# 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  
In general, NO\({}_{\mathrm{x}}\) is mainly generated at high temperatures and high concentrations, i.e., high pressure. Following the fundamental Arrhenius Equation (4), the reaction rate \(k\) increases exponentially with increasing T. The three reactions of the _Thermal NO\({}_{x}\)_ or _Zeldovich_ pathway, the prevalent pathway in gas turbines for flame temperatures above 1700 K [33], is shown in Equation (5). The NO\({}_{\mathrm{x}}\) generation rates depend on the concentration of the educts. Since all three pathways have two educts, respectively, the rate for molecular concentration depends on pressure squared, and, therefore, the rate of mass is linearly correlated with pressure. In practice, higher pressures demote the creation of radicals such as O, N, and OH, which are also educts of the thermal NO\({}_{\mathrm{x}}\) mechanism. In consequence, the dependency on pressure is less than linear. Moreover, the concentration of radicals such as N and O is highly dependent on temperature. \[k=A\cdot\exp\biggl{(}-\frac{E_{0}}{R_{m}T}\biggr{)} \tag{4}\]  
\[\begin{array}{l}\mathrm{N}_{2}+\mathrm{O}\ \overset{k_{1}}{\rightarrow} \mathrm{NO}\ +\ \mathrm{N}\ \ \ \frac{d[\mathrm{NO}]}{dt}=k_{1,f}[\mathrm{N}_{2}][\mathrm{O}]-k_{1,f}[\mathrm{ NO}][\mathrm{N}]\\ \mathrm{N}\ +\  
In combustors, most of the NO\({}_{\rm x}\) is created in hot zones with near-stoichiometric conditions [42]. Therefore, most of the correlations include the combustor inlet temperature \(T_{37}\), which directly affects the stoichiometric flame temperature \(T_{st}\), or directly uses it. Furthermore, most of the correlations include the effect of the combustor inlet pressure \(p_{37}\) on NO\({}_{\rm x}\) formation. In addition, the residence time \(\tau\) is known to affect the level of NO\({}_{\rm x}\), and is included in some of the correlations, which requires knowledge of the combustion chamber volume and flow field.  
NO\({}_{\rm x}\) emissions by the WET concept are expected to reduce significantly. Three main effects have an impact:  
* Reduced stoichiometric flame temperature \(T_{stf,nd}\) due to added steam, which acts as an inert species in the combustion process;
* Reduced combustor inlet temperature \(T_{37}\) due to reduced OPR and mixing with (colder) steam;
* Reduced combustion pressure \(p_{37}\) due to reduced OPR.  
The addition of steam not only affects the temperatures of the combustion process, but also has a chemical effect. As described in [33], important species such as O, H, and OH are affected in their concentration through the chemical influence of steam during the combustion process. However, there is no agreement within the scientific community on how the radical concentrations are affected [33]. A recent study with a methane flame suggested that the chemical effect leads to a further, minor reduction of NO\({}_{\rm x}\) generation [43].  
To compare relative NO\({}_{\rm x}\) emissions of the WET concept to an evolutionary TF203+ at the same technology level, available correlations were extended to include the effect of steam injection. Assuming that both engines use an RQL combustor, most of the NO\({}_{\rm x}\) is generated in near-stoichiometric conditions [42]. Thus, a change in overall equivalence ratio is assumed to have no significant influence on NO\({}_{\rm x}\) generation. Therefore, the _GasTurb_ correlation published in [38] is used as a basis for the NO\({}_{\rm x}\) emission, neglecting the ambient humidity term and extending it by the term \(TF\) as a technology factor, and by the steam correction factor \(R_{STM}\), to include the effect of steam injection:  
\[EI_{NOx}=32\ \frac{\rm g}{\rm kg}\cdot\exp\biggl{(}\frac{T_{37}-826\ \rm K}{194\ \rm K} \biggr{)}\cdot\Bigl{(}\frac{p_{37}}{2.965\cdot 10^{6}\ \rm Pa}\Bigr{)}^{0.4}\cdot TF\cdot R_{STM} \tag{6}\]  
The technology factor \(TF=0.72\) was calibrated to represent the NO\({}_{\rm x}\) emissions of state-of-the-art engines [44], and is assumed to be constant for the TF2030+ and the WET.