Collaborative Research: Understanding pressure drop-flow rate relationships in inertialess viscoelastic flows: effects of flow instability and stress-conformation hysteresis

CBET-0755269 Khomamii流体力学研究的一个主要成果是定量了解流量和压降之间的关系(功率要求)。虽然从牛顿流动的第一原理可以很好地理解这种关系，但对于粘弹性、聚合流动来说，情况很难如此。这一领域的重大进步无疑将对构成美国制造业经济重要组成部分的聚合物加工操作和基于聚合物的产品的基于知识的设计产生重大影响。这项研究的中心目标是定量地了解粘弹性聚合物溶液中的流动-微观耦合机制，这些机制反过来又决定了它们在可忽略的惯性条件下的摩擦阻力行为。具体地说，PI计划一个高度集成的研究计划，该计划将利用PI小组中最近开发的多尺度(微观)和连续级别的计算工具来研究有趣的摩擦阻力增强(FRE)现象，即当粘弹性聚合物溶液通过可变管道的流量超过临界值时，压降突然增加。根据流动几何形状的不同，这种压降的饱和值远远超过相同粘度的牛顿液体的压降。虽然FRE从20世纪60年代就已经在实验上被知道，但它还没有根据第一原理得到解释，主要是因为使用现实模型模拟多维和/或依赖时间的粘弹性流动存在计算瓶颈。人们提出了两种假设来解释FRE，即应力构象滞后(归因于弹性聚合物溶液收缩/膨胀时分子分解和松弛过程中固有的不对称性)和由一系列纯弹性流动不稳定性引起的非线性流动转变。在这些研究中，两者都将受到严格的考验。这项研究将开发急需的大规模多尺度或“微观-宏观”模拟，将连续统级有限元或谱求解器与随机微分方程的快速积分器相结合，以描述聚合物构型的演变。这将需要高效的并行算法来跟踪无惯性、粘弹性流动中的非线性流动转变，并利用它们来了解弹性诱导流动修改对摩擦阻力的影响。这两个私人投资机构拥有互补的专业知识，是开展这些努力的理想人选。NSF支持的TLSAMP、管道工程多样性计划和GEM将用于确保非洲裔美国人、西班牙裔美国人、土著美国人和女性学生的参与。将开发适合互联网的教学模块，以加强复杂流体、科学计算等更广泛领域的课程，并在现有的专注于复杂流体动力学的NSF-REU项目中进行。PIS还将利用各自机构广泛的外展基础设施，让K-12教师和高中生参与研究计划。

CBET-0755269KhomamiOne principal output of fluid mechanics research is the quantitative understanding of the relationship between flow rate and pressure drops (power requirements). While such relationships are well understood from first principles for Newtonian flows, it is hardly the case for viscoelastic, polymeric flows. Significant advances in this area will undoubtedly have pronounced impact on knowledge-based design of polymer processing operations and polymer-based products that constitute a significant portion of the U.S. manufacturing economy. The central goal of this research is the development of a quantitative understanding of the flow-microstructure coupling mechanisms in viscoelastic polymer solutions that in turn determine their friction drag behavior under conditions of negligible inertia. Specifically, the PIs plan a highly integrated research program that will leverage from recently developed multiscale (micro-macro) and continuum-level computational tools within the PIs' groups to investigate the intriguing phenomenon of friction resistance enhancement (FRE), where the pressure drop increases abruptly as the flow rate of a viscoelastic polymer solution through variable conduit, exceeds a critical value. Depending on the flow geometry, this pressure drop saturates at a value that greatly exceeds that for a Newtonian liquid of identical viscosity. While FRE has been known experimentally since the 1960s, it has not been explained based on first principles primarily due to the computational bottlenecks associated with the simulation of multi-dimensional and/or time-dependent viscoelastic flows using realistic models. Two hypotheses have been put forward to explain FRE, namely stress-conformation hysteresis (attributed to the inherent asymmetry in molecular unraveling and relaxation when an elastic polymer solution is subjected to contraction/expansion) and nonlinear flow transitions caused by a series of purely elastic flow instabilities. Both will be put to rigorous test in these studies. This study will develop much needed large-scale multiscale or 'micro-macro' simulations, integrating continuum-level finite element or spectral solvers with fast integrators of stochastic differential equations to describe the evolution of polymer configuration. This will require efficient parallel algorithms to track nonlinear flow transitions in inertialess, viscoelastic flows and their use to understand the effect of elastically-induced flow modifications on friction drag. The two PIs share complementary expertise and are ideally placed to undertake these efforts. NSF-supported TLSAMP, Pipeline Engineering Diversity Program and GEM will be used to ensure participation of African-American, Hispanic-American, Native-American and female students. Internet-ready instruction modules will be developed for enhancing curriculum in the broader areas of complex fluids, scientific computing and within an existing NSF-REU program that focuses on complex fluids dynamics. The PIs will also use the extensive outreach infrastructure at their respective institutions to involve K-12 teachers and high school students in the research program.