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: 1363266
• 负责人: Mihailo Jovanovic
• 金额: $ 32万
• 依托单位: University of Minnesota-Twin Cities
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2014
• 资助国家: 美国
• 起止时间: 2014-08-01 至 2017-05-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1363266&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和无序的（湍流）。飞机、船舶和潜艇周围的湍流对动能的耗散增加了它们运动的阻力（阻力）;维持飞机在巡航条件下所需的燃料中约有一半用于克服湍流施加的阻力。类似地，在风电场中，湍流降低了叶片的空气动力学效率，从而降低了能量捕获。了解和控制湍流在这些应用中起着重要的作用，并可能对美国经济，国家安全和环境产生重大影响。该奖项的更广泛影响范围从经济和环境效益到提高风电场，运输管道和车辆的性能。主要研究人员（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。本次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研究的新奇和跨学科性质。湍流的二阶统计可以通过实验或数值模拟获得。这些统计数据与理解流动物理学的基本原理和开发低复杂性模型有关。这种模型将用于控制设计，以抑制湍流。由于实验或数值的限制，通常情况下，只有有限数量的流场分量之间的某些时空相关性是可用的。因此，感兴趣的是以与已知动力学一致的方式完成流场的统计特征。这个反问题的方法依赖于由随机强迫线性化Navier-Stokes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允许PI完成速度场的相关数据。虽然系统动力学对容许相关性施加了线性约束，但这样的逆问题承认强迫相关性的许多解。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，将用于生成所识别的强制统计。