3.1 Configuration

To model and simulate the WET concept, the object-oriented modelling software NPSS is used [12]. The setup is based on the modelling used in Ref. [Reference Ziegler, Kaiser and Gümmer11]. The simulated WET configuration is shown as a simplified block diagram in Fig. 5 with station nomenclature. A geared fan is driven by a low-pressure turbine (LPT). Optionally a low-pressure compressor (LPC) can be simulated combined with the inner fan, also driven by the LPT. The high-pressure compressor (HPC) is driven by a high-pressure turbine (HPT). The steam from the vapourizer passes a steam turbine, supporting the low-pressure shaft and is then injected in a mixing duct in front of the burner. The HPT is cooled from a bleed after the mixing, and therefore a steam-air mixture and the LPT is cooled with an HPC bleed at an appropriate pressure level. The water recovered behind the condenser is fed to a water tank and from there through a feed pump to the vapourizer. The feed pump power is taken from the low-pressure spool.

Figure 5.

Simplified block diagram of the Water-Enhanced Turbofan with station nomenclature, adopted from Ref. [Reference Kaiser, Schmitz, Ziegler and Klingels8].

In addition to the configuration studied herein, other configurations are conceivable such as the partial use of ram air as a heat sink for high temperature operations. The impact of such configurational changes is not examined within the scope of this paper.

3.2 Fluid model

The fluid properties are modelled using two different fluid models. The water line (station W2-W5) is modelled using the industrial formulation 1997 (IF97) by the International Association for the Properties of Water and Steam [Reference Wagner, Cooper, Dittmann, Kijima, Kretzschmar, Kruse, Mareš, Oguchi, Sato, Stöcker, Šifner, Takaishi, Tanishita, Trübenbach and Willkommen15]. The core and bypass flows are simulated based on NASA Chemical Equilibrium with Applications (CEA) [Reference Gordon and McBride16]. The gas properties are calculated using the CEA formulation with seven terms for each species. An idealised combustion of C₁₂H₂₃ with oxygen is used for Jet-A1 kerosene. For high temperatures, an enthalpy correction due to dissociation of molecules is applied. The distribution of the water content across the different states of aggregation is computed using the saturation vapour pressure.

3.3 Turbomachinery

The turbomachinery is modelled using constant polytropic design efficiencies for compressors and constant isentropic design efficiencies for the turbines during design parameter variations. The used efficiencies are estimates for a year 2030+ technology level.

The off-design performance is modelled using public component maps. The inner and outer fan map is published in Ref. [Reference Cornell17] as ‘fan B’. For simplification, when an LPC is used the inner fan map is used to represent both the inner fan and the LPC combined. The HPC and HPT maps originate from the energy efficient engine (EEE) programme with more details on the programme published in Ref. [Reference Batterton18]. For the LPT and the steam turbine the map published in Ref. [Reference Flagg19] is used.

The flow path geometries of the core engine are based on typical geometric relationships and Mach numbers. The high-pressure spool mechanical speed is based on typical HPC tip speeds, the low-pressure spool mechanical speed is calculated from a maximum fan tip speed and a pre-set gear ratio. The radial position of the turbines are calculated from typical rim speeds. The stage numbers for the turbomachinery is calculated for a maximum work coefficient for each component. The HPT stage number is fix and the maximum work coefficient is ensured by an adjustment of the LPC pressure ratio in the multi-point design approach described in more detail in section 3.5. Using the mean radii and number of stages, the turbomachinery weights are calculated based on the scaling of weights of known designs.

3.4 Heat exchanger modelling

For the modelling of the heat exchangers in the performance calculations, a surrogate model is used. The evapourator is a spiral tube bundle heat exchanger whose tubes are wound around the engine axis so that the hot gas flow can flow radially outwards around the tubes and the water flows spirally (from the outside to the inside) through the tubes. The condenser is a cross-flow plate-fin heat exchanger with offset strip fins on the cold side. A sketch of the condenser and the definition of its outer dimensions no-flow length ${L_{no}}$, hot-flow length ${L_{hot}}$ and cold-flow length ${L_{cold}}$ is shown in Fig. 6.

Figure 6.

Sketch of the condenser with the definition of its outer dimensions as used subsequently.

As the input from the cycle calculation to the heat exchanger calculation, the inlet temperature, inlet pressure and inlet mass flow for the hot side and the cold side are used. In addition, for the condenser hot side the water content is used as an input. Based on these quantities and three main dimensions of the heat exchanger, a Latin hypercube sampling is performed for good coverage of the parameter space of interest.

The resulting points are then fed into a detailed heat exchanger calculation tool, Aspen Exchanger Design & Rating (EDR), solving iteratively for heat balance between the streams and metal, and pressure drop equations on both streams. Heat transfer coefficients and frictional pressure drop are based on empirical correlations. The heat exchanger matrix design is kept equal except the outer dimensions in form of the hot-flow length, cold-flow length and no-flow length. Therefore, plate distances, fin densities, tube diameters etc. are the same for all calculations and are determined by an initial design of both heat exchangers.

The resulting training data from the detailed heat exchanger calculation tool were then used to train a neural network that estimates the transferred heat and pressure losses based on the aforementioned inputs. The neural network consists of an input layer, two hidden layers and an output layer. To check the quality of the neural network, an additional test set is calculated with a detailed heat exchanger calculation tool and the results are compared to prediction of the neural network. The quality of the neural network used in this paper is shown in Table 1. The accuracy is considered sufficient for the studies in this paper. The root mean square (RMS) errors for the relative pressure losses are considered acceptable as the absolute pressure loss errors are considered to be within the margin of error for the conceptual design and trends are correctly depicted with the surrogate model. For the vapourizer cold side (water) a constant pressure loss is assumed that besides the heat exchanger contains additional pressure losses in the piping and is therefore omitted from Table 1.

Table 1.

Relative accuracy in terms of root mean square error (RMS) of the heat exchanger surrogate model based on the test dataset

3.5 Multi-Point design approach

For the design of the WET concept, an iterative multi-point design approach is used. A flow chart for the multi-point design approach is shown in Fig. 7. The required turbine cooling air is calculated from the cumulative thermal load across the included operating points. Furthermore, the thrust demanded by the aircraft at each operating point is calculated based on the needed water mass in the water tank and the fuel mass.

Figure 7.

Multi-point design scheme flow chart for the WET concept design.

As the design point for the engine model, a typical cruise point at 35,000 ft with Mach 0.78 at ISA atmospheric conditions is chosen. The main design parameters for the thermodynamic cycle are the turbine inlet temperature ${T_{040}}$, the overall pressure ratio $OPR$, the bypass ratio $BPR$, the turbine inlet water-air ratio $WA{R_{040}}$, the heated to cold bypass mass flow ratio ${w_{160}}/{w_{260}}$, and the water line pressure ${p_{w3}}$. To ensure a positive pinch point in the vapourizer, the temperature difference at the pinch point ${\rm{\Delta }}{T_{pinch,vap}}$ is used as a design variable and the $BPR$ is iterated. Instead of the bypass mass flow ratio ${w_{160}}/{w_{260}}$, the condenser exit temperature ${T_{e,\;cond}}$ is used as an input and ${w_{160}}/{w_{260}}$ is iterated. More details on these design parameters and their impact on the cycle can be found in Ref. [Reference Ziegler, Kaiser and Gümmer11]. In addition, the heat exchanger dimensions as mentioned in section 3.4 of the condenser and vapourizer are design variables and determine the transferred heat and pressure losses.

In the multi-point design, a take-off rotation operating point and maximum climb operating points at flight levels (FL) FL100, FL200, FL300 and at top of climb, FL350, are included. At these off-design operating points, compared to a conventional aero engine, an additional degree of freedom exists in form of the water-air ratio $WA{R_{040}}$, influencing the turbine inlet temperature ${T_{040}}$ and the water loss during take-off and climb.

After the most critical condenser operating point is determined later in section 4.0, it will be included as an additional operating point in the multi-point design iteration for the sizing of the condenser.

3.6 Cooling air assessment

The turbine cooling air is assessed using a conceptual design method that incorporates the impact of steam in the hot gas and the cooling air on the required amount cooling air. It is based on the work of Holland and Thake [Reference Holland and Thake20] and considers the impact of the heat capacity ratio of the hot gas and the cooling gas on the required cooling air. More details on the method and its application are also presented in Ref. [Reference Ziegler, Kaiser and Gümmer11]. In addition, the maximum material temperature is adjusted in the multi-point design iteration such that a defined turbine life parameter is met. This parameter is calculated based on the material temperature of all operating points (except the critical condenser operating point) shown in Fig. 7 by using a mission-representative time for which the engine remains at each operating point per flight. Thus, the impact of different temperatures during the climb phase on the required cooling air is represented.

3.7 Simplified aircraft modelling

A simplified aircraft model is used to assess the required thrust at all operating points of interest based on first order principles. For a single aisle medium range (2500nm design mission) aircraft with entry into service in the year 2030+, the drag polar for an Airbus A321 published in Ref. [Reference Sun21] was modified to have an increased best lift to drag ratio ($L/D$) estimated for the year 2030+. For the cruise phase, the simplified equations of motion are used. The lift ($L$) equals the weight ($W$) and the thrust ($F$) equals the drag ($D$). The drag is calculated on the basis of the required lift with the relation through the aforementioned drag polar.

For the climb, the required thrust is calculated based on a specified rate of climb (ROC). The flightpath angle $\gamma $ is calculated from the ROC and the true airspeed. The thrust results from these equations of motion for the climb phase:

\begin{align*}L = W \cdot \cos \!\left( \gamma \right)\\[-30pt]\end{align*}

(2) \begin{align}F = W \cdot \sin \!\left( \gamma \right) + D\end{align}

The ROC is calculated from a predefined climb profile of the design mission. The true airspeed results from a calibrated airspeed of 250kt up to FL100, 280kt up to the conversion altitude and a fixed Mach number of 0.78 beyond. The thrust is then assessed based on an estimate for the aircraft gross weight at the design mission for each altitude. The initial cruise altitude of the design mission is assumed to be FL350.

For take-off conditions, the thrust is calculated by simply scaling a reference thrust with the new maximum take-off weight:

(3) \begin{align}F = {F_{ref}} \cdot \frac{{{m_{MTOW}}}}{{{m_{MTOW,ref}}}}\end{align}

3.8 Fuel and water mass estimation

To determine the aircraft gross weight at each operating point, the fuel mass at the beginning of the design mission is estimated based on a reference fuel mass, which is scaled based on the fuel burn of the WET concept at the typical cruise point. For each operating point along the climb phase, the fuel mass is then calculated using a simple trapezoid integration of the fuel flow. For the typical cruise point (design point, mid cruise of 800nm typical mission), 25% of the total 2500nm design mission fuel is assumed.

Similarly, the size of the water tank is calculated by trapezoid integration of the difference between the water flow ${w_{w2}}$ and the recovered water flow ${w_{067w}}$ along the climb phase. In addition to the water mass used during the climb phase of the design mission, an additional 50% of the water mass are kept in the water tank for reserve.

3.9 Limitations

The engine model includes several assumptions limiting the accuracy in some aspects. The impact of the condenser size on the engine design in terms of engine length/nacelle drag or other aspects of integration besides the impact of additional weight is not taken into account. As a result, larger condenser designs appear more advantageous than if all installation effects were taken into account. This assumption was made in order not to limit the following results to a specific condenser integration (e.g. the one shown in Fig. 1), since there are several installation possibilities that could not be investigated in detail within the scope of this paper. Based on the report of Küchemann [Reference Küchemann and Weber14] no additional pressure loss results from the oblique installation and only a fixed design pressure loss is assumed for the flow deceleration before. The turbomachinery geometry is much simplified and needs a more detailed assessment for engine designs of interest. However, the total engine mass is dominated by the heat exchangers. The aircraft modelling only includes first order effects and therefore trade factors for specific fuel consumption and weight can differ from detailed aircraft assessments.

4.1 Multi-objective optimisation

For an initial analysis of the sensitivity of the condenser frontal area on the fuel burn, a multi-objective optimisation is performed. For this purpose, the NPSS engine simulation model is controlled by MATLAB, allowing for a parallelised optimisation with the variation of the non-dominated sorting genetic algorithm II (NSGA-II) implemented in the MATLAB Global Optimization Toolbox [22]. Using the multi-point design setup described above, the WET concept is optimised for fuel burn ${w_{fuel}}\left( x \right)$ and the condenser cold side area (${A_{cond,cold}} = {L_{no}} \cdot {L_{hot}}$) in a multi-objective optimisation:

(4) \begin{align}{\rm{minimize }}\ f\!\left( x \right) = \;\left[ {\begin{array}{*{20}{c}}{{w_{fuel}}\left( x \right)}\\{{A_{cond,\ cold}}\!\left( x \right)}\end{array}} \right]\end{align}

The design variables $x$ are ${T_{040}}$, $OPR$, $WA{R_{040}}$, ${\rm{\Delta }}{T_{pinch,vap}}$, ${T_{e,cond}}$, ${p_{w3}}$, the condenser hot flow length, the condenser no-flow length, the vapouriser width and the vapouriser number of windings as well as the $WA{R_{040}}$ at the off-design points. The condenser cold flow length is iterated in this first study such that a sustained operation (${w_{067w}} = {w_{W2}}$) is achieved at the typical cruise design point and the vapouriser mean tube diameter is set to a fixed radial distance from the LPT outer radius for a similar vapouriser installation as outlined in Fig. 1.

The result from the optimisation is a clearly visible Pareto front shown in Fig. 8. From 6,000 designs calculated during 15 generations of the optimisation process, 2,028 converged and are plotted in Fig. 8. As a reference, a design on the Pareto front is chosen that has a reasonable trade-off between fuel burn and condenser cold side area. The reference design is shown with an asterisk in Fig. 8. The design variables and their lower and upper bounds relative to the reference design are shown in Table 2. No additional constraints are applied to keep the computation time at an acceptable level.

Figure 8.

Pareto-optimum of fuel burn and condenser cold side area obtained using a genetic algorithm on the WET engine model. The reference design is marked with an asterisk.

Table 2.

Upper and lower bounds of the design variables in the multi-objective optimisation relative to the reference design

It can be seen that the Pareto front shows asymptotic behaviour in both objective functions. Compared to the reference design, an improvement in fuel burn of around 4% can be achieved at the cost of a condenser cold side area increase by more than 40%. On the other hand, the condenser frontal area can be reduced to around 78% of the reference design at the cost of a fuel burn increase of more than 10%. It is important to notice, that no penalty from the condenser installation is included. A large condenser frontal area could result e.g. in a longer nacelle, leading to a higher nacelle drag and therefore reducing the achievable fuel burn benefit with a larger frontal area even further. The major design parameters of the reference design shown in Fig. 8 are given in Table 3 and Table 4 for the typical cruise point and the maximum take-off thrust point.

Table 3.

Design parameters of the reference design at the typical cruise point (35000ft, M0.78, ISA)

Table 4.

Parameters of the reference design for the maximum take-off thrust point (sea level, M0.25, ISA+15K)

The Pareto front is dominated by the capacity of the condenser, as the flow velocity in the condenser increases with decreasing surface area on the cold side, which contributes quadratically to the pressure loss. In addition, to achieve the desired heat transfer, the condenser cold flow length has to increase with decreasing inlet area further increasing pressure loss. With increasing pressure loss, the cycle performance worsens and the required heat transfer by the condenser increases, exacerbating required cold side mass flow and heat transfer area. This leads to the rapid increase in fuel burn for smaller condenser cold side inlet areas.

The other design variables, ${T_{040}}$, $OPR$, $WA{R_{040}}$ and ${p_{w3}}$ vary only to a lesser degree along the Pareto front. This indicates that the optimisation of the cycle parameters can be decoupled from the condenser optimisation.

4.2 Additional design parameters affecting condenser size

In addition to the design variables in the multi-objective optimisation, additional design parameters exist that have a large lever on the condenser sizing and can be interpreted more in terms of a technology improvement.

One parameter is the water recovery factor ($WRF$), defining the amount of liquid water that can be recovered from the exhaust downstream of the condenser. The $WRF$ effectively reduces the required heat transfer in the condenser as less water has to be condensed from the exhaust with a higher $WRF$ to achieve a sustained water cycle. A higher $WRF$ is especially effective when the condenser pinch point temperature difference is small and a large area is required for a small amount of additional heat transfer.

Another parameter is the fan diameter. So far, a constant fan diameter was assumed and together with the thrust requirement a mass flow and fan pressure ratio result. The fan diameter can be limited by the aircraft installation, the nacelle weight and the requirement of variable geometry at low fan pressure ratios. A lower fan pressure ratio results in a lower temperature rise across the fan, resulting in a higher temperature difference for the heat transfer in the condenser.

Variable nozzles for the two bypass flows could be used to adjust the cold side mass flow of the condenser at different conditions and optimising the cycle performance at design conditions while reaching requirements from other operating points.

4.3 Critical operating points

4.3.1 Air temperature variations

An aero engine is exposed to different ambient temperatures at cruise altitudes due geographic, seasonal and daytime variations. As the heat exchange in the condenser is driven by the temperature difference between the cold bypass air and the core exhaust, the condenser performance will vary greatly with ambient temperature. So far only ISA conditions have been looked at for the condenser sizing in section 4.1. At lower ambient temperatures relative to the ISA conditions, the condenser is able to transfer more heat and therefore this case is not critical for the condenser sizing. On the other hand, higher ambient temperatures can significantly decrease the condenser transferrable heat. Therefore, the condenser should be sized to allow for operations at elevated temperatures. At the example of Europe and India, the spatial and temporal distribution of ambient air temperature compared to the ISA standard atmosphere at FL340 (pressure level 250 hPa) for the year 2022 is shown in Fig. 9. The underlying temperature data is taken from the ECMWF (European Centre for Medium-Range Weather Forecasts) ERA5 reanalysis model provided through Ref. [Reference Hersbach, Bell, Berrisford, Biavati, Horányi, Muásabateroz, Nicolas, Peubey, Radu, Rozum, Schepers, Simmons, Soci and Dee23]. It can be seen that the ambient temperature in Europe has an approximately normal distribution around the ISA conditions, while in India the ambient temperature at FL340 is mostly distributed between ISA+8 K and ISA+18 K.

Figure 9.

Distribution (spatial and temporally) of the ambient air temperature relative to the ISA standard atmosphere at FL340 (pressure level 250hPa) in Europe (30° N to 70° N, 20° W to 40° E) and India (0° N to 30° N, 65° E to 90° E) based on hourly reanalysis data of the ECMWF ERA5 model [Reference Hersbach, Bell, Berrisford, Biavati, Horányi, Muásabateroz, Nicolas, Peubey, Radu, Rozum, Schepers, Simmons, Soci and Dee23].

To allow for sustained operations of the WET concept at warm ambient conditions, the influence of different ISA temperature deviations as the sizing point of the condenser is studied. To avoid the use of an extremely large heat exchanger and its penalty during standard day conditions, an additional degree of freedom in operations at high ambient temperatures is the flight Mach number or calibrated air speed. For high ambient temperature operations a Mach number reduction down to 0.7 is investigated. This reduces the total temperature at the inlet by approximately 5K compared to the Mach number of 0.78.

Figure 10 shows the impact of different ambient temperatures on the condenser size and fuel burn at the ISA typical cruise point with a Mach number of 0.70 for both ISA+5K and ISA+10K sizing and a variation of the condenser no-flow length to achieve different cold-side flow areas. The cold-side mass flow is determined by a constant condenser outlet temperature during this study. From Fig. 10, a high sensitivity of the condenser sizing can be seen. Moving from ISA to ISA+5K with reduced flight Mach number 0.70 results only in a minor change in cold side area of 5% for equal fuel burn or about 0.5% increase in relative fuel burn for the same cold side area. The reduced flight Mach number effectively reduces the engine inlet total temperature to a similar level as in the ISA case. However, sizing the condenser for ISA+10K ambient conditions results in a need for a much larger condenser due to the reduced temperature difference between condenser hot side and cold side. With a reasonable trade-off between additional area and fuel burn the design at ISA+10K results in about 30% increase in condenser area and more than 2.5% increase in fuel burn at the ISA day typical cruise point.

Figure 10.

Impact of the ambient temperature and impact of water recovery factor, fan diameter and variable nozzles on the condenser sizing.

Increasing the $WRF$ by 4.3% compared to the reference design helps to significantly decrease this penalty. Due to the highly non-linear nature of the water vapour saturation pressure, to liquefy additional water a larger difference in temperature is required towards the end of the condensation process. As more of the liquefied water can be recovered from the exhaust with an increased $WRF$, the temperature to which the condenser hot side exhaust must be cooled for the sustained cycle increases. This helps to significantly reduce the required condenser size at high ISA deviations.

Sizing the condenser for ISA+15 K again aggravates the penalty, even with an increased $WRF$ compared to the reference design. However, it is shown in Fig. 10 that increasing the fan diameter by 9.1% compared to the reference design and increasing the mass flow through the condenser with a variable nozzle at high ambient temperatures in addition to the higher $WRF$ reduce the penalty of sizing the condenser for ISA+15 K to for example 10% more cold side area and 1.5% more fuel burn compared to the reference design.

4.3.2 Cruise altitude variation

With varying cruise altitude, the ambient temperature changes, which poses a challenge to the condensation process. In the standard atmosphere model, the ambient temperature decreases with altitude up to 36,089 ft (11 km) and is then constant in the remaining altitudes of interest for commercial aircraft. The thrust required for level flight at a given calibrated airspeed and aircraft mass is approximately constant and independent from the cruise altitude. However, the engine is able to deliver more net thrust at lower altitudes (higher maximum climb thrust at lower altitudes). Therefore, the engine is operated at lower part power when cruising at lower altitudes at a given calibrated airspeed and aircraft mass. While the increasing ambient temperature aggravates the heat transfer in the condenser, the part power operation changes the mass flows in the condenser in a favourable way for the heat transfer duty.

Figure 11 shows the performance at different cruise altitudes of the condenser sized at ISA+15K with $WR{F_{rel}}$ = 1.043, ${D_{fan,rel}} = 1.091$, ${A_{290,rel}} = 1.1$ from the previous section. For each cruise altitude, a calibrated airspeed of 230kt is assumed here as minimum feasible. When the water recovery is sufficient to produce excess water (${w_{W2}} - {w_{067w}} \lt 0\;{\rm{kg}}/{\rm{s}}$), a higher calibrated airspeed can be flown while keeping a closed water cycle. The nozzle adjustment to ${A_{290,rel}} = 1.1$ remains constant in Fig. 11 for simplicity, however, when sustained operations can be achieved by other means, the nozzle adjustment can be reduced. The cruise thrust at each point is estimated based on the typical cruise aircraft mass from the multi-point design. It can be seen that at ISA+15K conditions with the condenser sizing at FL350, the water cycle can remain closed for cruise levels between FL280 and FL360. For lower cruise levels at ISA+15K the ambient temperature is too high for sustained operations. For lower ISA temperature deviations, the possible cruise altitudes with a closed water cycle extend downwards and at ISA conditions a sustained cruise below FL100 is possible. At ISA conditions and high cruise altitudes, the heat transfer in the condenser is limited to prevent icing conditions in the exhaust. This can be achieved e.g. through cold side nozzle adjustments or partial blockage of hot side layers.

Figure 11.

Water recovery at cruise altitudes between FL100 and FL360 at different ISA conditions at typical cruise aircraft mass and a calibrated airspeed of 230kt with the condenser sized at ISA+15K with $WR{F_{rel}}$ =1.043, ${D_{fan,rel}} = 1.091$, ${A_{290,rel}} = 1.1$

Whether the sizing of the condenser with the shown performance at lower cruise altitudes is sufficient, needs a more detailed analysis. Parts of the flight where the closed water cycle cannot be achieved during the cruise phase would require water from the water tank in addition to the water for the climb phase.

4.3.4 Contrail avoidance

As the reduction of contrail climate impact is a major design goal of the WET concept, the contrail avoidance can become a critical sizing factor for the condenser design. Whether a contrail forms or not can be determined with the Schmidt-Appleman criterion [Reference Schmidt24–Reference Schumann26]. The mixing gradient

(5) \begin{align}G = \frac{{de}}{{dT}}\end{align}

with the partial pressure of water $e$ and temperature $T$ when mixing the engine plume with ambient air can be calculated from the exhaust and ambient conditions and is approximately constant for conventional turbofan engines. When the mixing line passes the saturation pressure with respect to liquid water condensation occurs during the mixing with ambient conditions and a contrail will form. When ambient conditions are saturated with respect to ice, the contrail is persistent. If the atmosphere is sub-saturated, the contrail disappears after a while.

For the WET concept, the mixing gradient is a function of the ambient temperature due to its dependence of the condenser effectiveness. At low ambient temperatures, the condenser rejects more heat and more liquid water can be recovered from the core exhaust (see Fig. 11). With less water in the engine exhaust, the partial pressure in the plume reduces and therefore the mixing gradient is reduced. A second effect specific to the WET concept is that liquid water droplets will remain in the core exhaust due to the non-perfect water recovery ($WRF \lt 1)$.

Similar to the qualitative assessment in Ref. [Reference Kaiser, Schmitz, Ziegler and Klingels8] on the impact of the WET concept on the contrail formation at the example of a single operating condition, a new assessment is made including the effect of ambient temperature on the condenser effectiveness. Also two scenarios are shown: in the first (optimistic) scenario the already liquefied water in the core exhaust remains liquid and therefore is not accounted in the partial pressure. In the second (conservative) scenario, the liquefied water droplets evapourate again completely after the mixing with the hot bypass (or could be in gaseous phase due to non-equilibrium flow) and therefore are accounted for in the partial pressure of water in the plume.

Figure 12 shows the lines of mixing for the WET concept with the condenser sized for typical cruise ISA+15K with the improvements $WR{F_{rel}}$ =1.043, ${D_{fan,rel}} = 1.091$, and the hot day nozzle adjustment ${A_{290,rel}} = 1.1$. The lines of mixing of the plume with ambient air are shown for three different ambient temperatures for the operation at 35,000ft and a flight Mach number of 0.78 with typical mission cruise thrust. For comparison, the mixing gradients of a conventional turbofan (TF) are illustrated. In all cases the mixing gradient of the WET concept is lower compared to the conventional turbofan. While the gradient for the turbofan is nearly independent of ISA deviation, the gradient gets progressively smaller with decreasing ambient temperature for the WET concept.

Figure 12.

Mixing of the engine plume with ice saturated ambient air for different ambient temperatures for a conventional turbofan and the WET concept. Scenario 1 assumes that all liquid water in the WET exhaust is in gaseous phase before mixing with ambient conditions. Scenario 2 assumes that all liquid water remains in liquid/solid phase during the mixing process with ambient air. In reality a transition from scenario 2 to scenario 1 is expected while the plume mixes with ambient air.

In the first scenario, as shown in Fig. 12, no contrail forms for the warm and normal ambient temperature with the WET concept, while the conventional turbofan produces a persistent contrail in all three cases. In the second scenario, where parts of the water in the exhaust exists in form of droplets (being in non-equilibrium conditions), the mixing gradient of the WET concept is much lower compared to the first scenario and no contrail forms for all cases. Comparing the mixing gradient of the cold ambient conditions with the normal ambient conditions, the partial pressure of water is only slightly lowered compared to the difference between the warm and normal day, which is caused by the limit in heat transfer in the condenser to avoid icing.

Overall, a significant reduction in contrail climate impact of the WET concept can be expected with the condenser sized for high ambient temperature conditions due to its improved performance at colder ambient conditions. Any change in physical properties of a WET concept contrail and a qualitative assessment of the reduction in climate impact are subject to further research. With such a qualitative assessment, the influence of the condenser size could be evaluated to include this effect in the optimisation of the concept regarding the climate impact in contrast to a fuel burn.