# The Water-Enhanced Turbofan as Enabler for Climate-Neutral Aviation
## 4 Engine Performance and Climate Impact Evaluation Methods  
### Thermodynamics  
The WET concept is modeled and simulated using the object-oriented modeling environment Numerical Propulsion System Simulation (NPSS). The engine components are represented as individual objects and connected as indicated in Figure 4. The objects are then calculated in sequential order, following the main gas path. The fluid conditions of the semi-closed water cycle are first guessed at the mixing station after station 31, and later matched to the conditions obtained after simulating the water line by iteration. The fluid conditions within the WET concept are simulated by combining two separate gas models, namely NASA Chemical Equilibrium with Applications (CEA) [24] for the main gas path, and the industrial formulation IF97 by the International Association for the Properties of Water and Steam (IAPWS) for the water line [25]. CEA is used to calculate the thermodynamic properties of equilibrium composition with high water-to-air ratios of up to 40% along the main gas path. For computational efficiency, the composition was precomputed and tabulated for variations of \(T,p\), fuel-to-air ratio (FAR), and water-to-air ratio (WAR). The relevant fluid properties, such as enthalpy \(h\) and entropy \(s\), were then obtained using the NASA CEA seven-term formulation for each species [26]. To avoid interpolation errors in the condensation region, the amount of liquid water was calculated with the saturation pressure rather than using the interpolated, tabulated value. IP97 was used in the water line for pure water, both liquid and vaporous. This is necessary, as CEA cannot appropriately represent the two-phase state in the vaporizer, and does not represent real gas effects. The latter are highly relevant at high pressures and medium temperatures in the gaseous state after evaporation. The deviation is maximum around the critical point (\(T_{\rm cr}=647\) K, \(p_{\rm cr}=22.1\) MPa), with up to 1 MJ/kg. Figure 3: Schematic of the resulting WET configuration with reduced complexity and full nacelle integration. To avoid conversion errors at the interfaces between the two fluid models, two measures were taken: First, a common reference state for enthalpy was defined in reference conditions (\(T_{\text{ref}}=298.15\) K, \(p_{\text{ref}}=101.325\) kPa). Both models were aligned at that reference state and at interfaces between both fluid models. In particular, when mixing the steam into the main gas path, the enthalpy, with respect to reference conditions, is kept constant. Thus, conservation of energy according to the first law of thermodynamics is ensured. Second, the NASA CEA integration constants were modified in such a way that the reference enthalpy of liquid water and CO\({}_{2}\) is zero, rather than that of H\({}_{2}\) and O\({}_{2}\), in the base formulation. This avoids a large, artificial enthalpy offset in mixtures of air and water. The heat exchangers were modeled in the performance model using only the high-level module characteristics, namely the pressure losses \(\Delta p\) on both sides, and the heat exchanger \(\epsilon\) effectiveness, which is defined as  
\[ \begin{array}{l}\epsilon=\frac{Q_{\text{actual}}}{\text{O}_{\text{max}}} \frac{Q_{\text{actual}}}{\text{min}\left\{n_{\text{c}}\cdot\left(h\left(C_{ \text{c}},T_{\text{e},in}\right)-h\left(C_{\text{c}},T_{\text{e},in}\right) \right);\,m_{\text{b}}\cdot\left(h\left(C_{\text{b}},T_{\text{b},in}\right) -h\left(C_{\text{b}},T_{\text{e},in}\right)\right)\right\}}\end{array}  \tag{1}\]  
using the enthalpies resulting from the respective compositions from hot side \(C_{h}\) and cold side \(C_{\text{c}}\), and temperatures \(T_{h}\) and \(T_{c}\). These values were obtained from 1D-simulations of the heat exchanger with linear discretization in hot gas path direction for both the vaporizer and the condenser.