Drag reduction and the nonlinear dynamics of Newtonian and viscoelastic turbulence

低速时，管道内或飞机上空的气流平稳而稳定。在更高的速度下，流动变得动荡——平滑的运动让位于波动的漩涡，这些漩涡消耗了流体的能量，使泵出流体通过管道或推动飞机在空中飞行变得更加困难。对于流动的液体，加入少量的非常大的聚合物分子可以显著地影响湍流涡流，减少它们对能源效率的有害影响。例如，这种现象被用在阿拉斯加的管道上，但人们对它的了解并不充分，而且目前还没有类似的技术来减少气体流动中的湍流能量消耗，因为聚合物不能在其中溶解。首席研究员小组最近的工作表明，聚合物溶液中湍流的许多特征也可以在简单流体（包括气体）的湍流中出现，这可能会导致在广泛的流动过程中提高能源效率的新方法。这一发现取决于对两种湍流的识别，一种是“主动”湍流，它在没有添加剂的情况下主导流动，并导致大量的能量消耗，另一种是“休眠”湍流，它从流体中消耗的能量要少得多。冬眠湍流在高水平的添加剂中很普遍，但在没有添加剂的情况下偶尔也会发生。所提出的工作的目的是根据上述观察更充分地表征湍流的空间和时间行为，并测试一些关于高减阻水平下湍流结构的特定假设。为此，将进行紊流模拟，并开发和实施一些新的数据分析方法。此外，第二次推力将首次系统地研究气流的“边缘”动力学，这些气流几乎没有湍流，因此阻力很小。所有这些研究都将利用聚合物溶液流动数学模型分析的新结果，用于计算和数据分析。这项工作的智力价值有几个方面。第一个是非常基本的：添加剂的减阻是湍流和复杂流体领域交叉的关键物理现象，因此，对这一现象的坚定理解将代表着重大的根本进步。第二点意义更为深远：长期以来，研究聚合物湍流减阻机理的动机之一是，了解这种情况可以揭示湍流减阻的一般机制，这将适用于聚合物添加不切实际或不可能的情况（例如在气体流动中）。即使在牛顿流体中也存在低阻力期，这一发现与在高水平减阻时发现的低阻力期非常相似，这自然表明，基于这一发现的新策略可能会被发现，这些策略可以减少阻力，从而提高各种涉及流动的过程的能源效率。这项工作产生的更广泛的影响包括：(1)本科生参与一个项目，该项目涉及在大型流动系统中实施减阻流体的实际问题——威斯康星大学麦迪逊分校的冷冻水冷却系统；(2)培养具有独特的多学科视角的研究生，将分子和连续介质计算方法与聚合物、流体动力学和动力系统理论的概念相结合；(3)湍流控制的基础：如果我们了解湍流的结构以及聚合物如何影响这种结构，也许我们可以通过可变形边界、电场/磁场或其他修改来模拟这些效果。更一般地说，通过对湍流的坚定理解，各种节能流动控制策略的严格开发将成为可能。

Graham1066223At low speed, flow in a pipe or over an aircraft is smooth and steady. At higher speeds, flow becomes turbulent -- the smooth motion gives way to fluctuating eddies that sap the fluid's energy and make it more difficult to pump the fluid through the tube or to propel the aircraft through the air. For flowing liquids, adding a small amount of very large polymer molecules can dramatically affect the turbulent eddies, reducing their deleterious effects on energy efficiency. This phenomenon is used, for example, in the Alaska pipeline, but it is not well-understood, and no comparable technology exists to reduce turbulent energy consumption in flows of gases, in which polymers cannot be dissolved. Recent work in the Principal Investigator's group has demonstrated that many of the features of turbulent flow in polymer solutions can also arise in turbulent flow of simple fluids, including gases, potentially leading to new approaches to improved energy efficiency in a wide range of flow processes. The discovery hinges on the identification of two kinds of turbulence, "active" turbulence, which dominates flows without additives and leads to substantial energy consumption, and "hibernating" turbulence, which drains much less energy from the fluid. Hibernating turbulence is prevalent at high levels of additives, but still occurs occasionally in their absence.The objective of the proposed work is to more fully characterize the spatial and temporal behavior of turbulent flows in light of the observations described above, and to test some specific hypotheses about the structure of turbulent flow at high levels of drag reduction. To do this, simulations of turbulent flows will be performed and a number of new approaches to data analysis will be developed and implemented. Additionally, a second thrust will, for the first time, systematically study the "edge" dynamics of flows that are just barely turbulent and thus have very low drag. All these studies will take advantage of new results in the analysis of mathematical models for flow of polymer solutions, for purposes of both computation and data analysis. The intellectual merit of this work has several dimensions. The first is very fundamental: drag reduction by additives is a key physical phenomenon at intersection between the fields of turbulence and complex fluids, so gaining a firm understanding of this phenomenon would represent a significant fundamental advance. The second is more far-reaching: One of the long-stated motivations for research into the mechanism of turbulent drag reduction by polymers is the potential that understanding this situation can shed light on general mechanisms for turbulent drag reduction that would apply to situations where polymer addition is impractical or impossible (e.g. in a gas flow.) The discovery that even in Newtonian flow there exist low drag periods very much like those found at high levels of drag reduction naturally suggests that new strategies based on this discovery might be found that can reduce drag and thereby increase energy efficiency in a wide variety of processes involving flow. Broader impacts arising from this work include: (1) Involvement of undergraduate students in a project involving practical issues of implementing drag reducing fluids in a large scale flow system -- the UW-Madison chilled water cooling system; (2) Education of graduate students with a unique multidisciplinary perspective, combining molecular and continuum computational methods with concepts of polymer and fluid dynamics and dynamical systems theory; (3)Foundations for turbulence control: if we understand the structure of turbulence and how polymers affect this structure, perhaps we can mimic those effects with deformable boundaries, electric/magnetic fields or other modifications. More generally, rigorous development of energy-saving flow control strategies of all kinds will be enabled by a firm understanding of turbulence.