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Radiation Heat Transfer Modelling with Computational Fluid Dynamics Radiation Heat Transfer Modelling with Computational Fluid Dynamics Yehuda Sinai Cover image: Magnum Fire, Kaibab National Forest, USA. Reproduced from Flickr First edition published 2022 by CRC Press 6000 Broken Sound Parkway NW, Suite 300, Boca Raton, FL 33487-2742 and by CRC Press 4 Park Square, Milton Park, Abingdon, Oxon, OX14 4RN CRC Press is an imprint of Taylor & Francis Group, LLC © 2022 HeatAndFlow Consultancy Limited Reasonable efforts have been made to publish reliable data and information, but the author and publisher cannot assume responsibility for the validity of all materials or the consequences of their use. The authors and publishers have attempted to trace the copyright holders of all material reproduced in this publication and apologize to copyright holders if permission to publish in this form has not been obtained. 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Library of Congress Cataloging-in-Publication Data Names: Sinai, Yehuda L., author. Title: Radiation heat transfer modelling with computational fluid dynamics/Yehuda L. Sinai. Description: First edition. | Boca Raton : CRC Press, 2022. | Includes bibliographical references and index. | Summary: “Radiation Heat Transfer Modelling with Computational Fluid Dynamics serves as a reference for principles of thermal radiation and its modelling in computational fluid dynamics (CFD) simulations. Including strategies for combining CFD and thermal radiation, the book covers computational techniques for solving the Radiative Transfer Equation, the strengths and weaknesses thereof, boundary and initial conditions, and relevant guidelines. Describing the strategic planning of a typical project, it includes spectroscopic properties of gases, some particulates, and porous media. The book is intended for researchers and professionals who simulate problems that involve fluid flow and heat transfer with thermal radiation”-- Provided by publisher. Identifiers: LCCN 2021050628 (print) | LCCN 2021050629 (ebook) | ISBN 9780367766115 (hardback) | ISBN 9780367767884 (paperback) | ISBN 9781003168560 (ebook) Subjects: LCSH: Heat--Radiation and absorption. | Heat--Transmission. | Computational fluid dynamics. Classification: LCC TJ260 .S577 2022 (print) | LCC TJ260 (ebook) | DDC 621.402/2--dc23/eng/20211123 LC record available at https://lccn.loc.gov/2021050628 LC ebook record available at https://lccn.loc.gov/2021050629 ISBN: 978-0-367-76611-5 (hbk) ISBN: 978-0-367-76788-4 (pbk) ISBN: 978-1-003-16856-0 (ebk) DOI: 10.1201/9781003168560 Typeset in Times by SPi Technologies India Pvt Ltd (Straive) Dedication ‘To the memory of my parents, Dolly and Reuben.’ Contents List of Figures ...........................................................................................................xi List of Tables ..........................................................................................................xvii Preface .....................................................................................................................xix Acknowledgements .................................................................................................xxi Disclaimer .............................................................................................................xxiii Author ....................................................................................................................xxv List of Symbols ....................................................................................................xxvii Acronyms ............................................................................................................xxxiii Chapter 1 Introduction ..........................................................................................1 Chapter 2 A Brief Outline of CFD ........................................................................7 2.1 Preliminaries ..............................................................................8 2.2 Governing Equations .................................................................9 2.3 Geometry and Meshing ...........................................................11 2.4 More Physics ...........................................................................13 2.5 Numerics ..................................................................................19 2.6 Problem Size ............................................................................20 Chapter 3 Outline of a Typical Process for CFD Analysis with Radiation .........21 Chapter 4 Fundamentals of Thermal Radiation ..................................................25 4.1 Basics .......................................................................................25 4.1.1 Electromagnetic Spectrum .........................................25 4.1.2 Black Bodies, Surface Behaviour, and Radiosity .......26 4.1.3 Speed of Light and Refractive Index ..........................32 4.1.4 Shape Factors .............................................................33 4.1.5 Introduction to the Electrical Analogy .......................34 4.1.6 Radiation Intensity .....................................................35 4.1.7 Radiative Flux ............................................................36 4.1.8 Diffusion, Anisotropy, and Collimation .....................37 4.1.9 Interfaces and Refraction ............................................40 4.1.10 Scattering ....................................................................42 4.1.11 The Meaning of ‘Incident’ and ‘Mean’ Radiation or Intensity ..................................................................44 4.1.12 Mean Radiant Temperature ........................................45 4.2 Introduction to the Radiative Transfer Equation and Opacity .....46 4.3 Estimation of a Characteristic Opacity, and Dimensionless Groups .............................................................50 vii viii Contents 4.4 Coupling between Flow and Radiation ...................................52 4.4.1 Coupling between Radiation and Turbulence.............57 4.5 Equilibrium or Non-Equilibrium? ...........................................60 4.6 The Meaning of ‘Semi-Transparent’ .......................................60 4.7 Semi-Transparent Slabs, Windows, Solar Radiation ...............61 Chapter 5 Modelling ...........................................................................................65 5.1 Boundary Conditions ...............................................................65 5.1.1 Opaque Walls ..............................................................67 5.1.2 Collimated Radiation ..................................................74 5.1.3 Semi-Transparent Boundaries (Windows) .................74 5.1.4 Inlets, Outlets and Openings ......................................79 5.1.5 Symmetry Planes ........................................................79 5.2 Initial Conditions .....................................................................79 5.3 Spectroscopic Properties .........................................................79 5.3.1 Overview ....................................................................81 5.3.2 Global Models ............................................................83 5.3.2.1 Grey Models ...............................................83 5.3.2.2 Weighted Grey Gas Models (WSGG).........84 5.3.2.3 Full-Spectrum k-Distribution (FSK) ...........85 5.3.3 Band Models ..............................................................86 5.3.3.1 Wide Band Models .....................................86 5.3.3.2 Narrow-Band Models (NBM) .....................87 5.3.4 Line-by-Line Models (LBLM) ...................................87 5.3.5 Summary of Pros and Cons of the Property Models .....................................................88 5.3.6 Porous Media ..............................................................88 5.3.7 Particulates .................................................................91 5.4 Solution Techniques ................................................................95 5.4.1 Transparent Media ......................................................95 5.4.2 Participating Media ....................................................96 5.4.2.1 Rosseland ....................................................97 5.4.2.2 Schuster–Schwarzschild .............................97 5.4.2.3 Zonal ...........................................................98 5.4.2.4 Finite Volume (FV) .....................................98 5.4.2.5 Spherical Harmonics (P ) ...........................98 N 5.4.2.6 Discrete Ordinates (S ) ...............................99 N 5.4.2.7 Discrete Transfer (DT) ................................99 5.4.2.8 Monte Carlo (MC) ......................................99 5.4.2.9 Hybrid Methods ........................................100 5.4.2.10 Scattering Capabilities ..............................101 5.4.2.11 Examples of Some Pitfalls ........................101 5.4.3 Comparisons of the RTE Solution Methods .............103 Contents ix 5.5 Estimation of Irradiation at Sub-Grid Objects in a CFD Simulation ..................................................................105 5.6 Computational Meshes ..........................................................106 Chapter 6 Quality Assurance.............................................................................107 Chapter 7 Examples ..........................................................................................109 7.1 Utility Boiler ..........................................................................109 7.2 Forensic Investigation of a Furniture Store Fire ....................113 7.3 Sensitivity Tests of Grey Gas Models for Pool Fires .............116 7.3.1 Physical and Numerical Modelling ..........................118 7.3.2 Results and Discussion .............................................121 7.3.2.1 Closed Compartment ................................121 7.3.2.2 Open Environment ....................................121 7.3.2.3 Vented Compartment ................................121 7.3.3 Final Remarks ..........................................................123 7.4 Headlight ...............................................................................123 Appendix A: Dimensionless Groups .................................................................127 Appendix B: The Electrical Analogy ................................................................131 Appendix C: Fresnel’s Equations .........................................................................133 Appendix D: Spherical Coordinates, and More on Scattering ..........................137 Appendix E: Exact Closed-Form Solution For An Infinite, Plane, Grey, Homogeneous, Absorbing-Emitting Slab Between Two Plates With Different Temperatures And Emissivities ...........................139 Appendix F: Exact Closed-Form Solution For An Infinite, Plane, Grey, Absorbing-Emitting Slab In Radiative Equilibrium Between Two Plates With Different Temperatures And Emissivities .........143 Appendix G: The Williams Theory For An Infinite, Plane, Grey, Homogeneous, Absorbing-Emitting, Isotropically Scattering Slab Between Two Plates With Different Temperatures And Emissivities .........145 Appendix H: Optically Thick Limit Of The Williams Theory For A Grey, Absorbing-Emitting And Scattering Slab ....................................147 Appendix I: Integrated Form Of The Radiative Transfer Equation .................149 Appendix J: Saturated Vapour Pressure Of Water ............................................151 Appendix K: A Steady-State 1-D Boundary Condition For Single and Double Semi-Transparent Slabs ...................................................153 References ..........................................................................................................157 Index ....................................................................................................................173