Comparison on NO_x Emission Empirical Models for In-Service Civil Turbofan Engines Under Different Control Modes

Nitrogen oxides (NO_x) emissions, as the primary pollutant of civil aero-engines, have gradually emerged as a new constraint in engine control design, especially for in-service engines affected by gas path component degradation, whose combustor operating temperature has significantly increased. However, most empirical NO_x emission models used in control design are developed for the nominal engine, so that their applicability for degraded engines remains to be validated. In this paper, two classical empirical NO_x emission models are compared for in-service civil turbofan engines under different control modes, i.e., low-pressure shaft speed (N1) mode and engine pressure ratio (EPR) mode. The first model is the P3-T3 model, which solely uses combustor entry pressure and temperature to calculate NO_x emissions. The second one is the Dopelheuer model, which additionally considers combustor-level parameters such as average reaction temperature and primary zone temperature. Simulations were conducted on a validated civil turbofan engine aero-thermal model. Both NO_x emission models produce simulation results for the nominal engine that are in good agreement with publicly available data. For degraded engines, the P3-T3 model predicts a slight NO_x decrease under N1 mode and a minor increase under EPR mode, contradicting the expected NO_x increase due to elevated combustor temperature. In contrast, the Dopelheuer model predicts NO_x increases under both control modes, consistent with physical expectations, with a more pronounced rise under EPR control due to better thrust maintenance and higher combustion states. These findings indicate that the Dopelheuer model more accurately captures the effect of degradation on NO_x emissions and can serve as a qualitative, trend-consistent tool for NO_x prediction in controller design for in-service gas turbine aero-engines.