Fluid Mechanics at Interfaces 2

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 Turbulent Channel Flow to Re τ = 590 in Discrete Mechanics 1Jean-Paul CALTAGIRONE and Stéphane VINCENT1.1 Introduction 11.2 Discrete mechanics formulation 41.3 Turbulent flow in channel 61.3.1 Analysis of a turbulent flow in a planar channel 61.3.2 Model of the turbulence in discrete mechanics 121.3.3 Application to a turbulent flow in a channel with Re τ =̷590 131.4 Conclusion 241.5 References 24Chapter 2 Atomization in an Acceleration Field 27Roger PRUD’HOMME2.1 Introduction 292.1.1 Two classic instabilities 292.1.2 Atomization 312.2. Generation of droplets through vibrations normal to the liquid layer 322.3 Rayleigh–Taylor instability at the crest of an axial wave 362.3.1 Size distribution of the drops 392.4 Recent work 402.5 Conclusion 402.6 References 41Chapter 3 Numerical Simulation of Pipes with an Abrupt Contraction Using OpenFOAM 45Tarik CHAKKOUR3.1 Introduction 453.2 Modeling an abrupt contraction in a pipe 463.2.1 Euler equations 463.2.2 Stability of the solver 483.2.3 Introducing the model 493.2.4 Boundary and initial conditions 513.3 Numerical results 543.3.1 Results with the boundary and initial conditions I 553.3.2 Results with the boundary and initial conditions II 673.4 Conclusion and future prospects 733.5 References 74Chapter 4 Vaporization of an Equivalent Pastille 77Roger PRUD’HOMME and Kwassi ANANI4.1 Introduction 784.2 Equations for the problem 814.3 Linear analysis of the liquid phase 824.3.1 The function G(u, Pe L) 824.3.2 Solution 834.3.3 The depth to which heat penetrates 844.4 Some results 854.4.1 Thermal perturbations 854.4.2 Response factor 874.5 Conclusion 914.6 References 92Chapter 5 Thermal Field of a Continuously-Fed Drop Subjected to HF Perturbations 95Roger PRUD’HOMME, Kwassi ANANI and Mahouton Norbert HOUNKONNOU5.1 Drops in a liquid-propellant rocket engine 965.2 A continuously fed droplet 985.3 Equations of the problem 995.3.1 Equations for the gaseous phase 995.3.2 Equations for the liquid phase 1015.4 Linearized equations 1025.5 Linearized equations for small harmonic perturbations 1035.6 Thermal field in the drop when neglecting internal convection 1035.7 Conclusion 1075.8 Appendix 1: Coefficients that come into play in linearized equations 1075.9 Appendix 2: Solving the thermal equation 1085.10 Appendix 3: The case of the equivalent pastille 1095.11 Appendix 4: 2D representation for the spherical drop 1115.12 References 113Chapter 6 Study of the Three-Dimensional and Non-Stationary Flow in a Rotor of the Savonius Wind Turbine 115Francis RAVELOSON, Delphin TOMBORAVO and Roger VONY6.1 Introduction 1156.2 Mathematical modeling of the problem 1166.2.1 Presentation of a physical model 1166.2.2 Simplifying hypotheses 1196.3 Numerical resolution 1206.3.1 Presentation of meshes 1206.3.2 Spatial discretization 1236.3.3 Temporal discretization 1236.3.4 Stability condition for the scheme 1246.3.5 Initial conditions 1256.3.6 Boundary conditions 1256.4 Validation of the results 1266.5 Results and discussion 1276.5.1 Influence of the advance parameter 1276.5.2 Influence of the angular position of the blades 1346.6 Conclusion 1446.7 Acknowledgments 1446.8 References 144List of Authors 147Index 149Summary of Volume 1 151