Fluid Mechanics at Interfaces 1: Methods and Diversity

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 1 focuses on the science of interfaces, in particular, using various scientific methods of analysis relating to space, speed and time. Our investigation takes us from the microscopic or small scale (starting with molecular and nanoscopic scales) to the macroscopic (including meso and interstellar scales), and also explores the laws of interfaces (classical mechanics, quantum mechanics and relativistic mechanics). Chapter 1 examines the questions raised by modeling interfaces in the presence of one or more fluid phases. Chapter 2 discusses the action of turbulence in liquid–vapor flows that contain both small, dispersed bubbles as well as large bubbles, with heat exchanges at the interfaces. In addition, a new model is presented, using large eddy simulation (LES). Chapter 3 studies an original method for calculating the drag force and thermal transfers in flows around networks of spherical particles, while Chapter 4 focuses on the relationships between interfaces and critical fluids. Chapter 5 examines shearing, which causes anomalies in the Brownian motion of particles in strongly fluctuating near-critical mixtures, and Chapter 6 introduces basic concepts related to combustion interfaces, raising the question of the combustion of solids, before ending with a brief presentation of the Rankine–Hugoniot theory and a historical overview of the research carried out in the field of combustion.

Table of Contents:
Preface ix Roger PRUD’HOMME, Stéphane VINCENT, Christian CHAUVEAU and Mahouton Norbert HOUNKONNOU Chapter 1. Modeling Interfaces with Fluid Phase 1 Roger PRUD’HOMME 1.1. The concept of an interface 3 1.1.1. Interface in physics and geometric surfaces 3 1.1.2. The concept of equilibrium in the domain of interfaces 6 1.2. Some examples of interfaces 6 1.2.1. Fluid phase change and separation interface 6 1.2.2. Solidification interface 7 1.2.3. Generalized interfaces 8 1.3. Mathematical description of an interfacial layer 10 1.3.1. Normal gradient and tangential gradient 12 1.3.2. Structure and kinematics of an interfacial layer 13 1.3.3. Bulk and surface quantities 16 1.3.4. Interface balances 17 1.3.5. Constitutive laws 20 1.4. Some additional information and examples of application 22 1.4.1. Effective surface tension between two miscible liquids 22 1.4.2. Terms that come into play in interface balance laws 23 1.4.3. Normal shockwave 24 1.4.4. Combustion waves 26 1.4.5. Thin premixed flame 29 1.4.6. Boundary layers 31 1.5. Conclusion 31 1.6. References 33 Chapter 2. Simulations of Turbulent Two-Phase Flows with Phase Change Using a Multifield Approach Combined with LES 37 Solène GOUÉNARD, Stéphane VINCENT and Stéphane MIMOUNI 2.1. Introduction 40 2.2. Computational model 42 2.2.1. Two-fluid model 43 2.2.2. Large Bubble Model 44 2.3. Filtered two-fluid equations 46 2.4. A priori LES study 47 2.4.1. Presentation of the test case 48 2.4.2. Order of magnitude of the subgrid terms 49 2.4.3. Comparison of turbulence models 52 2.4.4. ADM order 56 2.4.5. Effect of the filter 58 2.5. Comparison of turbulence models with true LES 61 2.5.1. Presentation of the METERO experiment 62 2.5.2. Presentation of the test case 63 2.5.3. Simulation results 63 2.5.4. Comparison between RANS and LES 64 2.5.5. ADM implementation 66 2.6. New phase change model for large interfaces 68 2.6.1. Implementation of the new heat flux model 68 2.6.2. Validation of the new heat transfer model 70 2.6.3. Sucking problem 71 2.6.4. Stefan problem 74 2.7. Conclusion 77 2.8. References 78 Chapter 3. An Original Approach to Extract Momentum and Heat Transfers from Particle-Resolved Simulations of Particulate Flows 83 Mohamed-Amine CHADIL, Stéphane VINCENT and Jean-Luc ESTIVALÈZES 3.1. Introduction 83 3.2. Numerical methodology 86 3.2.1. Viscous penalty method 86 3.2.2. Drag force and heat flux computation using Aslam extension 88 3.3. Isolated stationary sphere passed by a uniform flow 99 3.3.1. Drag force computation 100 3.3.2. Heat transfer computation 105 3.4. Face-centered cubic arrangement of stationary sphere passed by a uniform flow 107 3.4.1. Monodispersed face-centered cubic periodic arrangement of spheres 108 3.4.2. Bidisperse face-centered cubic periodic arrangement of spheres 111 3.5. Conclusion 113 3.6. Acknowledgments 114 3.7. References 114 Chapter 4. Interfaces and Critical Fluids 121 Roger PRUD’HOMME 4.1. Thermostatics of fluids in the vicinity of the critical point 123 4.1.1. Real fluids 123 4.1.2. A van der Waals fluid 125 4.1.3. Other laws for gases and dense liquids 128 4.2. Thermodynamics of fluids in the vicinity of the critical point 129 4.2.1. Universal exponents 129 4.2.2. Isobaric evolutions 131 4.2.3. Valid expressions of varying distance from the critical point 131 4.2.4. Summary of theoretical approaches 132 4.3. A specific mode of heat transmission: the piston effect 132 4.4. Expansion of a “drop” at critical pressure 136 4.5. Behavior of a pocket of supercritical fluid immersed into a high-temperature environment 139 4.6. Boiling near the critical point 142 4.7. Conclusion 146 4.8. References 146 Chapter 5. Shear-Induced Anomalies in the Brownian Motion of Particles in Strongly Fluctuating Near-Critical Mixtures 151 Daniel BEYSENS 5.1. Introduction 151 5.2. Theoretical background 152 5.2.1. Miscibility critical point in binary mixtures 152 5.2.2. Effect of shear flow 154 5.2.3. Colloid Brownian motion and shear flow 156 5.3. Experiments and methods 158 5.4. Results and discussion 161 5.5. Concluding remarks 163 5.6. Acknowledgements 163 5.7. Appendix: Light scattering (photon beating spectroscopy) 163 5.8. References 165 Chapter 6. Basics on Interfaces in Combustion 167 Roger PRUD’HOMME 6.1. Introduction 168 6.2. Non-premixed laminar combustion 172 6.2.1. Overview of a candle flame 172 6.2.2. Analytical solution of a diffusion flame: the Burke–Schumann problem 173 6.2.3. Numerical solutions 176 6.3. Turbulent non-premixed combustion 176 6.4. Premixed combustion 179 6.4.1. Propagation of a premixed flame 181 6.4.2. The combustion rate of the adiabatic, planar premixed flame 183 6.4.3. Concepts in turbulent premixed combustion 187 6.5. Plate combustion 188 6.6. Powders 191 6.6.1. Thermites 191 6.6.2. Solid propellant rockets 192 6.6.3. Spin-like combustion 196 6.7. Sprays and fireworks 197 6.8. Conclusion 199 6.9. Acknowledgments 200 6.10. Appendices 201 6.10.1. Appendix A: The Rankine–Hugoniot theory 201 6.10.2. Appendix B: Historical overview of research on combustion 212 6.11. References 214 List of Authors 219 Index 221 Summary of Volume 2 223