Iterative upscaling of fluid flows in nonlinear deformable porous media

非线性可变形多孔介质中流体流动的迭代放大

• 批准号: 0811180
• 负责人: Yalchin Efendiev
• 金额: --
• 依托单位: Texas A&M Research Foundation
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2008
• 资助国家: 美国
• 起止时间: 2008-07-01 至 2012-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0811180&HistoricalAwards=false
• 关键词: Iterative; upscaling; fluid; flows; nonlinear

The objective of this project is to develop numerical upscaling models for fluid flow through shape changing, inelastic, porous media, capable of shape recovery under pressure and temperature variations. Currently, the well-established models for poro-elastic media can only be applied to linear, elastic, porous solids. Moreover, macroscopic parameters such as average fluid pressure, and solid displacements are subject to various limitations. A key scientific contribution of the proposed research is modeling of the nonlinear coupling at the microscale between the fluid flow and solid deformation, due to both inelastic behavior of the solid and large pore-level displacements. The project will focus on fluid flow in various types of 3D pore geometries and different macroscopic parameters such as temperature, pressure and displacements. The homogenization method will be used to identify macroscopic equations and upscaled parameters which describe the effective media. Due to the complexity of the coupled fluid-structure interaction problem at the fine scale and the complex nonlinear response shape memory solids we will not attempt do derive closed form macroscopic equations. Instead, an efficient, easily parallelizable, Hybrid Multiscale Finite Element Model (HMFEM) which bypasses the explicit homogenization step by building fine-scale information directly into a coarse-scale computational grid will be developed. This numerical upscaling method will be applied to the analysis of a variable permeability filter with an SMA (Shape Memory Alloy) matrix, as a demonstration of the proposed methodology. Experimental verification of the numerical simulations will also be carried out.A porous SMA (Shape Memory Alloy) matrix makes possible devices with changing, temperature and/or stress dependent, porosity without the need for moving parts and active control mechanisms. The project will expand our understanding of tightly coupled multiphyics phenomena in such media. Design of novel temperature and pressure-controlled flow regulators with applications to filters, catalytic converters, separators and microfluidic sensors can only become possible with accurate mathematical modeling and numerical simulations of fluid flow in such deformable porous media. The project will also provide a sound theoretical understanding of upscaling strongly coupled fluid-structure interaction problems, extending current methods for engineering analysis and design of complex devices. While we focus on SMAs, SMAs encompass standard plastic materials and are representative of a broader class of shape changing materials such as Magnetic SMAs, Shape Memory Polymers and Ferroelectric materials. As a result, this work will be directly applicable to a more general class of inelastic, temperature-dependent materials.

该项目的目标是开发流体流动的数值放大模型，通过形状变化，非弹性，多孔介质，能够在压力和温度变化下恢复形状。目前，多孔弹性介质的成熟模型只能应用于线性、弹性、多孔固体。此外，宏观参数，如平均流体压力和固体位移受到各种限制。所提出的研究的一个关键科学贡献是在微观尺度上流体流动和固体变形之间的非线性耦合建模，这是由于固体的非弹性行为和大的孔隙水平位移。该项目将侧重于各种类型的3D孔隙几何形状和不同的宏观参数，如温度，压力和位移的流体流动。均匀化方法将被用来确定宏观方程和放大的参数，描述有效介质。由于精细尺度下流固耦合问题的复杂性和形状记忆固体的复杂非线性响应，我们将不尝试导出封闭形式的宏观方程。相反，一个高效的，易于并行化的，混合多尺度有限元模型（HMFEM），绕过显式均匀化步骤，通过建立精细尺度的信息直接进入一个粗尺度的计算网格将被开发。这种数值放大方法将被应用到分析的可变渗透率过滤器与SMA（形状记忆合金）矩阵，作为所提出的方法的演示。数值模拟的实验验证也将进行。多孔形状记忆合金（SMA）矩阵使得可能的设备与变化，温度和/或应力依赖，孔隙率，而不需要移动部件和主动控制机制。该项目将扩大我们对这种介质中紧耦合多物理现象的理解。应用于过滤器、催化转化器、分离器和微流体传感器的新型温度和压力控制的流量调节器的设计只能通过对这种可变形多孔介质中的流体流动进行精确的数学建模和数值模拟而成为可能。该项目还将提供一个良好的理论理解，放大强耦合的流体-结构相互作用问题，扩展目前的工程分析和复杂设备的设计方法。虽然我们专注于SMA，但SMA包括标准塑料材料，并且代表了更广泛的一类形状变化材料，如磁性SMA，形状记忆聚合物和铁电材料。因此，这项工作将直接适用于更一般的一类非弹性，温度依赖性材料。