Low-complexity Stochastic Modeling and Control of Turbulent Shear Flows

湍流剪切流的低复杂度随机建模和控制

• 批准号: 1739243
• 负责人: Mihailo Jovanovic
• 金额: $ 12.43万
• 依托单位: University of Southern California
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2017
• 资助国家: 美国
• 起止时间: 2017-01-04 至 2018-07-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1739243&HistoricalAwards=false
• 关键词: Low; complexity; Stochastic; Modeling; Control

Most flows in nature and in engineering applications are complex and disordered (turbulent). Dissipation of kinetic energy by turbulent flow around airplanes, ships, and submarines increases resistance to their motion (drag); about half of the fuel required to maintain the aircraft at cruise conditions is used to overcome the drag force imposed by the turbulent flow. Similarly, in wind farms, turbulence reduces the aerodynamic efficiency of the blades, thereby decreasing the energy capture. Understanding and controlling turbulent fluid flows plays an important role in these applications, and may critically impact US economy, national security, and the environment. The broader impacts of this award range from economic and environmental benefits to improved performance of wind farms, transporting pipes, and vehicles. The Principle Investigators (PIs) plan to organize a workshop on modeling and control of fluids at the Institute for Mathematics and its Applications. This workshop will be aimed at showcasing utility of control engineering and systems theory to an interdisciplinary audience of students, researchers, and professionals from the engineering, mathematics, and physics communities.The intellectual merit of this project's effort lies in the novelty and interdisciplinary nature of the research. Second-order statistics of turbulent flows can be obtained either experimentally or via numerical simulations. The statistics are relevant in understanding fundamentals of flow physics and for the development of low-complexity models. Such models will be used for control design in order to suppress turbulence. Due to experimental or numerical limitations it is often the case that only certain spatio-temporal correlations between a limited numbers of flow field components are available. Thus, it is of interest to complete the statistical signature of the flow field in a way that is consistent with the known dynamics. The approach to this inverse problem relies on a model governed by stochastically forced linearized Navier-Stokes equations. Here, the statistics of forcing are unknown and sought to explain the given correlations. Identifying suitable stochastic forcing will allow the PIs to complete the correlation data of the velocity field. While the system dynamics impose a linear constraint on the admissible correlations, such an inverse problem admits many solutions for the forcing correlations. The PIs will use nuclear norm minimization to obtain correlation structures of low complexity. This complexity translates into dimensionality of spatio-temporal filters that will be used to generate the identified forcing statistics.

自然界和工程应用中的大多数流动都是复杂且无序的（湍流）。飞机、船舶和潜艇周围的湍流造成的动能耗散增加了其运动的阻力（阻力）；维持飞机巡航状态所需的大约一半燃料用于克服湍流施加的阻力。同样，在风电场中，湍流会降低叶片的空气动力效率，从而减少能量捕获。了解和控制湍流在这些应用中发挥着重要作用，并可能对美国经济、国家安全和环境产生重大影响。该奖项的影响范围更广泛，从经济和环境效益到提高风电场、运输管道和车辆的性能。首席研究员 (PI) 计划在数学及其应用研究所组织一个关于流体建模和控制的研讨会。该研讨会旨在向来自工程、数学和物理界的学生、研究人员和专业人士等跨学科观众展示控制工程和系统理论的实用性。该项目的智力价值在于其新颖性和跨学科性质研究。湍流的二阶统计可以通过实验或数值模拟获得。这些统计数据有助于理解流动物理学的基础知识和开发低复杂性模型。此类模型将用于控制设计以抑制湍流。由于实验或数值限制，通常情况下只能获得有限数量的流场分量之间的某些时空相关性。因此，以与已知动力学一致的方式完成流场的统计特征是有意义的。解决这个反问题的方法依赖于由随机强制线性纳维-斯托克斯方程控制的模型。在这里，强迫的统计数据是未知的，并试图解释给定的相关性。识别合适的随机强迫将使 PI 能够完成速度场的相关数据。虽然系统动力学对允许的相关性施加了线性约束，但这种反问题允许有许多强制相关性的解决方案。 PI 将使用核范数最小化来获得低复杂度的相关结构。这种复杂性转化为时空滤波器的维度，该滤波器将用于生成已识别的强迫统计数据。