Optimal Flows for Thermal Transport

强制对流的热传输在住宅、商业和工业环境中普遍存在，例如在建筑物的供暖和制冷以及电力设备、车辆和云计算数据中心的冷却中。改进的热运输技术是提高整体能源效率的努力的重要组成部分。增强热传递的常见方法包括在流动中插入被动或主动障碍物或增加壁面的粗糙度。这些方法可以增强加热表面附近和远离加热表面的流体混合，但也增加了驱动流动所需的功率，因此效率的净收益往往是有限的。控制流动的新方法可能会产生更高的换热效率。该项目将开发一种系统的方法，以确定有用的流动和产生这些流动的强迫。该方法适用于偏微分方程组(PDE)的约束优化方法，这些方法最近被用来估计自然对流换热速率的上限。通过修改流体域几何、边界条件、约束和数值方法，该项目将识别与工程应用相关的新环境中的有效流动，并了解其有效性背后的物理机制。此外，该项目将为研究生提供支持和研究培训，为本科生提供暑期研究经验，并为初中生提供推广活动。该项目将在四个基本领域发现改善的流动，以加强热传输。它将扩展现有的定常2D方法，以有效地计算基准几何形状中的最优非定常2D流动，如槽道流动和冷热表面之间的闭合和开放区域。它还将开发与我们研究的2D域类似的3D域中的最佳流动的计算方法，并确定在可比域中3D流相对于2D流的收益。在模型热沉阵列中，比较了振荡驱动下的Navier-Stokes流动与最佳定常和非定常流动下的换热。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”的最佳流动。最后，对最佳渠道流的搜索将扩展到直线渠道中的多种初始最优模式和具有粗糙墙壁的渠道。该奖项反映了NSF的法定使命，并通过使用基金会的智力优势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.