Collaborative Research: Stochastic Models for Convective Heat Transfer: Algorithms and Experimental Validation

PI将合作开发和验证新的随机方法，以便在直接数值模拟和降阶对流传热模型中纳入和传播不确定性。不确定性可能与自由流湍流、热边界条件、几何粗糙度甚至输运系数和源项有关。在模拟方面，他们将采用广义多项式混沌方法——这是诺伯特·维纳（Norbert Wiener）开创性思想的扩展，但具有增强的鲁棒性和效率。它采用了概率分布函数和多项式函数表示之间的对应关系。在实验方面，他们将使用DPIV（数字粒子图像测速）和DPIT（数字粒子图像测温）来精确测量概率分布函数。实验的重点是分析与边界条件有关的不确定性。该工作将为对流换热的数据同化和严格的敏感性分析奠定基础，具有广泛的影响。所提出的方法将从根本上影响新实验的设计方式和可能解决的问题类型，而模拟和实验之间的相互作用将变得更有意义和更动态。反过来，这将在传热设备的设计中找到它的方式，并将提供一个严格的可靠性框架。在教育方面，新知识将有助于理解受噪声影响的非线性系统、随机动力学基础、数据同化和不确定性下的设计。PI计划将这些新想法纳入他们在加州理工学院和布朗大学教授的工程和应用数学课程。该奖项由化学和传输系统分部的热传输和热处理项目资助，是桑迪亚国家实验室和美国国家科学基金会在“建模、仿真、决策和新兴技术工程科学”领域联合项目的一部分。

The PI's will collaborate to develop and validate new stochastic approaches in order to incorporate and propagate uncertainty in direct numerical simulations and reduced-order models of convective heat transfer. The uncertainty may be associated with free stream turbulence, thermal boundary conditions, geometric roughness or even transport coefficients and source terms. On the simulation side, they will employ the generalized polynomial chaos approach -- an extension of Norbert Wiener's pioneering ideas but with enhanced robustness and efficiency. It employs a correspondence between probability distribution functions and polynomial functional representations. On the experimental side, they will use DPIV (Digital Particle Image Velocimetry) and DPIT (Digital Particle Image Thermometry) to measure accurately probability distributions functions. The emphasis of the experiments will be on analyzing uncertainties associated with boundary conditions.The proposed work will have broad impact as it will set the foundations of data assimilation and rigorous sensitivity analysis of convective heat transfer. The proposed approach will affect fundamentally the way new experiments are designed and the type of questions that may be addressed, while the interaction between simulation and experiment will become more meaningful and more dynamic. This, in turn, will find its way in the design of heat transfer equipment and will provide a rigorous reliability framework. On the education front, the new knowledge will contribute towards understanding nonlinear systems subject to noise, fundamentals in stochastic dynamics, data assimilation, and design under uncertainty. The PI's plan to incorporate these new ideas in engineering and applied mathematics courses that they teach at Caltech and Brown University. The award has been funded by the Thermal Transport and Thermal Processing Program of the Chemical and Transport Systems Division, and it is part of a joint program involving Sandia National Laboratory and the NSF in the area of "Engineering Sciences for Modeling, Simulation, Decision-Making and Emerging Technologies.