The underpinning mathematics for a novel wave energy converter: the FlexSlosh WEC

新型波浪能转换器的基础数学：FlexSlosh WEC

基本信息

批准号：
EP/W033062/1
负责人：
Hamid Alemi Ardakani
金额：
$ 10.12万
依托单位：
UNIVERSITY OF EXETER
依托单位国家：
英国
项目类别：
Research Grant
财政年份：
2022
资助国家：
英国
起止时间：
2022 至无数据
项目状态：
已结题

来源：
https://gtr.ukri.org/projects?ref=EP%2FW033062%2F1
关键词：
underpinning mathematics novel wave energy

项目摘要

The purpose of this small grant is to complete two steps in an important study that brings the power of mathematics to the problem of clean energy derived from waves. Ocean waves are a perpetual source of clean energy. Harvesting of this energy via Wave Energy Convertors (WECs) is one of the great challenges of the sustainable energy agenda. The proof of concept has been achieved, and the current overarching aim is to achieve power take-off (PTO) with commercial efficiencies, and this involves new GEOMETRIC modelling. Our proposed contribution to this agenda is to develop the underpinning mathematics for a class of next-generation floating WECs, in particular ducted wave energy converterswith flexible bottom topography, named FlexSlosh WEC.The FlexSlosh WEC is a freely floating rigid body in hydrodynamic interaction with exterior ocean surface waves, which extracts energy from its interior fluid sloshing over a flexible bottom topography. The flexible bottom may exploit novel use of deformable materials enabling the use of new distributed embedded energy converter technologies (DEEC-Tec) utilising distributed bellows action. The underpinning mathematics of the FlexSlosh WEC is based on a generalised Lie-Poisson bracket formulation of nonlinear partial differential equations for `dynamic coupling' between rigid-body motion and its interior dissipative shallow-water sloshing in two horizontal space dimensions, and computationally based on geometric and structure-preserving numerical analysis.Geometric and structure-preserving methods, which respect the underlying mathematical structure, i.e. specific geometric or topological, and conservation laws of the partial differential equations (PDEs) they solve, are a new generation of advanced numerical simulation techniques for evolutionary PDEs. Their advantages are being robust, stable, fast and precise for `long-time' computational modelling of highly-coupled nonlinear systems, which is so important for the development of a geometric optimisation tool for wave energy extraction with commercial efficiency.The fully coupled nonlinear system involves four subsystems: the interior fluid motion, the rigid body motion of the WEC, the elastic body modelling the flexible bottom topography, and the exterior wave motion. This project will concentrate on the first three. Poisson brackets, Lagrangians, Hamiltonians, and structure-preserving numerical schemes have been derived for these components as independent systems. Dynamic coupling brings in new challenges, in particular it is important to maintain the correct energy and momentum partition between components over long-time integration.The aim of the proposed research is (1) to develop new generalised Poisson bracket and Casimir invariants for the FlexSlosh WEC dynamics, i.e. dynamic coupling between rigid-body motion and its interior shallow-water sloshing and boundary coupling with the flexible bottom topography; and (2) to develop new finite difference energy- and potential-enstrophy-conserving symplectic scheme for long-time integration of the coupled nonlinear system.The proposed mathematical advances will develop the needed aspects of wave energy modelling in rigorous theoretical and numerical frameworks. By developing new continuum and discrete differential geometric pathways to transformation of ocean wave energy, the proposed underpinning mathematics project will contribute to the 2050 net zero target.

这项小赠款的目的是在一项重要的研究中完成两个步骤，该研究将数学的力量带到了从波浪中得出的清洁能量问题。海浪是永恒的清洁能源来源。通过波能转换器（WEC）收集这种能量是可持续能源议程的巨大挑战之一。已经实现了概念证明，目前的总体目的是以商业效率实现动力起飞（PTO），这涉及新的几何建模。我们提出的对该议程的贡献是为一类下一代浮动WECs开发基础数学，尤其是导管的波能转化器，以柔性底部形象为flexslosh wec。flexslosh wec。海面波，从其内部流体中提取能量在柔性底部地形上。灵活的底部可以利用可变形材料的新颖使用，从而实现使用分布式波纹管动作的新分布式嵌入式能量转换器技术（DEEC-TEC）。 Flexslosh WEC的基础数学基于刚性运动及其室内耗散浅水在两个水平空间，并基于基于基于两个水平的水平尺寸，以及基于基于两个水平的浅水沟渠的固定偏微分方程的普遍性 - 偏见支架公式。几何和结构保存数值分析。几何和结构保存方法，它们尊重潜在的数学结构，即特定的几何或拓扑或拓扑，以及它们求解的部分微分方程（PDE）的保护法，是新的高级数值模拟的新一代进化PDE的技术。它们的优势是强大，稳定，快速和精确的，用于对高耦合非线性系统的“长期”计算建模，这对于开发具有商业效率的波动能量的几何优化工具非常重要。系统涉及四个子系统：内部流体运动，WEC的刚体运动，弹性身体对柔性底部地形进行建模和外波动运动。该项目将集中于前三个。这些组件以独立系统的形式得出了泊松支架，拉格朗日人，哈密顿人和结构性的数值方案。动态耦合带来了新的挑战，特别是重要的是要在长期整合过程中保持正确的能量和动量分区。拟议的研究的目的是（1）为Flexslosh开发新的广义泊松支架和Casimir不变性WEC动力学，即刚体运动与其内部浅水宽度和边界耦合之间的动态耦合与柔性底部形状；（2）为长期整合耦合的非线性系统的长期整合而开发新的有限差差能和潜在的融合符合性方案。所提出的数学进步将在严格的理论和数值框架中发展波能模型的所需方面。通过开发新的连续体和离散的差别几何途径来转化海浪能，拟议的基础数学项目将有助于2050净零目标。