CAREER: Controlling Nonlinear Flow Interactions to Suppress Transition to Turbulence

在广泛的工程系统中（例如，飞机、汽车、管道和风力涡轮机），延迟流动从层流到湍流的转变可导致阻力减小和效率提高。 这项研究将研究复杂的（非线性）流动相互作用，这将抑制层流过渡到湍流，并实现减阻。 计算机模拟的通道流只结合基于壁的传感和驱动的流量将被用来证明过渡的延迟。 这项工作将教育和推广与基础研究紧密结合起来，增强了跨学科的流体动力学，系统建模和控制理论。 多学科的工作将传播到流体，动力系统和控制社区，以加强这些学科之间的沟通。 新开发的课程和本科生研究计划将促进工程高等教育。一项新的推广计划将帮助小学教师将工程学引入K-6教室。非线性流相互作用是过渡过程的核心。然而，以前的研究过渡控制集中在前非线性相互作用阶段，并没有利用这些相互作用的控制器综合的完整描述。所提出的努力取决于这样一个事实，即非线性流相互作用的动态约束的Navier-Stokes方程，在一个给定的时刻和跨时间实例。在数学上，这些物理约束可以表示为一组积分二次约束，提供了一个方便的框架建模非线性流相互作用的过渡控制综合。该项目旨在确定如何利用非线性流相互作用的这种表示来抑制通道流的直接数值模拟中的过渡，仅使用基于壁的传感和驱动。该项目的成果将为如何正式考虑非线性流相互作用以执行流控制、传感器选择和模型阶次降低提供指导，其方式可以推广到许多复杂的流configuration.This奖项反映了NSF的法定使命，并被认为值得通过使用基金会的智力价值和更广泛的影响审查标准进行评估来支持。

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.