Fluid Mechanics at Interfaces 1

1 Cover

2 Title Page

3 Copyright First published 2022 in Great Britain and the United States by ISTE Ltd and John Wiley & Sons, Inc. Apart from any fair dealing for the purposes of research or private study, or criticism or review, as permitted under the Copyright, Designs and Patents Act 1988, this publication may only be reproduced, stored or transmitted, in any form or by any means, with the prior permission in writing of the publishers, or in the case of reprographic reproduction in accordance with the terms and licenses issued by the CLA. Enquiries concerning reproduction outside these terms should be sent to the publishers at the undermentioned address: ISTE Ltd 27-37 St George’s Road London SW19 4EU UK www.iste.co.uk John Wiley & Sons, Inc. 111 River Street Hoboken, NJ 07030 USA www.wiley.com © ISTE Ltd 2022 The rights of Roger Prud’homme and Stéphane Vincent to be identified as the authors of this work have been asserted by them in accordance with the Copyright, Designs and Patents Act 1988. Library of Congress Control Number: 2021949304 British Library Cataloguing-in-Publication Data A CIP record for this book is available from the British Library ISBN 978-1-78630-816-0

4 Preface

5 1 Modeling Interfaces with Fluid Phase 1.1 The concept of an interface 1.2 Some examples of interfaces 1.3 Mathematical description of an interfacial layer 1.4 Some additional information and examples of application 1.5 Conclusion 1.6 References

6 2 Simulations of Turbulent Two-Phase Flows with Phase Change Using a Multifield Approach Combined with LES 2.1 Introduction 2.2 Computational model 2.3 Filtered two-fluid equations 2.4 A prioriLES study 2.5 Comparison of turbulence models with true LES 2.6 New phase change model for large interfaces 2.7 Conclusion 2.8 References

7 3 An Original Approach to Extract Momentum and Heat Transfers from Particle-Resolved Simulations of Particulate Flows 3.1 Introduction 3.2 Numerical methodology 3.3 Isolated stationary sphere passed by a uniform flow 3.4 Face-centered cubic arrangement of stationary sphere passed by a uniform flow 3.5 Conclusion 3.6 Acknowledgments 3.7 References

8 4 Interfaces and Critical Fluids 4.1 Thermostatics of fluids in the vicinity of the critical point 4.2 Thermodynamics of fluids in the vicinity of the critical point 4.3 A specific mode of heat transmission: the piston effect 4.4 Expansion of a “drop” at critical pressure 4.5 Behavior of a pocket of supercritical fluid immersed into a high-temperature environment 4.6 Boiling near the critical point 4.7 Conclusion 4.8 References

9 5 Shear-Induced Anomalies in the Brownian Motion of Particles in Strongly Fluctuating Near-Critical Mixtures 5.1 Introduction 5.2 Theoretical background 5.3 Experiments and methods 5.4 Results and discussion 5.5 Concluding remarks 5.6 Acknowledgements 5.7 Appendix: Light scattering (photon beating spectroscopy) 5.8 References

10 6 Basics on Interfaces in Combustion 6.1 Introduction 6.2 Non-premixed laminar combustion 6.3 Turbulent non-premixed combustion 6.4 Premixed combustion 6.5 Plate combustion 6.6 Powders 6.7 Sprays and fireworks 6.8 Conclusion 6.9 Acknowledgments 6.10 Appendices 6.11 References

11 List of Authors

12 Index

13 Summary of Volume 2

14 End User License Agreement

1 Chapter 1 Table 1.1. Balance equations for interfaces whose surface variables obey classic... Table 1.2. Examples of the constitutive laws of interfaces

2 Chapter 2Table 2.1. Expression of the subgrid terms appearing in the filtered two-fluid e...Table 2.2. Physical properties of the two phases in the phase inversion benchmar...Table 2.3. Classification of the subgrid terms according to their relative contr...Table 2.4. Classification of the subgrid terms according to their relative contr...Table 2.5. Physical properties of the two phases in the METERO test case Table 2.6. Time steps according to the flow regime and the turbulence model for ...

3 Chapter 4Table 4.1. Coordinates of the critical point of some bodies (Garrabos et al. 199...Table 4.2. Some properties in the vicinity of a critical point and the associate...

4 Chapter 5Table 5.1. Useful data: (a) Beysens et al. (1982); (b) see text; (c) Giddings an...

1 Chapter 1 Figure 1.1. Interfacial layer and interface. a) Gray rectangular zone obtained b... Figure 1.2. Capillary interface. Capillary surface at rest between a liquid and ... Figure 1.3. Eutectic colonies in CBr4-C2Cl6-naphthalene,V = 31 µm s-1 (Akamatsu... Figure 1.4. Examples of generalized interfaces. a) Thermal drop in a liquid. Figure 1.5. Orthogonal meshes. a) An example of a curvilinear coordinate system ... Figure 1.6. Coordinate surfaces and interfacial layer. Ci are the coordinate cur... Figure 1.7. Definition of the velocity vectorV for two common types of interfac... Figure 1.8. Different terms that come into play in the general equation of inter... Figure 1.9. Hugoniot adiabatic curve in the planes a) | The Mach number for the ... Figure 1.10. a) The line of mass flow rate (in both cases) and the Hugoniot adia... Figure 1.11. Comparison of the structures of the planar flame and the curved fla...

2 Chapter 2Figure 2.1. Initial conditions of the phase inversion benchmark. For a color ver...Figure 2.2. Order of magnitude of the normalized subgrid terms, top: for the oil...Figure 2.3. Relative error obtained by comparison between the modeled subgrid te...Figure 2.4. Correlation between the turbulence models and the subgrid terms eval...Figure 2.5. Comparison of the equivalent viscosity μ eqpredicted by DNS and the ...Figure 2.6. Relative error of the convection subgrid term (top) and the predicte...Figure 2.7. Order of magnitude of the normalized subgrid terms obtained with the...Figure 2.8. Relative error obtained by comparison between the modeled subgrid te...Figure 2.9. METERO flow pattern at X = 40 D. JL corresponds to the water velocit...Figure 2.10. Schematic view of the horizontal pipe of the METERO experiment (e.g...Figure 2.11. Slice of the mesh used for the simulation of the METERO test case. ...Figure 2.12. Qualitative comparison of the simulations performed with the WALE m...Figure 2.13. Average liquid velocity and average void fraction at X = 40D. Top t...Figure 2.14. Notations for the implementation of the new heat flux model. Red ci...Figure 2.15. Definition sketch of the 1D computational domain used for the simul...Figure 2.16. Simulation conditions at a given time for the sucking problem, the ...Figure 2.17. Schematic view of the temperature profile and vapor/liquid interfac...Figure 2.18. Evolution of the interface position obtained with the new heat tran...Figure 2.19. Average relative error for the interface position compared to the t...Figure 2.20. Simulation conditions at a given time for the Stefan problem, the l...Figure 2.21. Schematic view of the temperature profile and vapor–liquid interfac...Figure 2.22. Evolution of the interface position obtained with the new heat tran...

3 Chapter 3Figure 3.1. Details of a 2D discretization of the particle surface S and extrapo...Figure 3.2. Spherical coordinate system around a particle. The flow direction is...Figure 3.3.