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Combustion: is mixing the limit, or chemistry?

In most industrial burners the combustion rate is set by turbulent mixing, not by chemistry. That distinction tells you directly which model is appropriate.

The first decision in combustion modelling is what limits the reaction.

Mixing limited. Fuel and oxidiser enter separately and burn as soon as they meet. The rate is set by how fast they mix at molecular scale. Most industrial diffusion flames fall in this class. The eddy dissipation approach of Magnussen and Hjertager models this by relating the reaction rate to the turbulent kinetic energy and its dissipation rate [1].

Chemistry limited. The mixture is ready but the reaction is slow: low temperature, dilute mixture, ignition and extinction limits. Here the chemical time scale dominates and mixing-based models give the wrong answer.

The distinction is made by a dimensionless ratio of time scales (the Damköhler number): if the mixing time is much longer than the chemical time, the process is mixing limited.

Practical consequences

Running a detailed chemical mechanism on a mixing-limited problem increases the cost by orders of magnitude and adds nothing to accuracy — because chemistry is not what is limiting.

Conversely, if ignition delay, extinction or unburnt fuel (CO, UHC) is the question, a mixing-based model is inadequate; those quantities depend directly on the chemical time scale.

The critical input: air distribution

What a combustion analysis is most sensitive to is usually not the model but where the air enters and how much. The distribution of secondary air holes, the register opening, leakage air — these set the flame shape and temperature field more than the model does. See the boundary condition note.

Radiation cannot be neglected

At flame temperatures the dominant part of the heat going to the wall is radiative, and the combustion products are a participating medium. A combustion analysis without radiation gets the wall heat flux and the flame temperature wrong together. See the radiation note.

References

  1. Magnussen, B. F. & Hjertager, B. H. (1977). On mathematical modeling of turbulent combustion with special emphasis on soot formation and combustion. Symposium (International) on Combustion, 16(1), 719–729. DOI: 10.1016/S0082-0784(77)80366-4
  2. Modest, M. F. & Mazumder, S. (2021). Radiative Heat Transfer, 4th ed. Academic Press. ISBN 978-0-323-98406-5.

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