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

研究流体结构相互作用的非线性动力学有助于深入了解出现在许多科学学科和工程学几个分支中的一个广泛的物理主题。这些现象在广泛的范围内表现出来，为科学发现和丰富的技术应用提供了极好的机会。在像旋翼叶片或昆虫翅膀这样的情况下，由于某种机制的内在操作或其控制系统的动力学，身体受到复杂运动的影响，科学挑战更大。这项研究的目的是通过改进的多物理过程的数学计算模型，更好地了解细长体气动弹性动力学中的基本物理。该计划分为三个相互重叠的阶段，每个阶段都是在国际和平研究所发表的先前工作的基础上进行的。第一阶段集中于一系列新的自适应算法，基于Navier？Stokes方程的混合(或涡度-速度)公式。运动学拉普拉斯方程(KLE)技术将被用来创建时间涡度/空间速度分裂方法中的两个混合变量的完全解耦。由此得到的全局方案与非线性自适应ODE算法本质上兼容，提供了一种方法，其中针对所涉及的不同问题(流、结构、控制系统动态等)的子模型。可以被单独视为与主ODE例程接口的模块。这使得可以同时分析气动弹性问题和任何创新的控制策略，使其成为一个计算高效的自适应算法。第二阶段是对在气动弹性问题中起关键作用的振荡体后的旋涡脱落和尾迹动力学的定性研究。在第三阶段，将对创新的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是为涉及流体结构控制相互作用的复杂多物理问题的计算数学模型的进步，这些问题存在于许多工程设计中，也为更好地理解潜在物理提供了基本工具。这些耦合的多物理问题的实验分析是极其困难的。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外推变得复杂。在其他方面(如微型飞行器应用中的升力表面受到鸟类和昆虫飞行中观察到的扑翼生物机制的启发)，在复杂的旋转-平移运动中将传感器放置在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施的效率和灵活性，并提供一种解决这些困难的方法。更广泛的影响：这项工作将促进本科生和研究生的教与学，激励工程学学生在应用数学和计算力学的前沿领域领导研究。除了作为计算数学工具的内在科学价值外，这里提出的算法显然与许多学科的应用程序相关。特别是，在一个具有战略意义的新兴技术领域，风力涡轮机叶片的分析构成了一个具有挑战性的问题。目前基于复合材料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构成了巨大的挑战。它造成了一个严重的瓶颈，阻碍了美国风能的快速扩张。这项工作将通过与该地区的高科技公司和桑迪亚国家实验室合作开展的协同活动，对风力涡轮机叶片技术的开发产生变革性的影响。这些活动除了有助于促进当地经济外，还将帮助学生从工业研究环境中获得经验。这项工作本质上扩大了代表不足的群体在研究中的参与：参与研究的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。该课程以PI以前的经验为基础，并与现代语言领域的同事合作开发，旨在向研究生和本科水平的英语工程专业学生教授技术西班牙语，提供通往西班牙裔社区的沟通桥梁。通过密歇根理工学院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.