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Radiative Transfer in Combustion Systems: Fundamentals and Applications

1-56700-211-0 (Print)

Radiative Transfer in Combustion Systems: Fundamentals and Applications

Raymond Viskanta
Heat Transfer Laboratory, School of Mechanical Engineering, Purdue University, West Lafayette, USA


Destined to clarify the research, development, and design requirements in modern and computational terms needed for sustainable technological advances. Written for the combustion scientist/engineer to understand radiative effects on the pollution of the environment. Interrelates the process of thermodynamics, chemical kinetics, fluid mechanics, heat and mass transfer and turbulence. Includes computational design tools. Lays the foundation for modeling and prediction of chemically reacting combustion systems; collects data for operation of combustion devices. Analyzes the construction, use, and numerical results of combustion systems simulation.

460 pages, ©2005


Chapter 1: Introduction
1.1 Combustion in Nature and Technology
1.2 Physical Nature of Radiation
1.2.1 Duality of radiation phenomena
1.2.2 Identity of radiant energy and light
1.2.3 Electromagnetic spectrum
1.2.4 Thermal radiation
1.3 Electromagnetic Wave Theory
1.3.1 Propagation and attenuation of radiation
1.3.2 Reflection and refraction of radiation
1.4 Definitions
1.4.1 Intensity of radiation (radiance)
1.4.2 Radiant energy density
1.4.3 Irradiance
1.4.4 Radiant energy flux vector
1.4.5 Moments of intensity
1.4.6 Total radiant energy quantities
1.5 Interaction of Radiation with Matter
1.5.1 Absorption, scattering, and extinction (attenuation) coefficients
1.5.2 Scattering phase function
1.6 Interaction of Radiation with an Interface
1.7 Radiation Scaling Parameters
Chapter 2: Thermodynamics and Physics of Blackbody Radiation
2.1 Thermodynamics of Radiation
2.1.1 Isothermal cavity
2.1.2 Concept of a blackbody
2.1.3 Kirchhoff's laws
2.2 Concept of Emissivity
2.2.1 Definition of emissivity
2.2.2 Relation between absorptivity and emissivity
2.3 Radiation Pressure
2.4 Entropy of Radiation
2.5 Laws of Blackbody Radiation
2.5.1 Planck's law
2.5.2 Asymptotic forms of Planck's law
2.5.3 Stefan-Boltzmann law
2.6 Fractional Blackbody Functions
2.7 Spectral Distribution of Blackbody Radiation
Chapter 3: Basic Equations of Radiative Transfer
3.1 Radiative Transfer Theory and Its Postulates
3.2 Radiative Transfer Equation
3.3 Special Forms of the Radiative Transfer Equation
3.4 Integral Form of the Radiative Transfer Equation
3.4.1 Radiation along a homogeneous path
3.4.2 Radiating gas adjacent to a wall
3.4.3 Radiation from an isothermal gas volume
3.5 Conservation Equations
3.5.1 Radiant energy transport equation
3.5.2 Transport of radiant momentum
3.6 Radiative Transfer Regimes
3.6.1 Optically thin approximation
3.6.2 Optically thick approximation
3.7 Conservation Equations for Reacting Gas Mixtures
3.7.1 Conservation equations of mass, species, and momentum
3.7.2 Conservation equation of energy
3.7.3 Conservation equations for turbulent flows
Chapter 4: Radiation Characteristics of Gaseous Combustion Products
4.1 Introduction
4.2 Fundamental Concepts of Modern Radiation Physics
4.2.1 Fundamentals of gas molecular spectra
4.2.2 Microscopic radiative interactions
4.2.3 Relations between Einstein's probability coefficients and macroscopic coefficients
4.3 Line Models
4.3.1 Characterization of an isolated line
4.3.2 Total absorption by an isolated line
4.3.3 Line-by-line calculations of the absorption coefficient
4.4 Narrow-Band Models
4.4.1 Elsasser model
4.4.2 Statistical models
4.4.3 Decomposition-based narrow-band models
4.4.4 Nonhomogeneous gas models
4.5 Wide-Band Models
4.5.1 Box (top hat) model
4.5.2 Exponential wide-band model
4.5.3 Isothermal total band absorptance correlations
4.5.4 Exponential wide-band model for nonhomogeneous gases
4.6 Total Absorptance-Emittance Correlations
4.6.1 Database for CO2 and H2O
4.6.2 Empirical emittance-absorption correlations
4.6.3 Emipirical correlations for the total emittance of gaseous combustion products
4.7 Spectrum Integrated Hybrid Models for Total Emittance
4.7.1 SG and CK methods
4.7.2 Spectral line-based model
4.7.3 ADF and ADFFG approaches
4.8 Global Radiative Transfer Methods
4.8.1 Effective absorption coefficients
4.8.2 Mean absorption/emission coefficients
4.9 Concluding Summary Remarks
Chapter 5: Radiation Characteristics of Particles and Particle/Gas Mixtures
5.1 Introduction
5.2 Absorption and Scattering from a Single Sphere: Mie Theory
5.2.1 Mie efficiency factors
5.2.2 Limiting solutions for efficiency factors
5.2.3 Scattering distribution (phase) function
5.3 Absorption and Scattering by Nonspherical Particles
5.4 Radiation Characteristics of Polydispersions
5.4.1 Extincion coefficients and scattering albedo
5.4.2 Calculation of mean characteristics
5.5 Internal Distribution of Absorbed Radiation within an Irradiated Sphere
5.5.1 EM theory
5.5.2 Geometric optics approach
5.6 Radiation Characteristics of Soot Particles in Flames
5.6.1 Spectral absorption coefficient
5.6.2 Total directional emittance
5.6.3 Mean absorption coefficients of soot
5.7 Total Emittance of Gas/Soot Mixtures
5.8 Spectral Radiation Characteristics of Gas/Particle Mixtures
5.8.1 Spectral hemispherical characteristics
5.8.2 Total hemispherical characteristics of mixtures
5.9 Concluding Summary Remarks
Chapter 6: Radiation Exchange in Combustion Systems
6.1 Discussion of Radiation Exchange in Enclosures
6.2 Radiant Energy Balance at an Enclosure Wall
6.2.1 Radiation intensity leaving an enclosure wall
6.2.2 Integral equations for leaving intensity
6.3 Radiative Transfer in One-Dimensional Media
6.3.1 Radiative transfer in a plane layer
6.3.2 Radiative transfer in a cylindrical scattering medium
6.3.3 Radiative transfer in a spherical medium
6.4 Two-Dimensional Radiative Transfer
6.4.1 Two-dimensional rectangular enclosure
6.4.2 Radiative transfer in a finite-length cylindrical enclosure
6.5 Radiative Transfer in Multidimensional Enclosures Containing a Participating Medium
6.5.1 Results for diffuse enclosure walls
6.5.2 Special cases for multidimensional enclosures
6.6 Concluding Summary Remarks
Chapter 7: Computational Methods for Radiative Transfer
7.1 Selection of Method
7.2 Overview of Computational Methods
7.2.1 Directional treatment
7.2.2 Spectral treatment
7.3 Computation of Multidimensional Radiative Transfer
7.3.1 Multiflux methods (MFMs)
7.3.2 Differential (PN) approximation
7.3.3 Discrete ordinates method (DOM)
7.3.4 Finite volume method (FVM)
7.3.5 Discrete transfer method (DTM)
7.4 Critical Assessment of RTE Solution Methods
7.4.1 Comparison of radiative transfer models
7.4.2 Radiative transfer model validation
7.5 Modeling of the Spectral Nature of Radiative Transfer
7.5.1 Benchmark: Integration over the spectrum
7.5.2 WSGG model and enhancements
7.5.3 CK model extensions for gas mixtures
7.5.4 Gas/particle mixtures
7.6 Comparison of Global Results
7.6.1 Comparison of global computational results
7.6.2 Comparison of global and experimental results
7.7 Concluding Summary Remarks
Chapter 8: Combustion Phenomena Affected by Radiation
8.1 Introduction
8.2 Ignition of Solids
8.2.1 Ignition of an opaque exothermic solid by radiation
8.2.2 Ignition of a semitransparent solid by radiation
8.3 Ignition of a Vertical Slab by Radiation
8.4 Ignition of Solid Fuel in an Enclosure by Radiation
8.5 Radiation and Flame Spread
8.5.1 Upward and downward flame spread along a vertical solid
8.5.2 Opposed-flow flame spread
8.6 Effects of Radiation on Extinction of Laminar Diffusion Flames
8.7 Radiation-Affected Ignition of Solid-Gas Mixtures
8.7.1 Ignition of inert particles-oxidizer gas
8.7.2 Ignition of fuel spray-oxidizer mixture
8.8 Concluding Summary Remarks
Chapter 9: Radiation Effects in Laminar Flames
9.1 Introduction
9.2 Radiation Effects in Opposed-Flow Flames
9.2.1 Opposed-flow combustion model
9.2.2 Radiative transfer models
9.2.3 Diffusion flames
9.2.4 Premixed flames
9.2.5 Partially premixed flames
9.3 Radiation Effects in Axisymmetric Jet Diffusion Flames
9.4 Radiation Effects in Axisymmetric Luminous Diffusion Flames
9.4.1 Combustion and radiation models
9.4.2 Results of simulations
9.5 Diffusion Flame at an Axisymmetric Stagnation Point
9.6 Gas-Phase Radiation Effects on the Burning of Fuel
9.6.1 Laminar diffusion flame adjacent to a vertical flat plate burner
9.6.2 Combustion of a pyrolyzing fuel slab
9.7 Droplet Combustion
9.7.1 Model description
9.7.2 Modeling results
9.8 Concluding Summary Remarks
Chapter 10: Radiation in Turbulent Flames
10.1 Introduction
10.2 Radiation from Flames
10.2.1 Global radiation fraction measurements
10.2.2 Total incident radiant heat flux measurements
10.2.3 Spectral measurements
10.3 RTE for Turbulent Chemically Reacting Flows
10.3.1 RTE for turbulent flow
10.3.2 Optically thin and thick approximations for turbulent flow
10.4 Radiative Transfer in Turbulent Flames
10.4.1 Flame radiation: Mean-property model
10.4.2 Flame radiation: Stochastic model
10.4.3 Application of models and comparisons with data
10.5 Radiative Transfer in Turbulent Flames: Turbulence/Radiation Interaction Methods
10.5.1 Differential model
10.5.2 P1-approximation model
10.5.3 TRI model assessment
10.6 Modeling of Turbulent Nonpremixed Flames: Flamlet Model
10.6.1 Laminar flamlet model with radiation
10.6.2 Application of the flamlet model to radiating flames
10.7 Radiation in Luminous Turbulent Diffusion Flames
10.7.1 Soot formation model
10.7.2 Radiative transfer model for sooty flames
10.7.3 Application of models to luminous flames
10.8 Effect of Radiation on NOx Emissions in Nonpremixed Flames
10.9 Concluding Summary Remarks
Chapter 11: Radiative Transfer in Combustion Chambers
11.1 Introduction
11.2 Radiation Scaling Parameters for Turbulent Chemically Reacting Flows
11.3 Gas-Fired Combustion Chambers
11.3.1 Axisymmetric combustion chamber
11.3.2 Turbulence/combustion models
11.3.3 Turbulence/radiation models
11.3.4 Radiative transfer model
11.3.5 Model assessments
11.4 Accounting for Soot in Combustion Chambers
11.5 Three-Dimensional Rectangular Chambers
11.5.1 Mathematical model description
11.5.2 Model assessments
11.5.3 Swirling combustors
11.6 Radiative Transfer in Gas Turbine Combustors
11.6.1 Computation of radiative transfer
11.6.2 Comparison of calculated and measured spectral intensities
11.6.3 Modeling assessment
11.7 TRI in Combustion Chambers
11.7.1 Modeling of TRI
11.7.2 Results for confined turbulent diffusion flames
11.8 Concluding Summary Remarks
Chapter 12: Combustion and Heat Transfer in Furnaces
12.1 Introduction
12.2 Heat Transfer in a Well-Stirred Furnace
12.2.1 Steady-state heat transfer model for a well-stirred furnace
12.2.2 Dynamic well-stirred furnace
12.2.3 Model applications
12.3 One-Dimensional (Plug-Flow) Furnace Model
12.3.1 Batch plug-flow furnace model
12.3.2 Furnaces with continuously moving load
12.4 Cylindrical Turbulent Combustion Furnace Models
12.4.1 Model description
12.4.2 Turbulence/combustion and turbulence/radiation modeling
12.4.3 Applications to furnaces
12.5 Multidimensional Furnace Models
12.5.1 Model description
12.5.2 Turbulence/combustion and turbulence/radiation modeling
12.5.3 Industrial applications
12.6 Intensification of Heat Transfer in Furnaces
12.6.1 Enhancement of flame radiation
12.6.2 Heat recirculation
12.6.3 Heat transfer from impinging flame jets
12.7 Concluding Summary Remarks
Chapter 13: Two-Phase Turbulent Combustion
13.1 Introduction
13.2 Description of Radiative Transfer in Spray Combustion
13.2.1 Radiative transfer in spray combustion
13.2.2 Absorption and scattering coefficients of fuel droplets
13.2.3 Soot absorption coefficient
13.3 Spray Combustion in One-Dimensional Systems
13.4 Spray Combustion in a Cylindrical Furnace
13.4.1 Mathematical description of combusting sprays
13.4.2 Radiative transfer in spray combustion systems
13.4.3 Applications of spray combustion with radiation
13.5 Description of Radiative Transfer in Pulverized Coal Combustion
13.5.1 Radiation characteristics of pulverized coals
13.5.2 Radiation characteristics of flyash
13.6 Pulverized Coal Combustion in One-Dimensional Systems
13.7 Pulverized Coal Combustion in Furnaces
13.7.1 Radiative transfer in pulverized coal-fired furnaces
13.7.2 Applications to furnaces and boilers
13.8 Concluding Summary Remarks
Chapter 14: Unwanted Fires
14.1 Introduction
14.2 Scaling of Simple Fires
14.2.1 Scaling of pool fire
14.2.2 Scaling of vertical wall fire
14.3 Laminar Pool Fires
14.4 Radiation from Turbulent Pool Fires
14.4.1 Flame structure of pool fires
14.4.2 Radiation feedback in pool fires
14.4.3 Global modeling of irradiation from pool flames
14.5 Numerical Simulation of Pool Fires
14.6 Compartment (Enclosure) Fires
14.6.1 Phenomenological description
14.6.2 Radiative transfer modeling
14.6.3 Selected applications
14.7 Fire Suppression by Water Sprays
14.7.1 Radiation characteristics of water sprays
14.7.2 Evaporation of a water droplet
14.7.3 Applications to compartment fire suppression
14.8 Fire Spread through Fuel Beds
14.8.1 Phenomenological description
14.8.2 Radiative transfer in wildland fires
14.8.3 Fire-spread modeling
14.9 Concluding Summary Remarks
Chapter 15: Premixed Combustion in Inert Porous Media
15.1 Introduction
15.2 Physical and Mathematical Description of Combustion in a PIM
15.2.1 Physical description
15.2.2 Mathematical description
15.3 Radiative Transfer in porous media
15.3.1 Packed beds
15.3.2 Open-cell materials
15.4 Combustion in a Refractory Tube
15.4.1 One-dimensional model results
15.4.2 Two-dimensional model results
15.5 Overview of Premixed Porous-Media Combustors
15.6 Premixed Porous-Medium Burner
15.6.1 Mathematical burner description
15.6.2 Applications to burners
15.6.3 Applications to burners/heaters
15.6.4 Applications to PIM embedded heaters
15.7 Premixed Combustion in Porous Burners/Radiant Heaters
15.7.1 Model description
15.7.2 Results of applications
15.8 Concluding Summary Remarks