Computational Fluid-Structure Interaction

Methods, Models, and Applications

Yong Zhao, Xiaohui Su

• Publisher: Academic Press
• Year: 2018
• Print ISBN: 9780128147702
• eBook ISBN: 9780128147719
• Topic: Technology & Engineering
• Subtopic: Mechanical Engineering
• Index: Technology & Engineering

Computational Fluid-Structure Interaction: Methods, Models, and Applications provides detailed explanations of a range of FSI models, their mathematical formulations, validations, and applications, with an emphasis on conservative unstructured-grid FVM. The first part of the book presents the nascent numerical methods, algorithms and solvers for both compressible and incompressible flows, computational structural dynamics (CSD), parallel multigrid, IOM, IMM and ALE methods. The second half covers the validations of these numerical methods and solvers, as well as their applications in a broad range of areas in basic research and engineering.- Provides a comprehensive overview of the latest numerical methods used in FSI, including the unstructured-grid finite volume method (FVM), parallel multigrid scheme, overlapping mesh, immersed object method (IOM), immersed membrane method (IMM), arbitrary Lagragian-Eulerian (ALE), and more- Provides full details of the numerical methods, solvers and their validations- Compares different methods to help readers more effectively choose the right approach for their own FSI problems- Features real-life FSI case studies, such as large eddy simulation of aeroelastic flutter of a wing, parallel computation of a bio-prosthetic heart valve, and ALE study of a micro aerial vehicle

Chapter 1

Introduction

Abstract

In this chapter the background and engineering applications of fluid structure interaction are briefly introduced. Literature reviews on the three major components of fluid structure interaction, that is, computational fluid dynamics, computational structural dynamics, as well as moving boundaries, are given one by one.

Keywords

Fluid Structure Interaction; Computational Fluid Dynamics; Computational Structural Dynamics; Finite Volume Method; Moving Boundary

1.1 Background

The interaction of a flexible structure with a flowing fluid, in which it is submersed or by which it is surrounded, gives rise to a rich variety of physical phenomena with applications in many fields of engineering, for example, the stability and response of aircraft wings, the flow of blood through arteries, the response of bridges and tall buildings to winds, the vibration of turbine and compressor blades or hard disks for computer data storage, the opening and closing of heart valves, and the oscillation of heat exchangers. To understand these phenomena we need to model both the structure and the fluid and simulate their interaction to gain insights into the rich and complicated physics involved. However, in keeping with the overall theme of this volume, the emphasis here is on numerical methods, physical modeling, and their engineering applications. Furthermore, the applications are largely drawn from mechanical and aerospace engineering, although the methods and fundamental physical phenomena have much wider applications. In this book we emphasize recent developments and future challenges. The emphasis is on the enhanced physical understanding and the ease of simulating highly complex fluid–structure interaction (FSI) with accuracy, made possible by the numerical methods developed.

1.2 Computational Fluid Dynamics

Computational fluid dynamics (CFD), usually abbreviated as CFD, is a branch of fluid mechanics that uses numerical methods and algorithms to solve and analyze problems that involve fluid flows, heat transfer, and associated phenomena such as chemical reactions. The fundamental basis of almost all CFD problems is the Navier–Stokes equations. Numerical methods developed for CFD computations were first proposed by Richardson in his book Weather Prediction by Numerical Process [1], which forms the basis for modern CFD and numerical meteorology. Modern CFD has its origins dating back to the 1960s and 1970s, when universities and companies started to experiment with more and more sophisticated methods to solve more complicated fluid flow problems for engineering applications, such as aircraft designs, to take advantage of the development in computer technologies.

During the last decades significant progress has been made in CFD as a result of the development of powerful algorithms and fast supercomputers. In the meantime CFD has firmly established itself as the third approach in the field of fluid dynamics, equal to pure experiment and theory. Nowadays CFD has been used in a wide range of applications in many industries. Here are a few examples:

• • Aerospace/aeronautics
• • Automotive engineering
• • Astrophysics and cosmology
• • Atmospheric sciences
• • Building and construction: HVAC (heating, ventilation, and air conditioning) and wind engineering
• • Biomedical engineering
• • Chemical/petrochemical engineering
• • Energy/power generation
• • Earth science
• • Environmental engineering
• • Manufacturing/process engineering
• • Naval architecture and marine/offshore engineering
• • Oil and gas industry
• • Product design and optimization

CFD cannot completely replace experiments, both of which are complementary and have to be applied together to obtain optimal results. Phenomena that are too complex to be predicted by theory and too expensive or dangerous to be reproduced in the laboratory can now be simulated on supercomputers. Computational results that can be arbitrarily detailed and digitally processed for more comprehensive visualization are the advantages of CFD over experimental methods. Changes in the environment and parameters of the simulation can be made more accurate and faster in a computer simulation than in an experimental construction. CFD needs much less infrastructure and space, usually even less energy than laboratory experiments. These considerations mean that computational simulations are less expensive, especially because the same supercomputer can be used for many completely different simulations. The availability of computational results and data files together with the internet makes CFD portable all over the world and increases the effectiveness of research and development work. Nevertheless practical experiments are still necessary to create a basis for the validation of a numerical solver for each investigated problem.

A complete CFD program contains three main elements, a preprocessor, a solver, and a postprocessor. Preprocessing consists of a few software modules for the definition of the physical and chemical phenomena to be modeled, the generation of a computational grid, as well as the fluid properties and the specification of appropriate boundary conditions.

The flow simulation takes place in the solver of a CFD program. The governing analytic equations are discretized and solved for the node locations by iteration methods. Usually one of the three discretization approaches, finite difference method (FDM), finite elements method (FEM), or finite volume method (FVM) is used. An FV Runge–Kutta time-stepping algorithm is used in this book and is described in later chapters.

One of the main advantages of CFD mentioned previously is the detailed visualization of the results. This is accomplished by the postprocessing section of a CFD package. TECPLOT, one of the several commercial visualization tools, is mainly used in this book. Some examples for visualization options are domain geometry and grid visualization, vector plots, flow contour plots, or particle tracking. The output can be almost arbitrarily detailed and easily exported into other file formats to make the results portable.

1.3 Computational Structural dynamics

Similar to CFD, computational structural dynamics, usually abbreviated as CSD, is a branch of structural dynamics that uses numerical methods and algorithms to solve and analyze solid dynamics problems that involve single or multibody dynamics, including rigid or flexible, linear or nonlinear behaviors. The fundamental basis of CSD simulations are the Cauchy’s equations.

Over the last five decades a wide variety of numerical methods have been proposed for the numerical solution of partial differential equations of solid dynamics. Among these methods, the finite element method (FEM) has firmly established itself as the standard approach for problems in computational solid mechanics (CSM), especially with regard to deformation problems involving nonlinear material analysis. As it is contemporary the FVM is developed from early finite difference techniques and has similarly established itself within the field of CFD. Both classes of methods integrate governing equations over predefined control volumes, which are associated with the elements making up the domain of interest. Furthermore, both approaches can be classified as weighted residual methods where they differ in the weighting functions adopted.

In many engineering applications there is an emerging need to model multiphysics problems in a coupled manner. In principle, because of their local conservation properties the FVMs should be in a good position to solve such problems effectively. Over the last decade a number of researchers have applied FVMs to solve problems in CSM and it is now possible to classify these methods into two approaches, cell-centered and vertex-based ones. Subsequently such techniques have been applied to CSM problems using structured and unstructured meshes. With regard to these techniques it should be noted that when solid bodies undergo deformation the application of mechanical boundary conditions is the most effective if they can be imposed directly on the physical boundary. Obviously the cell-centered approximation may have difficulty in prescribing the boundary conditions, when complex geometries are considered and where displacements at the boundary are not prescribed directly and in a straightforward manner.

The second approach is based on some basic ideas of traditional FE methods, which employ shape functions to describe the variation of an independent variable, such as displacement, over an element and is therefore well suited to complex geometries. The approach can be roughly classified as a cell-vertex FVM.

Both the above-mentioned FV approaches apply strict conservation laws over a control volume and have demonstrated superiority over traditional FE methods with regard to accuracy. Some researchers have attributed this to the local conservation of independent variables as enforced by the control-volume methods employed and others to the enforced continuity of the derivatives of the independent variables across cell boundaries. In this book we solve both NS and Cauchy’s equations using a novel FVM scheme in which such treatment has expressed significant merit in the solver development of two-way FSI.

1.4 Moving Boundary

Moving boundary problems have important engineering applications in a variety of engineering fields such as solid and fluid dynamics, combustion, heat transfer, material sciences. Currently many techniques are devoted to solve the moving boundary problems, and these techniques are classified into three major groups, namely Eulerian method, arbitrary Lagrangian–Eulerian (ALE) method, and hybrid method, based on the property of computational grids used in the calculations. The following subsections give only a review of the methods used to tackle moving boundary problems.

1.4.1 Eulerian Method

In the Eulerian method the mesh is stationary and does not move or deform. Therefore fluid motion can be conveniently described with respect to this Eulerian reference frame. The Eulerian method includes the fictitious domain method (FDM), immersed boundary method (IBM), immersed object method (IOM), immersed membrane method (IMM), ghost cell method (GCM), ghost fluid method (GFM), and volume of fluid (VOF) method, etc. IOM and IMM will be reviewed in the following subsections.

1.4.1.1 Immersed Object Method

A novel and efficient IOM is proposed by the authors’ research group for numerical simulation of blood flows in prosthetic heart valves under physiological conditions and blood–leaflet interaction. The IOM is similar to the IBM in the sense that they both use a combination of Eulerian approach for the fluid and Lagrangian for the structure.

Peskin et al. [2–4] proposed IBM to simulate the natural heart and heart valves combining Eulerian flow equations and a Lagrangian description of heart walls and valves. The philosophy of the IBM is to treat the elastic material as a part of the fluid in which additional forces (arising from the elastic stresses) are applied. The fluid equations are solved on a regular mesh grid, the structure of which is not modified in any way by the presence of the immersed elastic bodies and the geometry of which may be quite complicated. The elastic material is tracked in Lagrangian fashion, by following a collection of representative material points. The spatial configuration of these points is used to compute elastic forces, which are applied to the nearby grid points of the fluid. The fluid velocity is updated under the influence of these forces, and the new velocity is then interpolated at the elastic material points, which are moved at the interpolated velocity to complete the time step. The IBM has been...

Table of contents

• Cover image
• Title page
• Table of Contents
• Copyright
• Preface
• Chapter 1. Introduction
• Chapter 2. Mathematical Formulation for Preconditioned Compressible Flow Solver
• Chapter 3. Mathematical Formulation for Incompressible Flow Solver
• Chapter 4. Mathematical Formulation for Computational Structural Dynamics
• Chapter 5. The Multigrid Method
• Chapter 6. Parallel Computation
• Chapter 7. The Immersed Object Method With Overlapping Grids
• Chapter 8. The Immersed Membrane Method and Fluid-Structure Interaction
• Chapter 9. Arbitrary Lagrangian–Eulerian (ALE) Method and Fluid-Structure Interaction
• Chapter 10. IOM FSI Model Validations and Applications
• Chapter 11. IMM FSI Model Validations and Applications for Incompressible Flows
• Chapter 12. IMM FSI Model Validations and Applications for Compressible Flows
• Chapter 13. ALE FSI Model Validations and Applications
• Index