Principles of Combustion 3D Cover Image

Book Review: Principles of Combustion, by Kenneth K. Kuo

Principles of Combustion 3D Cover Image

I was introduced to Principles of Combustion in 2011 during my employment as a research engineer. Throughout this position and while completing my PhD, I often referred back to this textbook to understand fundamental combustion phenomena including chemical kinetics and laminar flame propagation.

This post gives a detailed review of the Principles of Combustion textbook. It includes a description of the sections I have found most useful in my work, along with sections that I have found difficult to understand. The goal is to help readers better understand the content of the book prior to purchasing it for their own consumption.

Although this textbook can be difficult to read cover-to-cover, I have reviewed all of the material several times over the last six years. Along with “Fundamentals of Turbulent and Multiphase Combustion” by Kenneth Kuo and Ragini Acharya, it has been one of the conerstone textbooks used during my PhD research.

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Purchase the Textbook

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The following sections give a table of contents for the book review followed by all of the material covered. Alternative combustion textbooks are given in their own section at the end of the post.

Continue on to read the entire review.

Review Organization

The textbook review is organized into the following sections. Throughout the review, red text indicates organization and affiliate links and the red arrow in the bottom-right corner of the screen takes you back to the top of the page.

Overview of “Principles of Combustion”

principles of combustion photo

The second edition of Principles of Combustion gives a comprehensive description of the state-of-the art in combustion and reactive flow dynamics. It was published in 2005 and aims to fill the gap between basic understanding of combustion phenomena and the specialist textbooks in the field (e.g., combustion in gas turbines).

The main focus of this text is on developing a theoretical understanding of combustion principles, specifically focusing on chemical kinetics, detonation, deflagration, premixed flames, and diffusion flames. Focus is also given to theoretical formulations that lend themselves to “solution with the aid of digital computers” in fields such as Computational Fluid Dynamics (CFD).

The author states that the text is written for senior level combustion courses or with graduate student research in mind. However, as I noted above, it would also be useful for anyone with a research role in industry, especially those developing or working with CFD packages.

Target Audience

  • Combustion Engineers
  • Combustion Scientists/Researchers
  • CFD Developers
  • CFD Modelers

Table of Contents

    1) Review of Chemical Thermodynamics
    2) Chemical Kinetics and Reaction Mechanisms
    3) The Conservation Equations for Multicomponent Reacting Systems
    4) Detonation and Deflagration Waves of Premixed Gases
    5) Premixed Laminar Flames
    6) Gaseous Diffusion Flames and Combustion of a Single Liquid Fuel Droplet
    A) Evaluation of Thermal and Transport Properties of Gasses and Liquids
    B) Constants and Conversion Factors Often Used in Combustion
    C) Naming of Hydrocarbons and Properties of Hydrocarbon Fuels
    D) Periodic Table of Electronic Configurations of Neutral Atoms in Ground States

Strengths and Advantages

The main strength of Principles of Combustion is it’s comprehensive treatment of the subjects covered. The material listed in “Favorite Sections” below are outlined meticulously, and I have yet to find a better description for many of the concepts.

The textbook also includes many examples and exercises, which are generally missing in textbooks from this field. This makes it an ideal study companion or reference textbook for fundamental combustion principles.

The last main strength of Principles of Combustion is that it includes references to a number of studies that can be used as validation or verification tests for CFD simulations and theoretical models.

An example of the validation data is given in the image below which shows methane and hydrogen burning velocity plotted against equivalence ratio at different pressures (Reference: Lu, Ju, and Law, 2001 [1]). A list of figures with potential validation data is given in the “Validation Data” section below.

example validation data for combustion

Weaknesses and Limitations

Some difficulties arise from the comprehensive treatment used in this book. For very advanced topics (see “Difficult Sections” below), I had a hard time understanding the material even after several readings.

Furthermore, the text rarely includes simplifications in governing equations that are taken for granted in other textbooks. Although this is a major benefit, derivation of the simpler versions from those given here is many times left to the reader.

It is worth noting that experimental approaches are only briefly reviewed where applicable in this textbook. It may need to be pared with other textbooks or teachings for someone involved in experimental research on combustion.

Lastly, turbulent and multiphase combustion is also only briefly covered in Principles of Combustion. The reader interested in theses subjects should also review “Fundamentals of Turbulent and Multiphase Combustion” by Kenneth Kuo and Ragini Acharya.

Two Combustion Textbooks by Kenneth Kuo

About the Author

Dr. Kenneth Kuo is a distinguished professor of mechanical engineering at Pennsylvania State University. Retiring in 2011, he taught for 39 years and was director of the High Pressure Combustion Laboratory. He is recognized as on of the leading researchers in propulsion-related combustion. Over his career he published and edited 15 textbooks in the field of combustion and worked on more than 475 technical manuscripts.

Favorite Sections

The following headings outline my favorite sections within Principles of Combustion. Reviews from other readers may be available from the textbook on Amazon (United States, Canada, Germany, United Kingdom).

Chemical Kinetics (Chapter 2)

Chapter 2: Chemical Kinetics and Reaction Mechanisms

The chemical kinetics chapter is a great mix of theoretical concepts and application to specific fuel systems. I first read the entire chapter over the Christmas break in 2014. I had just started using multi-step reaction kinetics in my PhD work and was having a difficult time understanding the detailed mechanisms used in journal papers I was reading.

Sections 2.3 to 2.7 present the fundamentals of multi-step reactions including consecutive, competitive, opposing, chain branching, and chain terminating reactions. Section 2.8 gives a description of the Chemkin Package which helps to understand how everything fits together to solve a 1D flame propagation problem.

The second half of the chapter covers reaction mechanisms for specific fuel systems. Section 2.13 covers Hydrogen/Oxygen, while 2.14 covers the different pathways in hydrocarbon fuels including CO (Carbon Monoxide, 14.1.2), CH2O (Formaldehyde, 14.1.3), CH4 (Methane, 14.1.), C2H6 (Ethane, 14.1.5), C2H4 (Ethylene, 14.1.6), C2H2 (Acetylene, 14.1.7), and other higher hydrocarbons.

These sections were invaluable for understanding the hydrocarbon reaction mechanisms I was studying at the time based on the models of Westbrook and Dryer, 1984 [2], and Westbrook et al., 2009 [3]. Great validation data on Hydrogen and Methane flame structures and burning velocities is also given in Figures 2.31 and 2.32 on pages 253/254.

Other topics of interest that I did not review as thoroughly for my work, but that may be useful for others include: Surface reactions, NOX reaction mechanisms, pollution and particulate formation, sensitivity analysis, mechanism reduction, and Computational System Perturbation Methods (CSPM).

Transport/Conservation Equations (Chapter 3)

The full set of conservation equations for mass, momentum, and energy in planar, cylindrical, and spherical coordinates are nice addition to Principles of Combustion.

Although I slightly prefer the descriptions given in “Fundamentals of Turbulent and Multiphase Combustion“, both are more comprehensive than I have found elsewhere in the literature.

My most referred to sections in this chapter are Section 3.6 and 3.7 which outline the different forms of the energy equation and derivation of the multi-component diffusion equation without any assumptions. Many assumptions are often presented throughout the literature for these equations, and it is useful to have the full derivations handy.

1D Flame Equations (Page 358)

No equations have I lost more time looking for online than the 1D conservation equations for the state in front of and behind a standing flame. I always assume I can derive them when needed, and it always takes hours to figure it out.

Luckily, these equations are derived and presented in Chapter 4.2 of Principles of Combustion.

\rho_{1}u_{1} = \rho_{2}u_{2}
P_{1} + \rho_{1}u_{1}^{2} = P_{2} + \rho_{2}u_{2}^{2}
C_{P}T_{1} + \frac{1}{2}\rho_{1}u_{1}^{2} + q = C_{P}T_{2} + \frac{1}  {2}\rho_{2}u_{2}^{2}

I have this page bookmarked so that I can double check my flame simulations or theoretical models when needed.

Premixed Laminar Flame (Chapter 5)

Much of this chapter was difficult to read and understand on its own. However, the classical flame theories given in Sections 5.1 to 5.3 are important basic principles to understand in combustion.

Also, the “Effect of Chemical and Physical Variables on Flame Speed” described in Section 5.5 is very informative for understanding how different system parameters effect premixed flames.

Lastly, Chapter 5 gives many of the plots summarized in the “Validation Data” section below which can be used to validate and verify theoretical models or CFD simulations.

Transport and Thermal Properties (Appendix A)

Appendix A: Evaluation of Thermal and Transport Properties of Gases and Liquids

The final section of Principles of Combustion that I come back to frequently is Appendix A. This appendix gives typical relationships used for transport and thermophysical property evaluation in gases and liquids.

It includes correlations and mixture rules for specific heat capacity, viscosity, conductivity, and diffusivity under standard and high pressure conditions. This is the most comprehensive listing of these models I could find outside of the textbook “The Properties of Gases and Liquids” by Poling, Prausnitz, and O’Connell.

Validation Data

Besides developing a theoretical understanding, a second major benefit of this textbook is that it gives a substantial amount of actual research results from the literature.

These results are tremendously helpful as validation data for theoretical or simulation models. A list of the useful figures are given here for reference by the reader:

Planar Premixed Flames (Ambient Conditions)

  • Fig. 2.31: Species profile of H2 and CH4 flames
  • Fig. 2.32: Burning velocity of H2 and CH4 flames at different pressures
  • Fig. 5.10: Burning velocity for O3/O2 flames
  • Fig. 5.11: Temperature profile for O3/O2 flames
  • Fig. 5.12: Specie profile for O3/O2 flames
  • Fig. 5.24: Burning velocity for propane/air mixtures
  • Fig. 5.31: Burning velocity for 12 hydrocarbon fuels (C2H4C7H16)
  • Fig. 5.54: Burning velocity of hydrogen near its rich flammability limit

Planar Premixed Flames (Non-Ambient Conditions)

  • Fig. 5.34: Burning velocity vs temperature for C2H4, C3H8, and CH4
  • Fig. 5.35: Burning velocity vs temperature for higher hydrocarbons
  • Fig. 5.36: Burning velocity of CH4 with different O2/inert gas mixtures
  • Fig. 5.51: Burning velocity vs temperature for hydrogen/air flames
  • Fig. 5.52: Burning velocity vs pressure for hydrogen/air flames

Stretched Premixed Flames

  • Fig. 5.22: Flame radius vs time for propane/air mixtures
  • Fig. 5.23: Laminar flame velocity vs radius for propane/air mixtures
  • Fig. 5.25: Burning velocity vs Karlovitz number for propane/air mixtures
  • Fig. 5.21: Markstein lengths vs stoichiometry for hydrogen/air flames
  • Fig. 5.26: Markstein lengths vs stoichiometry for propane/air flames

Diffusion Flames

  • Fig. 6.13: Specie profiles for methane diffusion flames
  • Fig. 6.14: Radial temperature profile for methane diffusion flame
  • Fig. 6.15: Radial species profile for methane diffusion flame
  • Fig. 6.16: Radial specie profile for hydrogen diffusion flame
  • Fig. 6.17: Radial temperature profile for hydrogen diffusion flame at ambient pressure
  • Fig. 6.18: Radial temperature profile for hydrogen diffusion flame
    at non-ambient pressure

Difficult Sections

Although the level of detail in Principles of Combustion is generally very helpful, it can sometimes make it difficult to understand more complex topics.

Specific topics that were covered thoroughly, but that I still find difficult to understand after reading the textbook are briefly outlined in this section.

Markstein Length

I still have nightmares about one of my comprehensive examination questions asking to discus the Markstein Length of multiphase flames. Although I passed the exam, I still struggle with the concept in general and the nuances even for gas flames.

Section 4.1 to 4.3 in Principles of Combustion describes the concepts of flame stretch, Karlovitz Number, and Markstein Length. Although the discussions were thorough, I still struggled with these concepts after reading the text.

Hugoniot Relationships

Although I worked modeling detonation for several years as a Research Engineer, the Hugoniot relationships, generation of Hugoniot curves to describe detonation states, and determining Chapman-Jouguet properties always seemed overly complex to me.

Described in Sections 4.3 and 4.4, I found the description of these principles difficult to understand in the current text.

Mixture Fraction Space

If you have been studying Direct Numerical Simulation of turbulent or spray flames, you have probably come across the term “Mixture Fraction Space“. Although it makes sense in a very general way, I have not found a good description of this concept for someone just starting in the field.

Although the math is described briefly on Page 552 and 557 for laminar flames, Principals of Combustion does not seem to review it for turbulent or multiphase flames. This topic is described in more detail in Fundamentals of Turbulent and Multiphase Combustion, however the discussion stills seems quite complicated.

Alternative Textbooks

Below is a list of alternative textbooks on combustion and reactive flow dynamics. Note that the images and links are also affiliate and I will receive a small commission if you make a purchase after clicking.

Fundamentals of Turbulent and Multiphase Combustion by Kenneth Kuo

Fundamentals of Turbulent and Multiphase Combustion
Kenneth K. Kuo and Ragini Acharya

Combustion by Irving Glassman

Combustion, Fourth Edition
Irving Glassman and Richard A. Yetter

Combustion Physics by Chung Law

Combustion Physics
Chung K. Law

An Introduction to Combustion by Stephen Turns

An Introduction to Combustion, Third Edition
Stephen R. Turns

Combustion Theory by Forman Williams

Combustion Theory, Second Edition
Forman A. Williams

Below is a list of related textbooks mentioned in this review. Note that the images and links are also affiliate and I will receive a small commission if you make a purchase after clicking.

The Properties of Gases and Liquids by Poling, Prausnitz, and O'Connell

The Properties of Gases and Liquids
Bruce E. Poling, John M. Prausnitz, and John P. O’Connell

Summary of “Principles of Combustion”

Principles of Combustion is an excellent textbook in the field of combustion theory and modelling and one that has been on my bookshelf for over five years.

Along with its counterpart “Fundamentals of Turbulent and Multiphase Combustion”, it has been a go-to resource during my PhD studies and is recommended reading for any graduate students or industry researchers in this area.

My favorite sections include the description of chemical kinetics and laminar flame propagation, while I struggled with some more complex topics such as flame stretch and Markstein Numbers. One of the most useful features of the textbook is the inclusion of over 25 figures with validation data for CFD model and theory development.

If you would like to purchase the textbook you can do it through the amazon button above or using these text links for select countries: United States, Canada, Germany, United Kingdom.

Thank you for reading and if you have any questions please do not hesitate to reach out to or leave a comment below. I would love to hear from you!

Cat with Back Cover of Principles of Combustion


[1] T. Lu, Y. Ju, and C. K. Law, “Complex CSP for chemistry reduction and analysis,” Combustion and flame, vol. 126, pp. 1445-1455, 2001.
title={Complex {CSP} for chemistry reduction and analysis},
author={Lu, T. and Ju, Y. and Law, C.K.},
journal={Combustion and Flame},
[2] C. K. Westbrook and F. L. Dryer, “Chemical kinetic modeling of hydrocarbon combustion,” Progress in energy and combustion science, vol. 10, pp. 1-57, 1984.
title={Chemical kinetic modeling of hydrocarbon combustion},
author={Westbrook, C.K. and Dryer, F.L.},
journal={Progress in Energy and Combustion Science},
[3] C. K. Westbrook, W. J. Pitz, O. Herbinet, H. J. Curran, and E. J. Silke, “A comprehensive detailed chemical kinetic reaction mechansim for combustion of \textitn-alkane hydrocarbons from \textitn-octane to \textitn-hexadecane,” Combustion and flame, vol. 156, pp. 181-199, 2009.
title={A comprehensive detailed chemical kinetic reaction mechansim for combustion of \textit{n}-alkane hydrocarbons from \textit{n}-octane to \textit{n}-hexadecane},
author={Westbrook, C.K. and Pitz, W.J. and Herbinet, O. and Curran, H.J. and Silke, E.J.},
journal={Combustion and Flame},

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