Collaborative Research: Thermal Transport in Elastic Turbulence

P. Ligrani (SLU)， R. Handler （TAMU）聚合物添加剂，如聚丙烯酰胺，在液体中具有独特的特性，包括高度非线性、非牛顿行为。为了增强传输，聚合物在流动应变的作用下被拉伸，流动应变是由流线曲率等引起的。聚合物的可扩展性和由此产生的聚合物变形导致局部弹性应力的急剧增长，这一系列事件被称为Weissenberg不稳定性，当Weissenberg数大于大约1 / 2或0.5时发生。总体结果包括聚合物粘度的增加，在某些情况下，增加了3个数量级。这种变化也导致聚合物有效导热系数的增加和热传递的增强。然而，弹性湍流热输运的增加从未被研究过，因此，为了开发创新的方法来增强低雷诺数小尺度环境下的混合和热输运，将协调并进行弹性湍流热输运的实验和模拟。一个主要目的是确定利用弹性湍流增强热输运的有效性，通过实验和数值表征这一现象。将使用三维直接数值模拟（DNS）对测量量和非测量量的物理趋势进行数值模拟和预测。因此，另一个总体目的是加强对与弹性湍流相关的物理过程的基本理解，因为弹性湍流是由液体中受流动应变拉伸和收缩的聚合物引起的。由此产生的结果将是新的数值和解析模型来描述和表示相关的弹性湍流物理现象，特别是热输运。一般来说，将采用毫米级（或毫米级）设备和流动环境来产生旋转- couette和Dean流动几何形状的流动。这些流动各自提供剪切和流线曲率（离心效应），因此非常适合在稀聚合物溶液中产生弹性湍流。作为本研究的一部分，还将建立一个新的普朗特数模型和一个新的弹性湍流有效电导率模型。这将通过测量流动特性（时变和时均）和传热系数，以及使用非线性弹性模型（如FENE-P）的全三维直接数值模拟（DNS）来阐明聚合物溶液的特性。本研究遵循了最近几项重要的相关流体力学研究，因此，将解决关于聚合物添加剂对毫升级和微尺度液体流动中热传递的作用和影响的重要知识空白。因此，由于将提供新的物理理解，并且由于各种应用，目前的研究具有高度的变革性和相关性。近年来，人们非常关注与小型化有关的技术进步，特别关注微尺度和纳米尺度的技术，但也关注毫米尺度的设备。例如，制造技术和微加工的改进导致了各种不同类型的设备和传感器的小型化。预测这些设备内部和周围流体运动的能力对于其设计和优化至关重要。随着这些装置的长度尺度对液体流动的减小，效果变得显著，这在大型装置中是不存在的。由于这些部件的尺寸很小，速度也很低，因此它们内部的流动通常是层流的，混合和热输运的强度相对较低。因此，这种层流是微型装置的小尺寸所施加的限制的结果。这种流动以及与之相关的设备对于制药、医学、传热、生物医学工程和电子冷却等领域的一系列应用至关重要。在每种情况下，与这些应用领域相关的设备通常会通过增加混合和增强弹性湍流的输运而受益。这种混合对于上述应用领域内的各种情况都很重要，包括使用液体冷却电子元件，混合不同的化学成分以制造药品，涉及不同流体流相互作用和混合的芯片上实验室设备，以及用于从汽车到电器到空间系统（包括卫星）组件等设备的微型热交换器。

CBET 1336085PI: P. Ligrani (SLU), R. Handler (TAMU)Polymer additives, such as polyacrylamide, have unique characteristics in liquids, including highly non-linear, non-Newtonian behavior. To augment transport, the polymers are stretched in constriction by flow strain, which is induced by, for example, streamline curvature. The extensibility of the polymer and resulting polymer deformation, leads to a sharp growth in the local elastic stress, a sequence of events referred to as the Weissenberg instability, which occurs when the Weissenberg number is greater than approximately ½ or 0.5. Overall consequences include increased polymer viscosity, in some cases, by up to 3 orders of magnitude. Such changes also lead to increases in effective polymer thermal conductivity, and augmentation of thermal transport. However, such increases in thermal transport from elastic turbulence have never before been investigated, and thus, to develop innovative methods to enhance mixing and thermal transport in small-scale environments at low Reynolds numbers, experiments and simulations will be coordinated and conducted on thermal transport in elastic turbulence. One principal aim is to determine the efficacy of using elastic turbulence to augment thermal transport, by characterizing the phenomena both experimentally and numerically. Numerical modeling and prediction of the physical trends of both measured and non-measured quantities will be performed with three-dimensional Direct Numerical Simulations (DNS). As such, another overall intent is enhancement of fundamental understanding of the associated physical processes associated with elastic turbulence, as it is induced in liquids by polymers subject to stretching and constriction by flow strain. A resulting product will be new numerical and analytic models to describe and represent the related elastic turbulence physical phenomena, especially thermal transport. Generally, milliscale (or millimeter-scale) devices and flow environments will be employed to produce flows in the rotating-Couette and Dean flow geometries. These flows each provide shear and streamline curvature (centrifugal effects) and thus are ideally suited to producing elastic turbulence in dilute polymer solutions. As part of this research, a new Prandtl number model and a new effective conductivity model for elastic turbulence will also be developed. This will be facilitated by measurements of flow characteristics (time-varying and time-averaged) and heat transfer coefficients, and fully three-dimensional direct numerical simulations (DNS) with non-linear elastic models, such the FENE-P, to elucidate polymer solution characteristics. The present study follows several important recent, related fluid mechanics investigations, and as such, will address important gaps in knowledge regarding the effects and influences of polymer additives on thermal transport in milliscale and microscale liquid flows. As such, the present study is highly transformational and relevant because of the new physical understanding which will be provided, and because of the variety of applications. In recent years, much attention has been devoted to technological advances related to miniaturization, with particular attention to technologies at the micro-scale and nano-scale, but also to milli-scale devices. For example, improvements in manufacturing technology and micro-fabrication have led to the miniaturization of a variety of different types of devices and sensors. The ability to predict the fluid motion in and around these devices is essential for their design and optimization. As the length scales of these devices decrease for liquid flows, effects become significant which are not present in larger-scale devices. Because of the small dimensions and very low speeds which are involved, the flows within these components are generally laminar, with relatively low magnitudes of mixing and thermal transport. Such laminar flows are thus a consequence of the limitations imposed by the small sizes of the miniature devices. Such flows, and the devices associated with them, are vital and important for a range of applications in areas such as pharmaceutics, medicine, heat transfer, biomedical engineering, and electronics cooling. In every case, the devices associated with these application areas would generally benefit by increased mixing and augmented transport from elastic turbulence. Such mixing is important for a variety of situations within the mentioned application areas, including the use of liquids to cool electronic components, mixing of different chemical components to manufacture pharmaceuticals, lab-on-a-chip devices which involve the interaction and mixing of different fluid streams, and miniature heat exchangers for use in devices ranging from automobiles, to appliances, to components within space systems, including satellites.