Fluid Mechanics at Interfaces 2

Fluid Mechanics at Interfaces 2
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Interfaces are present in most fluid mechanics problems. They not only denote phase separations and boundary conditions, but also thin flames and discontinuity waves. <i>Fluid Mechanics at Interfaces 2</i> 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.<br /><br />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.<br /><br />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.

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Группа авторов. Fluid Mechanics at Interfaces 2

Table of Contents

List of Tables

List of Illustrations

Guide

Pages

Fluid Mechanics at Interfaces 2

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 Field1

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. 3.3.1.1. Variation in mean flow rate and mean enthalpy

3.3.1.2. Variation in mean mass

3.3.1.3. Glyphs and contour line

3.3.1.4. Isosurfaces

3.3.2. Results with the boundary and initial conditions II. 3.3.2.1. Mesh for a quarter of the domain

3.3.2.2. Variations in the mean flow rate

3.3.2.3. The vector field and isosurfaces

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

A

C, D

E

F, H

I, L, N

O, P, R

S, T, V

Summary of Volume 1

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Отрывок из книги

Case Studies and Instabilities

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Chapters 4 (R. Prud’homme and K. Anani) and 5 (R. Prud’homme, K. Anani and M.N. Hounkonnou) study the evaporation of droplets subject to HF (high-frequency) perturbations, a possible cause of instabilities in injection engines. The Heidmann model, which replaces the droplets in motion in the combustion chamber by a single continuously fed droplet, is complexified by taking into account the finite conduction heat transfer phenomenon. This accentuates the damping of oscillations in the evaporation rate. We study the temperature field within the drop, as well as the response factor of a spherical drop to the high-frequency pressure field created by the engine. A pastille-shaped model of the drop is used, replacing the spherical drop, which makes it possible to go further with linearized calculations.

Finally, Chapter 6 (F. Raveloson, D. Tomboravo and R. Vony) presents the study of the interface, which is the surface of rotor blades in a Savonius wind turbine. A non-stationary and 3D flow is studied.

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