Optimal Flows for Thermal Transport

强制对流的热传输在住宅、商业和工业环境中无处不在，例如建筑物的加热和冷却以及电力设备、车辆和云计算数据中心的冷却。改进的热传输技术是努力提高总体能源效率的一个重要部分。增强热传输的常用方法包括在流动中插入被动或主动障碍物或增加壁面粗糙度。这些方法可以增强靠近和远离加热表面的流体的混合，但也增加了驱动流动所需的功率，因此效率的净增益通常是有限的。操纵流动的新方法可以产生上级传热效率。该项目将开发一种系统的方法，以确定有用的流量和产生它们的强迫。该方法适应约束优化方法的偏微分方程（PDE），最近被用来估计自然对流传热率的上限。通过修改流动域的几何形状，边界条件，约束和数值方法，该项目将确定有效的流量在新的设置相关的工程应用，并了解其有效性的物理机制。此外，本项目还将为研究生提供支持和研究培训，为本科生提供夏季研究经验，并为初中和高中学生提供推广活动。本项目将在四个基本领域发现改善热传输的改进流。它将扩展现有的定常二维方法，以有效地计算最佳的非定常二维流动的基准几何形状，如通道流和封闭和开放的区域之间的冷热表面。它还将开发计算方法的最佳流在3D域，类似于我们已经研究过的2D域，并确定收益从3D流相对于2D流在可比域。在模型热沉阵列中，将比较具有振荡驱动的Navier-Stokes流与最佳定常和非定常流的热传递。此外，该项目还将通过将目标函数更改为域中最高温度的近似值来表征与处理器冷却相关的“热点”的最佳流。最后，对最佳渠道流量的研究将扩展到直渠道和粗糙壁渠道的多种初始最佳模式。该奖项反映了NSF的法定使命，并通过使用基金会的知识价值和更广泛的影响审查标准进行评估，被认为值得支持。

Thermal transport by forced convection is ubiquitous in residential, commercial, and industrial settings, for example in the heating and cooling of buildings and the cooling of power equipment, vehicles, and cloud-computing data centers. Improved thermal transport technologies are an important part of efforts to improve overall energy efficiency. Common methods of thermal transport enhancement involve inserting passive or active obstacles in flows or increasing the roughness of walls. These methods can enhance mixing of fluid both near and away from heated surfaces but also increase the power needed to drive the flow, so the net gain in efficiency is often limited. New ways of manipulating flows may yield superior heat transfer efficiency. This project will develop a systematic approach to identify useful flows and the forcing that generates them. The approach adapts constrained optimization methods for partial differential equations (PDE) that have been used recently to estimate upper bounds on rates of heat transfer by natural convection. By modifying the flow domain geometries, boundary conditions, constraints, and numerical methods, this project will identify effective flows in new settings relevant to engineering applications and understand the physical mechanisms underlying their effectiveness. In addition, this project will provide support and research training for graduate students and summer research experiences for undergraduate students, and outreach activities for middle and high school students.This project will discover improved flows for thermal transport enhancement in four fundamental areas. It will extend the existing steady 2D method to efficiently compute optimal unsteady 2D flows in benchmark geometries such as channel flows and closed and open domains between hot and cold surfaces. It will also develop computational methods for optimal flows in 3D domains that are analogous to the 2D domains we have studied and determine the gains from 3D flows relative to 2D flows in comparable domains. In model heat sink arrays, the heat transferred by Navier-Stokes flows with oscillatory driving to that for the optimal steady and unsteady flows will be compared. In addition, this project will also characterize the optimal flows for “hot spots,” relevant to processor cooling, by changing the objective function to an approximation of the maximum temperature in the domain. Finally, the search for optimal channel flows will be extended to multiple initial optimal modes in straight channels and to channels with rough walls.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.