If the temperature field in a combustion analysis is 5% off, that is usually acceptable. The same error produces deviations of a factor in a NOx prediction.
The reason: exponential dependence
Thermal NOx formation depends exponentially on temperature; at typical flame temperatures a few hundred degrees changes the formation rate by factors. A NOx prediction therefore depends on the accuracy of the temperature peak, not the mean.
In a turbulent flame the temperature fluctuates. NOx computed from the mean temperature comes out markedly below the true value, because the mean of an exponential function exceeds the function of the mean. Serious NOx calculations therefore account statistically for the temperature fluctuation.
The post-processing approach
NOx concentrations are very low and do not affect the main flow, the temperature field or the density. That gives a practical convenience: NOx can be computed in a separate step on the converged combustion solution. Different mechanisms and coefficients can be tried without rerunning the main solution.
Three formation routes, treated separately
- Thermal NOx. From atmospheric nitrogen at high temperature. The route most sensitive to the temperature peak.
- Prompt NOx. At the flame front via hydrocarbon radicals. Proportionally important in rich mixtures and at low temperature.
- Fuel NOx. From nitrogen bound in the fuel. Dominant in coal and heavy fuels, absent in natural gas.
A reduction study conducted without knowing which route dominates intervenes in the wrong place: changing the fuel does nothing if thermal NOx dominates — the peak temperature has to come down.
How to use the result
The absolute accuracy of NOx predictions is limited. What is reliable is comparative use: which of two burner arrangements, run with the same method, produces less NOx. See the significant digits note.
References
- 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
- Modest, M. F. & Mazumder, S. (2021). Radiative Heat Transfer, 4th ed. Academic Press. ISBN 978-0-323-98406-5.