CAREER: Dynamics of Fluid-Structure-Control Interaction in Rotating Aerodynamic Bodies

摘要流固相互作用的非线性动力学研究提供了对许多科学学科和工程分支中出现的一个广泛的物理主题的见解。这些现象在广泛的尺度上表现出来，为科学发现提供了极好的机会，并具有丰富的技术应用。在像旋翼叶片或昆虫翅膀这样的情况下，由于某种机构的内在运行或其控制系统的动力学，物体受到复杂运动的影响，科学挑战就更大了。本研究的目的是通过改进多物理场过程的数学计算模型，更好地理解细长体气动弹性动力学的基础物理。该计划分为三个重叠的阶段，每个阶段都建立在PI先前发表的工作基础上。第一阶段的重点是一系列新的自适应算法，基于纳维耶？斯托克斯方程。运动学拉普拉斯方程（KLE）技术将用于创建一个完全解耦的两个混合变量在时间/速度在空间分裂的方法涡度。由此产生的全局方案本质上与非线性自适应ODE算法兼容，提供了一种方法，其中涉及的不同问题（流，结构，控制系统动力学等）的子模型可以作为与主ODE例程接口的模块单独处理。这允许同时分析气动弹性问题以及任何创新的控制策略，使其成为一个计算效率高的自适应算法。第二阶段包括定性研究在气动弹性问题中起关键作用的振荡体背后的涡落和尾迹动力学。在第三阶段，将对创新风力涡轮机叶片原型及其相关控制策略进行定量研究。智力价值：这项工作的智力价值在于为复杂的多物理场问题提供了计算数学模型的进步，这些问题涉及许多工程设计中存在的流体结构控制相互作用，也为更好地理解底层物理提供了基本工具。这些耦合多物理场问题的实验分析是非常困难的。在某些情况下（如风力涡轮机叶片），巨大的尺寸差异使从风洞到原型尺度的实验数据的外推复杂化。在其他领域（如微型飞行器应用中使用的升力表面，灵感来自鸟类和昆虫飞行中观察到的扑翼生物机制），将传感器放置在复杂旋转平移运动的小型机构上的纯粹任务几乎是无法克服的。如果成功，这里开发的创新数学模型将提高计算实现的效率和灵活性，并提供解决这些困难的方法。更广泛的影响：这项工作将促进本科和研究生水平的教学和学习，激励工程专业的学生在应用数学和计算力学的前沿进行研究。除了作为计算数学工具的内在科学价值外，本文提出的算法与许多学科的应用具有明显的相关性。特别是，风力涡轮机叶片的分析构成了具有战略意义的新兴技术领域中的一个具有挑战性的问题。目前基于复合层压板的叶片技术是劳动密集型的，需要高素质的劳动力，并且在运输物流和起重机能力方面提出了巨大的挑战。这构成了阻碍美国风能快速发展的关键瓶颈。通过与位于该地区的高科技公司和桑迪亚国家实验室合作的协同活动，这项工作将对风力涡轮机叶片技术的发展产生变革性影响。除了促进当地经济发展外，这些活动还可以帮助学生从工业研究环境中获得经验。这项工作从本质上扩大了未被充分代表的群体在研究中的参与：PI和一名博士生都是西班牙裔，另一名博士生是女性。作为教育计划的一部分，将用西班牙语教授一系列关于可再生能源和可持续发展的课程。基于之前PI的经验，并与现代语言领域的同事合作开发，该项目旨在向研究生和本科阶段讲英语的工程专业学生教授西班牙语技术，为西班牙裔社区提供沟通桥梁。通过密歇根理工大学的远程学习计划在全国范围内推广，它将有助于可持续能源劳动力的快速扩张。

ABSTRACTStudying the nonlinear dynamics of fluid structure interaction provides insights into a widespread physical topic which makes appearances in many scientific disciplines and several branches of Engineering. These phenomena manifest themselves at a wide range of scales and present excellent opportunities for scientific discovery with a richness of technical application. In cases like a rotor blade or an insect wing, where a body is subject to a complex motion due to the intrinsic operation of a certain mechanism or the dynamics of its control system, the scientific challenge is still greater. The objective of the research is to provide a better understanding of the underlying physics in slender body aeroelastic dynamics through improved mathematical computational models of the multiphysics process. The program is divided into three overlapping phases each of them building upon previous work the PI has published. The first phase focuses on a new series of adaptive algorithms, based on the hybrid (or vorticity-velocity) formulation of the Navier?Stokes equations. The kinematic Laplacian equation (KLE) technique will be used to create a complete decoupling of the two hybrid variables in a vorticity in time/velocity in space split approach. The resulting global scheme is intrinsically compatible with non-linear adaptive ODE algorithms, providing a way in which the submodels for the different problems involved (flow, structure, control system dynamics, etc.) may be treated individually as modules that interface with the main ODE routine. This allows for the simultaneous analysis of the aeroelastic problem together with any innovative control strategy into a single computationally efficient self adaptive algorithm. The second phase consists of qualitative studies on vortex-shedding and wake dynamics behind oscillating bodies, which play a critical role in the aeroelastic problem. In the third phase, quantitative studies on prototypes of innovative wind turbine blades, and their associated control strategies, will be conducted. Intellectual Merit:The intellectual merit of this work is the advancement of computational mathematical models for the com- plex multiphysics problems involving fluid structure control interaction that are present in many engineering designs, providing also a fundamental tool for a better understanding of the underlying physics. The experimental analysis of these coupled multiphysics problems is extremely difficult. In some cases (like wind turbine blades), huge size differences complicate extrapolation of experimental data from the wind tunnel to the prototype scale. In others (like the lifting surfaces used in Micro Air Vehicle applications inspired in the flapping-wing biological mechanisms observed in bird and insect flight), the sheer task of placing sensors on a small scale mechanism in complex rototranslational motion becomes almost insurmountable. If successful, the innovative mathematical models developed here will improve the efficiency and flexibility of the computational implementation and provide a way to tackle these difficulties. Broader Impacts:This work will promote teaching and learning at undergraduate and graduate levels, motivating engineering students to lead research at the frontiers of applied mathematics and computational mechanics. Besides their intrinsic scientific value as computational mathematics tools, the algorithms proposed here have a clear relevance to applications in many disciplines. In particular, the analysis of wind turbine blades constitutes a challenging problem in an emergent technological field of strategic relevance. Current blade technology based on composite laminates is labor intensive, requires a highly qualified workforce, and poses huge challenges in terms of transport logistics and crane capacity. It creates a critical bottleneck that hampers a rapid expansion of wind energy in the US. This work would have transformative effects in the development of wind turbine blade technology through synergistic activities in collaboration with high tech companies located in the region and with Sandia National Labs. Besides contributing to boost the local economy, these activities would help students to gain experience from an industrial research setting. This work intrinsically broadens the participation of underrepresented groups in research: both the PI and one PhD student involved are Hispanic, and the other PhD student is a woman. As part of the educational plan, a set of courses in renewable energies and sustainability will be taught in Spanish. Building upon previous PI's experience, and developed in collaboration with colleagues from the modern languages area, this aims to teach technical Spanish to English speaking engineering students at graduate and undergraduate level, providing a communicational bridge towards the Hispanic community. Expanded nationwide through Michigan Tech's Distance Learning Program, it would contribute to the rapid expansion of the sustainable energy workforce.