Radiation Heat Transfer Modelling with Computational Fluid Dynamics

Yehuda Sinai

• Publisher: CRC Press
• Year: 2022
• Print ISBN: 9780367766115
• eBook ISBN: 9781000567069
• Edition: 1
• Topic: Physical Sciences
• Subtopic: Thermodynamics

This book serves as a preliminary reference for the principles of thermal radiation and its modelling in computational fluid dynamics (CFD) simulations.

Radiation Heat Transfer Modelling with Computational Fluid Dynamics covers strategies and processes for synthesizing radiation with CFD setups, 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, the book includes the spectroscopic properties of gases, some particulates and porous media.

FEATURES

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• Fills a gap between existing CFD and thermal radiation textbooks and elaborates on some aspects of user manuals.

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• Aims at (1) CFD practitioners who are newcomers to thermal radiation and are looking for a preliminary introduction thereon and (2) modellers familiar with thermal radiation looking for a precursory introduction to CFD. The book is tilted somewhat towards the first group.

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• Provides guidelines for choosing the right model, the strategic planning of the modelling and its implementation.

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• Outlines the pitfalls of some solution techniques.

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• Describes how radiation is included in the variety of boundary condition types offered by CFD codes.

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• Helps to develop the practical skills required to plan, implement and interpret thermal radiation within the typical CFD code.

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• Addresses a wide variety of physical circumstances in which thermal radiation plays a role.

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• Offers ample references for readers searching for additional details.

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• Includes several examples of practical applications, including fire, a utility boiler and car headlights in cold environments.

This book is intended for researchers and professionals who wish to simulate problems that involve fluid flow and heat transfer with thermal radiation.

1 Introduction

DOI: 10.1201/9781003168560-1

Thermal radiation is one of three recognised modes of heat transfer, the other two being conduction and convection. Phase change and the associated latent heat is sometimes described as a mode too. In some cases the contribution of radiation to the total heat transfer is small or negligible compared with the other modes, but in other cases it is comparable with or larger than the other modes. Several examples in which radiation plays a role follow:

• Process and energy
  1. Solar energy. Direct sunlight is exploited in solar heating panels and solar farms, and it is necessary to understand the interaction of radiation with the atmosphere and the device.
  2. Glass manufacturing. Heat transfer in glass furnaces, which operate at high temperatures. Burners above the glass maintain its molten state, required during the manufacture.
  3. Furnaces and boilers at power stations. Heat is used to generate steam in the boiler, and radiation is typically the dominant contributor thereto. Decarbonisation is of course leading to a decline of power generation employing fossil fuels but they are widespread at present.
• Built environment
  1. Thermal dynamics of buildings. The building structure is affected by radiation arriving from the external environment and from internal heat sources, and such matters affect indoor air quality, comfort and emissions.
  2. Thermal comfort, affected by direct sunlight as well as diffuse radiation in the so-called shortwave and longwave ranges.
• Transport
  1. Combustion chambers in turbojets. Combustion is used to produce the high-energy gases which drive the turbine at the rear of the turbojet. The turbine drives the compressor and generates thrust, and thermal radiation is a major side-effect of the process, needing careful design of the components.
• Environment
  1. Meteorology and climatology. Interactions of the atmosphere with incoming solar radiation as well as with radiation reflected and emitted by the ground, the sea and the atmosphere itself. This includes the interaction with gases as well as particulates such as water droplets (e.g. in clouds), ice crystals, soot, and dust. This topic is of course key in relation to climate change.
  2. Remote sensing. Measurement of entities at the ground and in the atmosphere by terrestrial and satellite-born instruments.
• Safety
  1. Fire. Radiation is often the dominant factor inside the flame with implications for any structures engulfed by it. Radiation is also relevant at locations remote from the flame. Radiation plays a key role in the coupling between the flame and the fire (fuel) source for certain types of fire. Fire simulation is undertaken during design or emergency planning, or as part of forensic investigation of an accident.
  2. Gas flares at oil and gas facilities (e.g. oil and gas platforms). These need to be designed with acceptable radiation at locations where workers may be present.
  3. Explosions. Radiation may play a role in the rapid initial phase, but the slower fireball which follows it can also cause much harm and damage.
• Medicine
  1. Biomedical imaging. Measurement of electromagnetic waves passing through the body, leading to diagnostic tools which are more informative than X-rays.

Thermal radiation is an electromagnetic phenomenon, and is special and complex; special because it is capable of delivering energy remotely (unlike the other modes of heat transfer), and complex because it can depend not only on spatial co-ordinates and time, but also on direction, the spectroscopic properties of the medium though which the waves are travelling, and the wavelength of the waves. The mechanisms which influence the evolution of radiation are absorption (in which energy is transferred from the radiation field to the medium), emission (in which energy is transferred from the medium into the radiation field), and scattering (which involves direction change of the radiation field due to inhomogeneities). Refraction occurs when the medium’s refractive index varies. There is substantial excellent literature on general heat transfer and on radiative transfer. For general heat transfer the reader is referred to typical examples such as (Simonson, 1988; Rohsenow, Hartnett and Cho, 1998; Holman, 2018; Lienhard IV and Lienhard V, 2012; Böckh and Wetzel, 2012; Incropera, DeWitt, Bergman and Lavine, 2017), and more, including some classics specifically on thermal radiation which are out of print (Chandrasekhar, 1960, 2013; Busbridge, 1960; Hottel and Sarofim, 1967; Sparrow and Cess, 1978; Ozisik, 1985; Brewster, 1992; Viskanta, 2008), as well as what can be described as the two leading contemporary books in this area (Modest, 2021; Howell, Menguc, Daun and Siegel, 2021). Important supplementary material, such a references, errata, and coding are provided for both of the latter books: Modest at http://booksite.elsevier.com/9780123869449/ and Howell at http://www.thermalradiation.net/. Climatology and atmospheric physics is of course an important topical issue, e.g. (Liou, 2002; Jacobson, 2005; Bohren and Clothiaux, 2006; Salby, 2012; Kondrat’Yev, 1965), and a little more will be said about multiphase aspects below. This book will generally avoid citing these references repeatedly, albeit with the occasional exception.

Reference has already been made above to waves: Thermal radiation may be represented both in terms of electromagnetic waves or bundles of energy called photons (associated with quantum theory), and the material in this book cites both approaches, as is typical in the literature, which refers to the ‘wave-particle duality’. Normally the behaviour of solids, liquids, and interfaces is described more effectively by wave theory, whereas that of gases by quantum theory.

It is important to distinguish immediately between radiative transfer in non-participating (i.e. radiatively transparent) media on the one hand, and in participating media on the other. In a transparent medium, the opacity (defined in Section 4.2) is zero or very small, so that there is negligible absorption, emission, or scattering of radiation, and significant exchange only occurs between surfaces; this is known as surface-to-surface radiation, and the medium is normally described as optically thin or transparent. If the opacity is O(1), i.e. of the order of 1, or large, the medium is said to be participating; in such a medium absorption and emission, as well as scattering, may exist in various proportions. Generally, poor conductors, known as dielectrics, enable long-range propagation, whereas good conductors are opaque. The general situation is governed by a complex (integro-differential) equation known as the radiative transfer equation (abbreviated here as RTE and described in Section 4.2), for which analytical solutions are rare, but several numerical algorithms are available in software packages. Simple engineering methods, using electrical circuit analogies or equivalents, are sometimes employed too, even for participating media (rarely nowadays), but the general computational algorithms are much easier to use, and are more flexible, albeit with a central processing unit (CPU) penalty. It should be noted that the electrical analogy, strictly speaking, is not a solution to the problem but is rather a reformulation. It uses surface-to-surface, surface-to-gas and gas-to-gas view factors, which require evaluation, either from existing tables or from solutions of the RTE. If the opacity is large, the medium is described as optically thick (and opaque in the limit); in such circumstances the radiative process is dominated by exchange between surfaces and the medium if variations in the medium are small, and the so-called ‘diffusion approximations’ are valid. If variations within the medium are not small, then exchanges within the medium are important too, but the larger the opacity, the smaller the distances over which such exchanges are occurring. Having said all this, it should be remembered that modern radiation solvers are capable of analysing the complete range of opacities, albeit at a non-negligible computational costs in some situations.

The applications quoted above illustrate the very diverse spheres in which radiation plays a role. Given the focus of this book on radiation in the context of CFD, it is thermal radiation which is the most relevant here. Magnetohydrodynamics (MHD) and relativistic phenomena are specialist fields which are beyond the scope of this book.

Another sphere which is beyond the scope of this book is the growing field of nanotechnology, involved for example in the behaviour of composites and microelectronics. If separations between bodies are smaller than the dominant electromagnetic wavelength, then near-field and coherence issues are introduced, heat fluxes can increase by orders of magnitude, the radiative transfer equation approach (Section 4.2) breaks down, polarisation becomes non-random and important (the waves are coherent), and the full Maxwell equations are required for analysis. The reader is referred to (Modest, 2021; Howell et al., 2021) and current literature for details. The current book considers the more common situations, which are in the far field, with separations between bodies larger than the dominant electromagnetic wavelength, and with incoherent radiation.

On occasion, use is made in this book of the term ‘fluid’. This term refers to a gas or liquid. Molten solids are modelled as fluids too, and CFD can address non-Newtonian flows.

As far as CFD is concerned, an opaque object will simply manifest as a boundary condition for the radiation solver outside the solid (e.g. in terms of a surface emissivity). The CFD model may, however, include the interior of the opaque object, for example, by using conjugate heat transfer (CHT) functionality. Such a utility involves a mesh inside the opaque object, with conduction accounted for (as an example), and volumetric thermal radiation usually excluded. Radiation in semi-transparent solids can be modelled as stationary fluids, or in the case of some CFD packages, explicitly as non-opaque solids; that pertains to glass.

A comment is made here about the magnitude of radiative fluxes compared with the contributions of other modes of heat transfer. Generalisations should be treated with caution, but allowing for that caveat, in forced convection regimes temperatures need to be relatively high for radiation to be significant compared with the other heat transfer modes, whereas in natural or mixed convection regimes radiation can be of the same order as convection at room temperatures. Since radiation scales on the fourth power of temperature, its contribution increases rapidly with temperature, but as an illustration of the unwise assumption that radiation is always unimportant at ambient temperatures, consider the natural convection regime in the air at a nominal 20^oC say, at large Rayleigh number (in the turbulent domain). Using correlations, e.g. (Incropera et al., 2017), the convective heat transfer coefficient is estimated to be 1.56∆T^1/3, where ∆T is the temperature difference between a surface and the bulk fluid adjacent to it (see Sections 4.3 and 5.1.1). For temperature differences of 1 and 10 Celsius, this yields 1.56 and 3.36 W m⁻² K⁻¹, respectively. Turning now to radiative exchange at the same surface with another surface (made of similar material) facing it, the radiative heat transfer coefficient can be estimated to be about 5.4ε, where ε is the surface emissivity (Section 4.1.2). Thus, the convective and radiative fluxes are comparable unless the surface emissivity is very small.

After the introduction, this book proceeds to describe the principal models available for spectroscopic properties, as well as computational techniques for solving for the radiative field given the local properties. It then continues to compare the models, and provides some examples which involve CFD and radiation.

Regarding the range of applicability of the material in this book, much has general applicability, but the emphasis is on typical engineering scenarios and conditions and on heat transfer, with parts of the book focused on a temperature range from ambient to 2000°C, typical say of phenomena from scenarios under ambient conditions to turbojet combustion chambers. Tools for analysing radiative transfer are of course used in areas other than heat transfer too, for example, lighting, optics, remote sensing, nuclear shielding, biophysics and astrophysics. The latter is a discipline in which much of the early pioneering work on radiation was formulated.

Finally, the author wishes to point out that whilst this book focuses on theoretical (computational) approaches, great debt is of course owed to the many experiments which have and continue to be undertaken, and which provide insight into the phenomena, key data, and avenues for validation of theory. Some analytical results are quoted in this book in order to explain and highlight concepts, and to provide some benchmarks against which the computational methods may be tested. Benchmarks are either exact analytical solutions or highly accurate analytical or numerical solutions.

This book aims to provide an overview in a generic fashion, but it will on occasion dip into specific applications. Also, since the material relates to radiation modelling in the context of CFD, relevant CFD aspects are discussed, but great detail of the substantial general topic are avoided, and the interes...

Table of contents

• Cover Page
• Half Title page
• Title Page
• Copyright Page
• Contents
• List of Figures
• List of Tables
• Preface
• Acknowledgements
• Disclaimer
• Author
• List of Symbols
• Acronyms
• 1 Introduction
• 2 A Brief Outline of CFD
• 3 Outline of a Typical Process for CFD Analysis with Radiation
• 4 Fundamentals of Thermal Radiation
• 5 Modelling
• 6 Quality Assurance
• 7 Examples
• Appendix A Dimensionless Groups
• Appendix B The Electrical Analogy
• Appendix C Fresnel’s Equations
• Appendix D Spherical Coordinates, and More on Scattering
• Appendix E Exact Closed-Form Solution for an Infinite, Plane, Grey, Homogeneous, Absorbing-Emitting Slab between Two Plates with Different Temperatures and Emissivities
• 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
• Appendix G The Williams Theory for an Infinite, Plane, Grey, Homogeneous, Absorbing-Emitting, Isotropically Scattering Slab between Two Plates with Different Temperatures and Emissivities
• Appendix H Optically Thick Limit of the Williams Theory for a Grey, Absorbing-Emitting and Scattering Slab
• Appendix I Integrated form of the Radiative Transfer Equation
• Appendix J Saturated Vapour Pressure of Water
• Appendix K A Steady-State 1-D Boundary Condition for Single and Double Semi-Transparent Slabs
• References
• Index