Fluid-Structure Interactions and Uncertainties: Ansys and Fluent Tools

ISBN-13: 9781848219397 / Angielski / Twarda / 2017 / 284 str.

Bouchaib Radi; Abdelkhalak El Hami

Opis

This book is dedicated to the general study of fluid structure interaction with consideration of uncertainties. The fluid-structure interaction is the study of the behavior of a solid in contact with a fluid, the response can be strongly affected by the action of the fluid. These phenomena are common and are sometimes the cause of the operation of certain systems, or otherwise manifest malfunction. The vibrations affect the integrity of structures and must be predicted to prevent accelerated wear of the system by material fatigue or even its destruction when the vibrations exceed a certain threshold.

Spis treści

Preface ix

Chapter 1. Fluid Structure Interaction  1

1.1. Introduction  1

1.2. Fluid structure interaction problem 2

1.2.1. Fluid structure coupling methods  5

1.2.2. Temporal coupling 8

1.2.3. Spatial coupling  11

1.3. Vibroacoustics 14

1.3.1. Vibrations of three–dimensional solids 15

1.3.2. Acoustics of fluids 17

1.3.3. Numerical methods for calculating a structure coupled with a stagnant fluid  18

1.4. Aerodynamics 21

1.4.1. Aeroelastic problems 23

1.4.2. Aerodynamic loads  26

1.4.3. Problem equations 29

Chapter 2. Fluid Structure Interaction with Ansys/Fluent  35

2.1. Presentation of Ansys 35

2.2. Coupling with Ansys 37

2.2.1. Types of coupling analysis  38

2.3. Example of fluid structure interaction using the physics environment 40

2.3.1. Fluid in motion  40

2.3.2. Stagnant fluid 48

2.4. Example of interaction using Fluent 54

Chapter 3. Vibroacoustics  59

3.1. Introduction  59

3.2. Equations of the acoustic and structure problems 60

3.2.1. Equation of the acoustic problem  60

3.2.2. Boundary conditions of the acoustic problem 61

3.2.3. Equation of the structure problem  62

3.2.4. Boundary conditions of the structure problem 62

3.3. Vibroacoustic problem  63

3.3.1. Problem statement 64

3.3.2. Boundary conditions at the interface 65

3.3.3. Finite element approximation  66

3.4. Study of an elastic plate coupled with a fluid cavity  86

3.4.1. Equations of the coupled fluid structure problem 87

3.4.2. Variational formulation of the fluid 88

3.4.3. Variational formulation of the plate 92

3.4.4. Numerical results 94

3.5. Study of the propeller of a boat  97

3.5.1. Numerical results 99

Chapter 4. Aerodynamics 103

4.1. Introduction  103

4.2. Computational method  104

4.2.1. Conformal mesh  104

4.2.2. Immersed boundary methods 105

4.2.3. Volume–based fictitious domain methods  106

4.3. Aerodynamic problem s resolution 107

4.3.1. Mobile domain 107

4.3.2. Weak formulation 108

4.3.3. Evaluating the energy of the system 111

4.3.4. Numerically solving the system 116

4.3.5. Discretization by finite elements 120

4.4. Finite element method for the solid 123

4.4.1. Discretization 124

4.4.2. Assembling the system  126

4.4.3. Solving the system of algebraic equations 126

4.4.4. Integration by Gaussian quadrature 126

4.4.5. Advancing the time step using the Hilbert Hugues Taylor algorithm 127

4.4.6. Linearization using the Newton Raphson algorithm  129

4.5. Finite volumes for the fluid  130

4.5.1. Generic transport equation  130

4.5.2. Conservation property of the method  131

4.5.3. The different steps in the method  131

4.5.4. Integrating the model equation  132

4.5.5. Control volumes  133

4.5.6. Physical interpolation 135

4.5.7. Evaluating the flux through the faces  135

4.5.8. Centered scheme  136

4.5.9. Upwind scheme  138

4.5.10. Hybrid scheme  139

4.5.11. Discretization 139

4.6. Coupling procedures 141

4.6.1. Coupling strategies  141

4.6.2. Implicit partitioned coupling 142

4.7. Numerical results 145

4.7.1. Static analysis 145

4.8. Study of a 3D airplane wing 150

4.8.1. Modal analysis 153

4.9. Transient analysis 154

Chapter 5. Modal Reduction for FSI  163

5.1. Introduction  163

5.2. Dynamic substructuring methods  164

5.2.1. Linear problems  165

5.2.2. Nonlinear problems  167

5.3. Nonlinear substructuring method  169

5.3.1. Vibrational equations of a substructure 170

5.3.2. Fixed–interface problem  171

5.3.3. Static bearing problem  172

5.3.4. Representing the system with the linear Craig Bampton basis 173

5.3.5. Model reduction using the approach of Shaw and Pierre 174

5.3.6. Assembling the substructures  176

5.4. Proper orthogonal decomposition for flows 178

5.4.1. Properties of POD modes 179

5.4.2. Snapshot POD 179

5.4.3. Finding low–order expressions for dynamic systems  180

5.5. Dynamic substructure/acoustic subdomain coupling  185

5.5.1. Basic equations  187

5.5.2. Variational formulations 190

5.5.3. Discretization by finite elements 191

5.5.4. Calculating the local modes 194

5.5.5. Modal synthesis  196

5.6. Numerical simulation 199

5.6.1. Elastic ring 199

5.6.2. Boat propeller 206

Chapter 6. Reliability–based Optimization for FSI 211

6.1. Introduction  211

6.2. Reliability in mechanics  212

6.2.1. Random variables 212

6.2.2. Reliability function  214

6.3. Failure in mechanics  215

6.3.1. Failure scenarios  216

6.3.2. Expression of the failure probability 217

6.4. Reliability index  217

6.4.1. Rjanitzyne Cornell index 217

6.4.2. Hasofer Lind index  218

6.5. Mechanoreliability coupling 218

6.5.1. Reliability–based calculation methods  219

6.5.2. Monte Carlo method 220

6.5.3. FORM/SORM approximation methods 221

6.6. Reliability–based optimization in mechanics  224

6.6.1. Deterministic optimization  225

6.6.2. Different approaches to RBDO  226

6.6.3. Classical approach 228

6.6.4. Hybrid approach  229

6.6.5. Frequency–based hybrid approach  231

6.7. SP method 234

6.7.1. Formulation of the problem  234

6.8. Numerical results 237

6.8.1. Reliability calculation for an airplane wing 237

6.8.2. Application of RBDO to the airplane wing 239

Bibliography 253

Index 263