Finite Element Approximation of the Extended Fluid-Structure Interaction (eXFSI) Problem

Abstract

This contribution is the second part of three papers on Adaptive Multigrid Methods for the eXtended Fluid-Structure Interaction (eXFSI) Problem, where we introduce a monolithic variational formulation and solution techniques. To the best of our knowledge, such a model is new in the literature. This model is used to design an on-line structural health monitoring (SHM) system in order to determine the coupled acoustic and elastic wave propagation in moving domains and optimum locations for SHM sensors. In a monolithic nonlinear fluid-structure interaction (FSI), the fluid and structure models are formulated in different coordinate systems. This makes the FSI setup of a common variational description difficult and challenging. This article presents the state-of-the-art in the finite element approximation of FSI problem based on monolithic variational formulation in the well-established arbitrary Lagrangian Eulerian (ALE) framework. This research focuses on the newly developed mathematical model of a new FSI problem, which is referred to as extended Fluid-Structure Interaction (eXFSI) problem in the ALE framework. The eXFSI is a strongly coupled problem of typical FSI with a coupled wave propagation problem on the fluid-solid interface (WpFSI). The WpFSI is a strongly coupled problem of acoustic and elastic wave equations, where wave propagation problems automatically adopts the boundary conditions from the FSI problem at each time step. The ALE approach provides a simple but powerful procedure to couple solid deformations with fluid flows by a monolithic solution algorithm. In such a setting, the fluid problems are transformed to a fixed reference configuration by the ALE mapping. The goal of this work is the development of concepts for the efficient numerical solution of eXFSI problem, the analysis of various fluid-solid mesh motion techniques and comparison of different second-order time-stepping schemes. This work consists of the investigation of different time stepping scheme formulations for a nonlinear FSI problem coupling the acoustic/elastic wave propagation on the fluid-structure interface. Temporal discretization is based on finite differences and is formulated as a one step-θ scheme, from which we can consider the following particular cases: the implicit Euler, Crank-Nicolson, shifted Crank-Nicolson and the Fractional-Step-θ schemes. The nonlinear problem is solved with a Newton-like method where the discretization is done with a Galerkin finite element scheme. The implementation is accomplished via the software library package DOpElib based on the deal.II finite element library for the computation of different eXFSI configurations.

Moving Surface Boundary Layer Control Analysis and the Influence of the Magnus Effect on an Aerofoil with a Leading-Edge Rotating Cylinder

“…The detailed analysis of the increment of C L max and stall angle is presented in the following table: From the Table-2, it is clear that for NACA 0021 aerofoil the computational gain is higher than the experimental gain for all the velocity ratios, except for case of the zero velocity ratio. Noteworthy, the numerical study does not include the effect of fluid-structure interaction (FSI) [41][42][43][44][45][46][47][48][49][50][51]. Thereby, the associated vibration is neglected in the numerical results.…”

“…This preliminary study indicates the feasibility of practical implementation of leading edge cylinders for thick aerofoil in aviation, wind turbine, and other applications. The use of the above-mentioned modifications to the aerofoil would add further layer of complexity for the structural health monitoring (SHM) system due to the addition of cylinder-driven vibrations [41][42][43][44][45][46][47][48][49][50][51].…”

A Review of Piezoelectric Material-Based Structural Control and Health Monitoring Techniques for Engineering Structures: Challenges and Opportunities

“…For the damage/delamination studies, to identify skin/stiffener debonding and de- While extensive SHM advancement has been accomplished, a great deal of work is still needed for more practical applications of SHM in composite materials [111]. Through a down-select procedure based on the control and health monitoring of structural design for the space vehicle, the tested SHM sensors and their sensing techniques were chosen [112]. To design online SHM systems for aerospace vehicles or aircraft, an extended fluid-structure interaction was proposed.…”

“…To design online SHM systems for aerospace vehicles or aircraft, an extended fluid-structure interaction was proposed. It is a strongly coupled version of a standard FSI problem with a wave propagation problem coupled, in which the wave propagation prob-lem is posed on the moving mesh which is automatically adopted from the FSI problem at each time stage [112].…”

“…Although they have been the focus of intense study for many decades, computational approximation and simulation of fluid-structure interactions remain an undeniably difficult topic with many unsolved problems and concerns, and the "arbitrary Lagrangian-Eulerian" method is a standard framework for solving fluid-structure interaction problems, as we emphasize [112].…”