Algorithms, Theory, and Applications for Fiber Coating Systems

光纤涂层系统的算法、理论和应用

• 批准号: 2309774
• 负责人: Hangjie Ji
• 金额: $ 29.07万
• 依托单位: North Carolina State University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2023
• 资助国家: 美国
• 起止时间: 2023-07-01 至 2026-06-30
• 项目状态: 未结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=2309774&HistoricalAwards=false
• 关键词: Algorithms; Theory; Applications; Fiber; Coating

Thin liquid films flowing down a vertical fiber, a phenomenon known as fiber coating, is a fundamental component in various engineering applications such as mass and heat exchangers for thermal desalination, water vapor, and ultra-fine particle capture. These liquid films spontaneously exhibit intriguing interfacial instabilities, leading to trains of traveling droplets and irregular wavy patterns. Although there have been extensive studies on the modeling of fiber coating dynamics, the inherent nonlinearity and degeneracy of these models often present analytical and computational challenges in broader applications. This research project aims to develop a hybrid numerical and machine learning framework that accelerates the computation and facilitates the control of large-scale stiff problems associated with fiber coating systems. The development of these techniques can lead to a prototype for real-time simulation and prediction in fiber coating applications. Parts of the project will be incorporated into the investigator’s courses on scientific computing and data science. This project will also provide research training opportunities for both undergraduate and graduate students. This project will employ analytical approaches, numerical simulations, and machine learning techniques to develop theory and algorithms for challenging free-surface flow problems that arise from fiber coating systems. Such problems are characterized by fourth-order highly-nonlinear partial differential equation (PDE) systems, which are sensitive to traditional numerical methods and data-driven machine-learning approaches. The objectives of the project are organized around three interconnected aspects: 1) Analysis of the regularity and structure of traveling droplets described by coupled PDE systems. The derived structures will be utilized to develop simplified dynamical systems from full-order models for individual droplets. A prototype control problem will be studied to establish the foundation for control design of general fiber coating systems; 2) Development of robust and structural-preserving algorithms for simulating and learning fiber coating dynamics. This involves bridging physics-based modeling principles, PDE theory, and neural ordinary differential equation techniques for long-time sequential learning and reduced-order modeling. The data-driven learning techniques developed for high-order nonlinear degenerate PDEs in this project are expected to advance scientific machine learning for stiff physical systems; 3) A real-world large-scale application will serve as a case study for the theoretical understanding and verification of the developed algorithms.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.

流入垂直纤维的薄液膜，一种称为纤维涂层的现象，是各种工程应用中的基本组件，例如用于热淡化，水蒸气和超细颗粒捕获的质量和热交换器。这些液体膜自发地表现出有趣的界面不稳定性，从而导致旅行液滴和不规则的波浪形图案。尽管已经对纤维涂料动力学建模进行了广泛的研究，但这些模型的继承非线性和退化通常会在更广泛的应用中提出分析和计算挑战。该研究项目旨在开发一个混合数值和机器学习框架，以加速计算并促进控制与纤维涂料系统相关的大规模僵硬问题。这些技术的开发可以导致用于实时仿真和纤维涂料应用中的原型。该项目的某些部分将纳入研究人员的科学计算和数据科学课程中。该项目还将为本科生和研究生提供研究培训机会。该项目将采用分析方法，数值模拟和机器学习技术来开发理论和算法，以挑战纤维涂料系统引起的自由表面流问题。此类问题的特征是四阶高度非线性偏微分方程（PDE）系统，这些方程对传统的数值方法和数据驱动的机器学习方法敏感。该项目的目标是围绕三个相互联系的方面组织的：1）耦合PDE系统描述的行进液滴的规律性和结构分析。派生的结构将用于开发从单个液滴的全阶模型中开发简化的动态系统。将研究原型控制问题，以建立一般纤维涂料系统控制设计的基础； 2）开发用于模拟和学习纤维涂料动力学的稳健和结构性保留算法。这涉及基于物理学的建模原理，PDE理论和中性普通微分方程技术，用于长期顺序学习和降低阶。该项目中针对高级非线性退化PDE开发的数据驱动的学习技术有望推动僵硬的物理系统的科学机器学习。 3）现实世界中的大规模申请将作为对已发达算法的理论理解和验证的案例研究。该奖项反映了NSF的法定任务，并通过评估该基金会的知识分子优点和更广泛的影响来审查标准。