# The Water-Enhanced Turbofan as Enabler for Climate-Neutral Aviation
## 4 Engine Performance and Climate Impact Evaluation Methods
### Climate Impact Methodology
#### 4.5.2 Contrails
In case parts or all of the unrecovered liquid water were to evaporate again, the gradient of the mixing line with the ambience of the WET concept would increase. Subsequently, the core and warm bypass (station 9a + 29a) mix with the cold bypass (station 9a + 29a + 19a). Finally, the engine plume mixes with ambience as indicated by the dashed-dotted line. For the depicted ambient conditions, the WET concept would not trigger contrails. In Figure 5, the exhaust conditions at station 9 are shown for the reference TF2030+, followed by the flow deceleration in the ambient frame of reference (station 9a). Subsequently, it mixes with the bypass air (station 9a + 19a) and then with the ambience along the dashed-dotted mixing line. As this line crosses the vapor saturation curve with respect to water, the formation of contrails would be expected for the TF2030+. As the ambient conditions modeled here are dry air, the contrails would not be persistent, and would dissipate once the plume is mixed with enough ambient air such that the mixture is no longer saturated with respect to ice. Figure 5: Partial pressure of water \(e\) over temperature \(T\) at different engine stations. Circles refer to the WET concept, and triangles to the reference TF2030+. Mixing of the core and bypass air is shown by dotted lines. Mixing of the engine plume with ambience is shown with a dashed–dotted line. Ambient conditions are ISA at 35,000 ft with dry air. While the TF2030+ would produce contrails, no contrails would form for the WET concept. The gradient \(G\) of the final mixing line for the WET concept is \(G_{WET}=0.946\) Pa/K, and for the TF2030+, almost twice as high with \(G_{TF2030+}=1.817\) Pa/K. When considering the liquid water in the WET exhaust and assuming all would evaporate, the resulting WET concept gradient would be \(G_{WET}=1.476\) Pa/K, which is still smaller than that of the TF2030+. The critical ambient temperature \(T_{c}\), below which contrails would form when the ambience is saturated (with respect to liquid water), is lower for the WET concept. Using the approximation of [PERSON] [32] for the critical temperature \(T_{c}\) at a relative humidity of 100%,  
\[T_{C}[^{\circ}\mathrm{C}]=-46.46+9.43\ln(G-0.053)+0.72(\ln(G-0.053))^{2} \tag{3}\]  
a critical temperature \(T_{C,WET}=-47.5\)\({}^{\circ}\)C (ISA+6.8 K) is observed for the WET concept, and \(T_{C,TF2030+}=-40.9\)\({}^{\circ}\)C (ISA+13.4 K) for the TF2030+ results. For lower relative humidity, the critical temperature is lower. To transform these findings into a quantifiable reduction in contrails, a simulation of representative missions will be necessary in a next step. As the third effect, water emissions are lower overall due to lower fuel burn. In addition, due to higher water recovery than water injection, the water content in the exhaust is lower than that of the TF2030+. Hence, a potential contrail would also contain less water overall, with potentially lower optical density and/or volume, and, hence, radiative forcing. The surplus water recovery can either be recollected to the tank for the subsequent mission, or released in particle form with low optical density. The model used in this paper does not incorporate detailed models to quantify the impact on contrails and contrail-induced cirrus clouds of the Schmidt-Appleman effect, nor the lower water emission effect. Therefore, only a 50% reduction in contrail climate impact for the \(APGMP_{100}\) will be assumed in this paper, based on the particle reduction effect. The other two effects suggest that the effect could be notably higher.