# Radiative Transfer in Combustion Systems: Fundamentals and Applications

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

## Description

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

## Table of Contents:

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

1.3 Electromagnetic Wave Theory

1.3.1 Propagation and attenuation of radiation

1.3.2 Reflection and refraction of radiation

1.4.1 Intensity of radiation (radiance)

1.4.2 Radiant energy density

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

2.1.2 Concept of a blackbody

2.2 Concept of Emissivity

2.2.1 Definition of emissivity

2.2.2 Relation between absorptivity and emissivity

2.5 Laws of Blackbody Radiation

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

4.2 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

4.3.1 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

4.4.3 Decomposition-based narrow-band models

4.4.4 Nonhomogeneous gas 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

4.7.2 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

5.2 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

5.5.2 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

7.2 Overview of Computational Methods

7.2.1 Directional 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

8.2.1 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

9.2 Radiation Effects in Opposed-Flow Flames

9.2.1 Opposed-flow combustion model

9.2.2 Radiative transfer models

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

9.8 Concluding Summary Remarks

Chapter 10: Radiation in Turbulent Flames

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

11.2 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

11.4 Accounting for Soot in Combustion Chambers

11.5 Three-Dimensional Rectangular Chambers

11.5.1 Mathematical model description

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

11.7.2 Results for confined turbulent diffusion flames

11.8 Concluding Summary Remarks

Chapter 12: Combustion and Heat Transfer in Furnaces

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

12.4.2 Turbulence/combustion and turbulence/radiation modeling

12.4.3 Applications to furnaces

12.5 Multidimensional Furnace Models

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

13.2 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

14.2 Scaling of Simple Fires

14.2.1 Scaling of pool fire

14.2.2 Scaling of vertical wall fire

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

15.2 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

15.3.2 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

15.7.2 Results of applications

15.8 Concluding Summary Remarks