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.

沿垂直纤维流动的薄液膜（这种现象称为纤维涂层）是各种工程应用的基本组成部分，例如用于热脱盐、水蒸气和超细颗粒捕获的质量交换器和热交换器。这些液膜自发地表现出有趣的效果。尽管对纤维涂层的建模进行了广泛的动力学研究，但这些模型固有的非线性和简并性通常在更广泛的应用中提出了分析和计算挑战。开发一种混合数值和机器学习框架，可加速计算并促进与纤维涂层系统相关的大规模刚性问题的控制。这些技术的开发可以产生用于纤维涂层应用中的实时模拟和预测的原型。该项目的部分内容将纳入研究者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发展理论。以及挑战自由表面流动问题的算法此类问题的特点是四阶高度非线性偏微分方程（PDE）系统，该系统对传统数值方法和数据驱动的机器学习方法很敏感该项目的目标围绕三个目标进行组织。相互关联的方面： 1）分析由耦合偏微分方程系统描述的行进液滴的规律和结构，将利用导出的结构从单个液滴的全阶模型开发简化的动力系统，以建立原型控制问题。通用光纤涂层控制设计基础2) 开发用于模拟和学习光纤涂层动力学的稳健且结构保持的算法，这涉及桥接基于物理的建模原理、偏微分方程理论和神经常微分方程技术，以进行长时间顺序学习和降阶建模。 - 该项目中为高阶非线性简并偏微分方程开发的驱动学习技术有望促进刚性物理系统的科学机器学习；3）现实世界的大规模应用将作为理论理解和验证的案例研究；发展该奖项反映了 NSF 的法定使命，并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，被认为值得支持。