# The Water-Enhanced Turbofan as Enabler for Climate-Neutral Aviation
## 4 Engine Performance and Climate Impact Evaluation Methods
### Climate Impact Methodology
#### 4.5.3 Nitrogen Oxide Emissions
This simple semi-empirical approach to model NO\({}_{\rm x}\) emissions is subject to high uncertainty for significant changes in combustor architecture, operating conditions, and technology level. Published experimental data regarding kerosene combustion with steam addition, shown in Figure 6, is used to derive \(R_{STM}\). There, the relative NO\({}_{\rm x}\) emissions of wet combustion to emissions of dry combustion at a constant equivalence ratio are shown. For all of the data points, the combustor was supplied with premixed steam and air. The inlet conditions (\(p_{3}\), \(T_{3}\)) were kept constant in each experiment. Despite the scatter of experimental data, a clear trend towards \(>\)80% emission reduction for \(WAR\), greater than 0.12, can be seen. From stationary applications, some correlations for the effect of steam injection exist. In the work of [PERSON] [47], combustors were investigated which were originally made for water injection, but adjustable to steam injection by dividing the water-to-fuel ratio by a constant factor, representing the differences in heat capacity and missing evaporation heat [48]. A similar difference for water and steam injection was reported by [PERSON] and [PERSON] [49]. As these correlations for the effect of steam are a function of the water-to-fuel ratio rather than the water-to-air ratio, a difference in \(R_{STM}\) was predicted for different equivalence ratios. This, however, is not in agreement with the experimental data for kerosene combustion shown in Figure 6, where no clear dependency on equivalence ratio is observable. Moreover, the effect on the stoichiometric flame temperature \(T_{\text{st}}\) is independent of the overall fuel-to-air ratio. Therefore, a new term is proposed to consider the steam injection:  
\[R_{STM}=\exp\left(\frac{-2.465\;WAR^{2}-0.915\;WAR}{WAR^{2}+0.0516}\right) \tag{7}\]  
Figure 6: Relative \(\text{NO}_{\text{x}}\) emissions \(R_{STM}\) (dry volumetric ppm) between dry and wet operations at constant eqivalence ratio from published experimental data [45; 46]. Premixed steam and air with constant inlet temperature \(T_{37}\) for each data set and atmospheric pressure. The proposed term shown in Equation (7), based on the available experimental data of [45], is shown with a dashed–dotted line. “Nozzle 1” and “Nozzle 3” refer to the nozzle types as published in [45]. Note that the experimental data are based on volumetric ratios, and it is assumed that the derived term can be applied as a gravimetric ratio in Equation (6), due to nearly constant molar mass ratios of \(\text{NO}_{\text{x}}\) and the combustion gases. which is derived using the experimental data published in [PERSON] et al. [45] for the measurements with their \"Nozzle 3\", exhibiting lower NOx reduction compared to \"Nozzle 1\", yielding a more conservative estimate. The constants in Equation (7) are a fit of the published data for \(\Phi=0.7\) at \(WAR=0.1\) and \(WAR=0.15\), as well as for \(\Phi=0.9\) at \(WAR=0.2\). The form of the formula was selected to replicate a steep characteristic up to \(WAR=0.1\), and a diminishing effect towards higher WAR. The absolute NOx emission for the cycle presented in Section 4.2 was assessed using Equations (6) and (7). The effective WAR in the primary zone of the combustor might be lower than the overall WAR to ensure flame stability. Hence, simulation of NOx emissions was investigated for three effective levels: 50%, 75%, and 100% of the overall WAR at Station 37. To assess the individual influence of the three parameters \(T_{37}\), \(p_{37}\), and \(WAR\), the \(EI_{NO_{x}}\) was calculated, varying each parameter separately while keeping the other two parameters at the value of the TF2030+. The ratio of the resulting \(EI_{NO_{x}}\) compared to the TF2030+ is shown in Table 3. The reduction in the flame temperature due to the introduction of steam has the biggest impact, with a reduction of 84-95%. The reduced \(T_{3}\) alone would reduce the \(EI_{NO_{x}}\) by 45%.