Fluid Mechanics at Interfaces 2 : Case Studies and Instabilities

Interfaces are present in most fluid mechanics problems. They not only denote phase separations and boundary conditions, but also thin flames and discontinuity waves. Fluid Mechanics at Interfaces 2 examines cases that involve one-dimensional or bi-dimensional manifolds, not only in gaseous and liquid physical states but also in subcritical fluids and in single- and multi-phase systems that may be pure or mixed. Chapter 1 addresses certain aspects of turbulence in discrete mechanics, briefly describing the physical model associated with discrete primal and dual geometric topologies before focusing on channel flow simulations at turbulence-inducing Reynolds numbers. Chapter 2 centers on atomization in an accelerating domain. In one case, an initial Kelvin–Helmholtz instability generates an acceleration field, in turn creating a Rayleigh–Taylor instability which ultimately determines the size of the droplets formed. Chapter 3 explores numerical studies of pipes with sudden contraction using OpenFOAM, and focuses on modeling that will be useful for engines and automobiles. Chapters 4 and 5 study the evaporation of droplets that are subject to high-frequency perturbations, a possible cause of instabilities in injection engines. The Heidmann model, which replaces the droplets in motion in a combustion chamber with a single continuously-fed droplet, is made more complex by considering the finite conduction heat transfer phenomenon. Finally, Chapter 6 is devoted to a study of the rotor blade surface of a Savonius wind turbine, considering both a non-stationary and a three-dimensional flow. Cover Half-Title Page Title Page Copyright Page Contents Preface 1. Turbulent Channel Flow to Reτ = 590 in Discrete Mechanics 1.1. Introduction 1.2. Discrete mechanics formulation 1.3. Turbulent flow in channel 1.3.1. Analysis of a turbulent flow in a planar channel 1.3.2. Model of the turbulence in discrete mechanics 1.3.3. Application to a turbulent flow in a channel with Reτ = 590 1.4. Conclusion 1.5. References 2. Atomization in an Acceleration Field List of symbols 2.1. Introduction 2.1.1. Two classic instabilities 2.1.2. Atomization 2.2. Generation of droplets through vibrations normal to the liquid layer 2.3. Rayleigh–Taylor instability at the crest of an axial wave 2.3.1. Size distribution of the drops 2.4. Recent work 2.5. Conclusion 2.6. References 3. Numerical Simulation of Pipes with an Abrupt Contraction Using OpenFOAM 3.1. Introduction 3.2. Modeling an abrupt contraction in a pipe 3.2.1. Euler equations 3.2.2. Stability of the solver 3.2.3. Introducing the model 3.2.4. Boundary and initial conditions 3.3. Numerical results 3.3.1. Results with the boundary and initial conditions I 3.3.2. Results with the boundary and initial conditions II 3.4. Conclusion and future prospects 3.5. References 4. Vaporization of an Equivalent Pastille List of symbols 4.1. Introduction 4.2. Equations for the problem 4.3. Linear analysis of the liquid phase 4.3.1. The function G(u,PeL) 4.3.2. Solution 4.3.3. The depth to which heat penetrates 4.4. Some results 4.4.1. Thermal perturbations 4.4.2. Response factor 4.5. Conclusion 4.6. References 5. Thermal Field of a Continuously-Fed Drop Subjected to HF Perturbations List of symbols 5.1. Drops in a liquid-propellant rocket engine 5.2. A continuously fed droplet 5.3. Equations of the problem 5.3.1. Equations for the gaseous phase 5.3.2. Equations for the liquid phase 5.4. Linearized equations 5.5. Linearized equations for small harmonic perturbations 5.6. Thermal field in the drop when neglecting internal convection 5.7. Conclusion 5.8. Appendix 1: Coefficients that come into play in linearized equations 5.9. Appendix 2: Solving the thermal equation 5.10. Appendix 3: The case of the equivalent pastille 5.11. Appendix 4: 2D representation for the spherical drop 5.12. References 6. Study of the Three-Dimensional and Non-Stationary Flow in a Rotor of the Savonius Wind Turbine 6.1. Introduction 6.2. Mathematical modeling of the problem 6.2.1. Presentation of a physical model 6.2.2. Simplifying hypotheses 6.3. Numerical resolution 6.3.1. Presentation of meshes 6.3.2. Spatial discretization 6.3.3. Temporal discretization 6.3.4. Stability condition for the scheme 6.3.5. Initial conditions 6.3.6. Boundary conditions 6.4. Validation of the results 6.5. Results and discussion 6.5.1. Influence of the advance parameter 6.5.2. Influence of the angular position of the blades 6.6. Conclusion 6.7. Acknowledgments 6.8. References List of Authors Index Summary of Volume 1 Other titles from iSTE in Fluid Mechanics