Compressible Flow Propulsion and Digital Approaches in Fluid Mechanics

This book aims to provide an efficient methodology of solving a fluid mechanics problem, based on an awareness of the physical. It meets different objectives of the student, the future engineer or scientist: Simple sizing calculations are required to master today's numerical approach for solving complex practical problems.

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