The article presents the procedure for how to establish a mathematical model of nitrogen oxides formation based on the theory of dimensional analysis. The model is based on selected physical quantities (parameters) measurable during regular operation of a heat generation plant. The objective of using dimensional analysis to describe nitrogen oxides formation is to show that between operating parameters of the combustion equipment and the NOx formation there is a significant correlation.
The obtained results, which are further described in this article, have proved this fact. The obtained formula expressing nitrogen oxides formation, based on dimensional analysis, applies universally to any boiler fuelled by coal, gas or biomass. However, it is necessary to find C, m, n constants for the formula by experiment, individually for each type of boiler and used fuel. The experiment is based on on-line measurements of selected operational parameters for a given boiler, combusting a certain type of fuel with its actual moisture content and calorific value. The methodology, described in this article, helps to find relationships between the operational parameters and the formation of NOx emissions for a particular furnace. The developed mathematical model has been validated with boilers fuelled by black coal and biomass. Both the results obtained from direct measurements of NOx in both types of boilers, and the results obtained by calculation using equation based on the dimensional analysis, are in a very good accord. When burning coal, the variation between NOx expression from the model and the on-line measurements ranges between -12.23 % and + 9.92 %, and for burning biomass between -0.54 % and 0.48 %.
The intention of the authors is to inform the professional community about the suitability of the dimensional analysis to describe any phenomena for which there is currently no exact mathematical formulation based on differential equations or empirical formulas. Many other examples of dimensional analysis applications in practice may be found in the work of Čarnogurská and Příhoda (2011).
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