大关注。我们最近的贡献推翻了一个长期存在的基本假设，在MDR湍流动力学收敛到一个不变的“最终状态”。它指向了一个与过去50年MDR研究完全不同的方向。拟议的工作将揭示这种非收敛动力学的性质。G2是解决一个长达数十年的争论是否DR是从根本上归因于高拉伸粘度（粘性理论）或弹性（弹性理论）的聚合物溶液。G3建立在我们最近开发的VATIP（通过迭代传播进行涡轴跟踪）方法的基础上，该方法允许进行全自动和无偏的湍流涡分析。它将消除当前VATIP算法中的一个关键约束，并将其推广到研究所有涡类型。G4将围绕核心VATIP程序开发一个工具箱，包括涡的统计分类和直接提取其生命周期动力学，用于基础湍流研究。这些目标建立在我们最近在基础研究和方法开发方面的突破基础上，旨在最大限度地发挥这些进步的影响。G1和G2将解决该领域最重要的基本问题。对这些问题的物理理解将指导减阻聚合物的设计和选择，以应用于流体输送和石油钻探和回收。G3和G4的方法学发展不仅将支持我们对粘弹性湍流的基本研究，还将通过将重点从流图像的轶事观察转移到涡动力学的系统和统计分析来催化湍流研究的范式转变。

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.