Fluid Mechanics at Interfaces 1

Roger Prud'homme is the Emeritus Research Director at CNRS, France. His most recent research topics have included flames, two-phase flows and the modeling of fluid interfaces.Stéphane Vincent is Professor at the Gustave Eiffel University, France. He leads the Heat and Mass Transfer team of the MSME laboratory. His research focuses on models and numerical methods for multiphase flows.

• Preface ixRoger PRUD’HOMME, Stéphane VINCENT, Christian CHAUVEAU and Mahouton Norbert HOUNKONNOUChapter 1. Modeling Interfaces with Fluid Phase 1Roger PRUD’HOMME1.1. The concept of an interface 31.1.1. Interface in physics and geometric surfaces 31.1.2. The concept of equilibrium in the domain of interfaces 61.2. Some examples of interfaces 61.2.1. Fluid phase change and separation interface 61.2.2. Solidification interface 71.2.3. Generalized interfaces 81.3. Mathematical description of an interfacial layer 101.3.1. Normal gradient and tangential gradient 121.3.2. Structure and kinematics of an interfacial layer 131.3.3. Bulk and surface quantities 161.3.4. Interface balances 171.3.5. Constitutive laws 201.4. Some additional information and examples of application 221.4.1. Effective surface tension between two miscible liquids 221.4.2. Terms that come into play in interface balance laws 231.4.3. Normal shockwave 241.4.4. Combustion waves 261.4.5. Thin premixed flame 291.4.6. Boundary layers 311.5. Conclusion 311.6. References 33Chapter 2. Simulations of Turbulent Two-Phase Flows with Phase Change Using a Multifield Approach Combined with LES 37Solène GOUÉNARD, Stéphane VINCENT and Stéphane MIMOUNI2.1. Introduction 402.2. Computational model 422.2.1. Two-fluid model 432.2.2. Large Bubble Model 442.3. Filtered two-fluid equations 462.4. A priori LES study 472.4.1. Presentation of the test case 482.4.2. Order of magnitude of the subgrid terms 492.4.3. Comparison of turbulence models 522.4.4. ADM order 562.4.5. Effect of the filter 582.5. Comparison of turbulence models with true LES 612.5.1. Presentation of the METERO experiment 622.5.2. Presentation of the test case 632.5.3. Simulation results 632.5.4. Comparison between RANS and LES 642.5.5. ADM implementation 662.6. New phase change model for large interfaces 682.6.1. Implementation of the new heat flux model 682.6.2. Validation of the new heat transfer model 702.6.3. Sucking problem 712.6.4. Stefan problem 742.7. Conclusion 772.8. References 78Chapter 3. An Original Approach to Extract Momentum and Heat Transfers from Particle-Resolved Simulations of Particulate Flows 83Mohamed-Amine CHADIL, Stéphane VINCENT and Jean-Luc ESTIVALÈZES3.1. Introduction 833.2. Numerical methodology 863.2.1. Viscous penalty method 863.2.2. Drag force and heat flux computation using Aslam extension 883.3. Isolated stationary sphere passed by a uniform flow 993.3.1. Drag force computation 1003.3.2. Heat transfer computation 1053.4. Face-centered cubic arrangement of stationary sphere passed by a uniform flow 1073.4.1. Monodispersed face-centered cubic periodic arrangement of spheres 1083.4.2. Bidisperse face-centered cubic periodic arrangement of spheres 1113.5. Conclusion 1133.6. Acknowledgments 1143.7. References 114Chapter 4. Interfaces and Critical Fluids 121Roger PRUD’HOMME4.1. Thermostatics of fluids in the vicinity of the critical point 1234.1.1. Real fluids 1234.1.2. A van der Waals fluid 1254.1.3. Other laws for gases and dense liquids 1284.2. Thermodynamics of fluids in the vicinity of the critical point 1294.2.1. Universal exponents 1294.2.2. Isobaric evolutions 1314.2.3. Valid expressions of varying distance from the critical point 1314.2.4. Summary of theoretical approaches 1324.3. A specific mode of heat transmission: the piston effect 1324.4. Expansion of a “drop” at critical pressure 1364.5. Behavior of a pocket of supercritical fluid immersed into a high-temperature environment 1394.6. Boiling near the critical point 1424.7. Conclusion 1464.8. References 146Chapter 5. Shear-Induced Anomalies in the Brownian Motion of Particles in Strongly Fluctuating Near-Critical Mixtures 151Daniel BEYSENS5.1. Introduction 1515.2. Theoretical background 1525.2.1. Miscibility critical point in binary mixtures 1525.2.2. Effect of shear flow 1545.2.3. Colloid Brownian motion and shear flow 1565.3. Experiments and methods 1585.4. Results and discussion 1615.5. Concluding remarks 1635.6. Acknowledgements 1635.7. Appendix: Light scattering (photon beating spectroscopy) 1635.8. References 165Chapter 6. Basics on Interfaces in Combustion 167Roger PRUD’HOMME6.1. Introduction 1686.2. Non-premixed laminar combustion 1726.2.1. Overview of a candle flame 1726.2.2. Analytical solution of a diffusion flame: the Burke–Schumann problem 1736.2.3. Numerical solutions 1766.3. Turbulent non-premixed combustion 1766.4. Premixed combustion 1796.4.1. Propagation of a premixed flame 1816.4.2. The combustion rate of the adiabatic, planar premixed flame 1836.4.3. Concepts in turbulent premixed combustion 1876.5. Plate combustion 1886.6. Powders 1916.6.1. Thermites 1916.6.2. Solid propellant rockets 1926.6.3. Spin-like combustion 1966.7. Sprays and fireworks 1976.8. Conclusion 1996.9. Acknowledgments 2006.10. Appendices 2016.10.1. Appendix A: The Rankine–Hugoniot theory 2016.10.2. Appendix B: Historical overview of research on combustion 2126.11. References 214List of Authors 219Index 221Summary of Volume 2 223