Compressible Flow Propulsion and Digital Approaches in Fluid Mechanics

Michel Ledoux, Professor at University of Rouen. Abdelkhalak Elhami, Professor at INSA Rouen.

Preface ix

Chapter 1 The Flow of Viscous Fluids Flow in the Vicinity of a Wall: Boundary Layers and Films 1

1.1 Introduction 1

1.2 Characteristics and classification of boundary layers 1

1.2.1 Boundary layers – various approaches 4

1.3 The outer boundary layers: an analytical approach 4

1.3.1 The laminar boundary layer developed by a flat plate in a uniform flow 4

1.3.2 The turbulent boundary layer 8

1.4 Examples of analytical approach: outer flows 13

1.5 Examples of analytical approach: inner flows 23

1.6 Outer boundary layers: integral methods 43

1.6.1 Principle of the integral method 43

1.6.2 Applications of integral methods 46

1.7 Channels and films 62

Chapter 2 One-dimensional Compressible Flows: Fully Reversible Flows 77

2.1 Introduction 77

2.2 One-dimensional adiabatic and reversible flows 78

2.2.1 Hypotheses adopted 78

2.2.2 Writing the laws 79

2.2.3 Other useful relations 79

2.2.4 Fundamental relations 85

2.2.5 Calculation of flow rate in a piping system 88

2.2.6 De Laval nozzle 92

2.3 Applications Reversible adiabatic flows 95

Chapter 3 One-dimensional Compressible Flows: Irreversible Flows 125

3.1 Introduction 125

3.2 Irreversible flow: straight shock wave 125

3.2.1 Establishing the fundamental relations 125

3.2.2 Applications 129

3.3 Partially irreversible flows: shock wave in a nozzle 144

3.3.1 Change of the generating state by the shock wave 144

3.3.2 Applications 146

3.4 Conclusion 156

Chapter 4 Modeling and Numerical Simulations 159

4.1 Introduction 159

4.2 Methodology description and simulation approach 160

4.3 Modeling and simulation of coupled systems 163

4.3.1 Mathematical formulation Behavior equations 163

4.3.2 Fluid–structure coupling conditions 164

4.4 Variational formulation 165

4.5 Finite element approximation 165

4.5.1 Approximation of physical unknowns 166

4.5.2 Integration of variational forms 166

4.6 The vibro-acoustic problem 166

4.7 The hydro-elastic problem 167

4.8 Applications 168

4.9 Conclusion 196

Chapter 5 Numerical Simulation of a Vertical-axis Wind Turbine 197

5.1 Introduction 197

5.2 Construction of the rotor geometry and definition of the computational domain 197

5.2.1 Mesh 199

5.2.2 Discretization scheme 202

5.2.3 System resolution and convergence 205

5.3 Analysis of the results 206

5.3.1 Validation of the CFD model 206

5.3.2 Influence of the characteristic parameters 210

5.4 Conclusion 216

Appendix 217

Bibliography 265

Index 269