CAREER: Controlling Nonlinear Flow Interactions to Suppress Transition to Turbulence

在广泛的工程系统（如飞机、汽车、管道和风力涡轮机）中，延迟流动从层流到湍流的转变可以减少阻力并提高效率。该研究将研究复杂的（非线性）流动相互作用，这将抑制层流过渡到湍流并实现阻力减少。仅结合基于壁的感应和流动驱动的通道流动的计算机模拟将用于演示过渡中的延迟。这项工作紧密结合了教育和推广与基础研究，加强跨学科流体动力学，系统建模和控制理论。多学科工作将传播到流体、动力系统和控制社区，以加强这些学科之间的交流。新开发的课程和本科生研究计划将促进高等工程教育。一项新的拓展计划将帮助小学教师在K-6课堂上介绍工程学。非线性流动相互作用是过渡过程的核心。然而，以往对过渡控制的研究主要集中在前非线性相互作用阶段，并没有对这些相互作用进行完整的描述。所提出的努力取决于非线性流动相互作用在给定的时间瞬间和跨时间实例受到Navier-Stokes方程的动态约束这一事实。在数学上，这些物理约束可以表示为一组积分二次约束，为过渡控制综合的非线性流动相互作用建模提供了方便的框架。该项目旨在确定如何利用非线性流动相互作用的表征来抑制通道流动的直接数值模拟中的过渡，仅使用基于壁的传感和驱动。该项目的结果将为如何正式解释非线性流动相互作用以执行流动控制，传感器选择和模型阶数减少提供指导，这种方式可以推广到许多复杂的流动配置。该奖项反映了美国国家科学基金会的法定使命，并通过使用基金会的知识价值和更广泛的影响审查标准进行评估，被认为值得支持。

In a wide range of engineering systems (e.g., airplanes, cars, pipelines, and wind turbines), delaying transition of flow from laminar to turbulent can lead to reduced drag and improved efficiency. The research will study complex (nonlinear) flow interactions that will suppress laminar transition to turbulence and achieve drag reduction. Computer simulations of a channel flow incorporating only wall-based sensing and actuation of the flow will be used to demonstrate the delays in transition. The effort closely integrates education and outreach with foundational research that enhances interdisciplinary fluid dynamics, systems modeling, and control theory. The multidisciplinary work will be disseminated to the fluids, dynamical systems, and controls communities to enhance communication between these disciplines. Newly developed courses and undergraduate research initiatives will promote higher education in engineering. A new outreach program will help elementary school teachers introduce engineering into K-6 classrooms.Nonlinear flow interactions are at the heart of the transition process. Yet, previous studies on transition control have focused on the pre-nonlinear interaction stage and have not exploited a complete description of these interactions for controller synthesis. The proposed effort hinges on the fact that nonlinear flow interactions are dynamically constrained by the Navier-Stokes equations, both at a given time instant and across time instances. Mathematically, these physical constraints can be expressed as a set of integral quadratic constraints, providing a convenient framework for modeling nonlinear flow interactions for transition control synthesis. This project seeks to determine how such representations of nonlinear flow interactions can be exploited to suppress transition within direct numerical simulations of a channel flow, using only wall-based sensing and actuation. The outcomes of this project will provide guidance on how to formally account for nonlinear flow interactions to perform flow control, sensor selection, and model-order reduction in a manner that can be generalized to many complex flow configurations.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.