Sensitivity Analysis and Optimization of a Liquid Cooling Thermal Management System for Hybrid Fuel Cell Aircraft

The objective of this work is to perform a comprehensive system analysis of a liquid-cooling thermal management system for a hybrid-electric aircraft using fuel cells for general aviation by sizing and optimizing the system with respect to a given objective. A sensitivity analysis on the different design parameters and model assumptions is also performed and their impact on the aircraft and its performances will be assessed. Firstly, the case study is defined and an optimization is run with some initial assumptions leading to a feasibility study for the implementation of this system. The sensitivity analysis is then undergone for the chosen coolant type and fuel cell stack temperature selected after the first optimization. Incorporating the findings of this analysis, a second optimization is run on the thermal management system with improved inputs in order to demonstrate a scenario with reduced penalty on the aircraft. Preliminary results show that implementing this hybrid propulsion system along with its thermal management is feasible with a reduction in payload and range. In addition, it can be concluded that initial assumptions and design choices are shown to have a significant impact on the system’s sizing and should be considered in aircraft sizing design loops.


Introduction
The shift towards creating decarbonized aircraft has accelerated in recent years, resulting in a progressive electrification of aircraft systems.Among the various possible approaches in electrification is the hybridization of the conventional propulsion system.For this hybridization, fuel cells seem to be a promising solution due to their higher specific energy and energy densities compared to traditional battery sources [1].However, one drawback with fuel cells is that they typically exhibit efficiencies of around 50% meaning they produce as much heat as they do power.An adequate thermal management system (TMS) is needed to manage these heat loads.Nonetheless, adding such TMS on an aircraft can impact the aircraft sizing and its performance, as the system may add some mass, drag and even power consumption.
A fuel cell liquid-cooling TMS has been previously developed for a hybrid aircraft case study [2].The objective of this work is to perform a comprehensive system analysis, which includes optimizing the system with respect to a given objective, and conducting a sensitivity analysis on the different input parameters and model assumptions.Performing a sensitivity analysis helps to understand the uncertainty of a model by attributing it to the design parameters and quantifying their impact.Knowing how the model reacts to certain parameters can provide useful information and aid in designing the system, such as to increase efficiency or manage different trade-offs.The sensitivity analysis can also be used to identify the most critical inputs and prepare for various scenarios if these inputs cannot be controlled or depend on external factors.The TMS sizing, optimization and analyses are done using FAST-OAD, which stands for Future Aircraft Sizing Tool -Overall Aircraft Design [3].It is an aircraft sizing and optimization tool that relies on the open-source framework OpenMDAO.Section 2 presents the liquid-cooling system studied in this paper, while Section 3 provides the chosen case study and methodology for the optimization and sensitivity analysis of the system.The results are shown in Section 4 and concluding remarks are presented in Section 5.
2. Liquid-cooling system 2.1.Architecture Fuel cell cooling is usually divided into three methods: air cooling, liquid cooling and evaporative cooling.For this study, liquid cooling has been chosen due to it being the most mature system for high-heat applications and it is assumed that 35% of the total fuel cell energy needs to be dealt with by this TMS [4].The liquid-cooling thermal management system is shown in Figure 1.A polymer electrolyte exchange membrane fuel cell (PEMFC) is considered and this system is separated into two cooling loops.For this fuel cell to operate, it requires a constant inflow of hydrogen and oxygen at the correct operating conditions.These include the operating temperature and pressure.The primary cooling loop focuses on dissipating the fuel cell heat.First, the excess heat is used to evaporate and preheat the hydrogen to a certain temperature before dissipating the rest to the ambient air via a ram air heat-exchanger (HEX).The secondary cooling loop is used to condition the oxygen/air and hydrogen supply to the fuel cell at the required operating conditions.By utilizing ambient air, the air needs to be compressed to increase its operating pressure.This compression leads to an excess in heat from the increase in air temperature.Similarly to the primary loop, the excess heat is used to finish the hydrogen heating and the rest is evacuated via another ram air HEX.An initial variation of this architecture utilizing solely the compressed air heat to evaporate and preheat the hydrogen, has been previously studied but not deemed operational at lower altitudes.At first a low temperature (LT) PEMFC at 70°C will be studied, cooled with a 40% potassium formate coolant (KFO).These choices are justified by the low temperature PEMFC's maturity and the KFO's large temperature range between freezing and boiling points.The complete list of initial assumptions for the TMS and components' efficiencies is given in [2].

Sizing and fuel mass penalty
The TMS is sized by first computing the thermal requirements associated with cooling the fuel cell for the defined case study.This includes the coolant mass flows for both cooling loops, as well as the HEX requirements.Once, these requirements are defined, the HEXs are iteratively sized to ensure the correct heat transfer area.The other components are modeled as in [2].The TMS component models do not include the power and water management of the fuel cell system, neither the humidifier for the air supply system.The total drag, mass and power required by the TMS can be calculated, as well as an additional kerosene fuel mass penalty ∆M f term to consider the effect of adding such a subsystem on an aircraft.This is explained in more detail in [5].

Case study
The Daher Kodiak 900 will serve as the reference aircraft and will be retrofitted to accomodate the hybrid propulsion system with the same maximum take-off mass (MTOM).The TMS will be sized at ISA conditions with respect to its cruise phase design parameters shown in Table 1.A hybridization factor of 33% will be considered, amounting to 220.7 kW of power for the fuel cell to provide.Retrofitting the aircraft involves a reduction in the reference propulsion system, which is done here by a proportional scaling law.For the addition of the fuel cell stack and balance of plants (BoP) components (excluding the TMS) a specific power of 1 kW/kg is considered [6].Furthermore, the space allocation for the integration of the hybrid system, is not considered at this stage.

Initial TMS optimization
For the optimization of the TMS, the objective function is given in Equation 1, with M T M S the mass of the TMS in itself and ∆M f the fuel mass penalty.The design variables are the coolant and ambient air mass flows in each of the cooling loops.
Once the TMS is optimized, a feasibility study implemented on the Kodiak 900 is conducted.Moreover, it may be interesting to analyze the different trade-offs of the TMS.For example by reducing the drag of the system through the ambient air mass flow and inlet capture area, the heat exchangers will increase in size, and consequently mass, to compensate for the lower cooling capability of the fluid.A Pareto front can provide useful information on these trade-offs and one representing the mass vs. drag of the system is presented in Section 4.

Sensitivity analysis
Prior to starting the sensitivity analysis, the variables that can be assumed to be kept constant during this analysis are identified.These include the core geometry of the HEX, as well as the ram air inlet type.In addition, all components not directly pertaining to cooling design choices will remain constant throughout the analysis.These include generic component efficiencies and types, such as the pumps, valves, compressors, etc.For the variables chosen in the sensitivity analysis given in Table 2, their values will be randomly varied simultaneously to see the effect on the TMS and any possible correlations.These variables include the coolant type of the TMS, the fuel cell efficiency and stack temperature, ISA temperature difference, coolant tank and evaporator / HEX material, and the HEX design effectiveness.If the variables are generally uncorrelated, then the local one at a time (OAT) method can be used for the sensitivity analysis where one variable at a time will vary and the others will be kept constant.

Final TMS optimization
With the findings of the sensitivity analysis, a final optimization is performed with improved TMS design choices and these results can be compared to the initial optimization.

Initial TMS optimization
The fuel cell system and TMS characteristics are shown in Table 3.A breakdown of the TMS drag, mass, hydrogen fuel mass, power required, the fuel mass penalty, as well as the mass of the fuel cell stack and other BoP components is given.The TMS and stack / BoP weighs a total estimated 550 kg, this does not include the mass of the hydrogen fuel, its tank and the fuel mass penalty.With these optimized results, a feasibility study is conducted.The fuel, operational empty mass (OEM) and payload mass breakdown for the reference aircraft and hybrid aircraft is shown in Table 4.By recalculating the fuel weight and OEM, the resulting hybrid aircraft payload is reduced to 440 kg.Assuming an average mass of 85 kg per passenger, this payload accounts for 5 people onboard.The reference aircraft and hybrid aircraft initial optimization OEM breakdowns are given in Figures 2 and 3 respectively.For the hybrid aircraft, the additional TMS mass and FC stack and other BoP components are highlighted.In addition, by running the optimization with different design variable ranges, a Pareto front showing the trade off between the TMS drag and mass can be obtained, as shown in Figure 4.This does not include the mass of the hydrogen fuel or tank.The contour plot in Figure 5 is created from a surrogate model (R 2 ≈ 1.00) of the fuel mass penalty in terms of the TMS drag and mass and the initial optimization point with minimum fuel mass penalty observed is highlighted.Overall, it can be seen that several TMS configurations are possible while having similar fuel mass penalties.nature of the TMS model, it might not reflect the actual relationship between the design variables and output.Therefore, Kendall's and Spearman's correlation coefficients were computed to test non-linear and monotonic relationships respectively.In all tested cases, there does not appear to be strong direct correlations between the design variables themselves, thus the OAT sensitivity analysis method can be used.

Sensitivity analysis A Pearson's pairwise correlation matrix between the design variables and output is shown in
For the OAT analysis, the coolant type and FC stack temperatures results will be given as examples.The coolant type is varied and the impacts on the objective function are given in Figure 7.As is shown, there are some significant differences between the options portrayed.The coolant with the least total mass is the water and not the initial assumption of KFO.This is due to it having the highest specific heat capacity.For the FC stack temperature analysis in Figure 8, the higher temperature result in lower total mass as there is a greater temperature difference between the coolant and stack and less coolant is required.

Final TMS optimization
Incorporating the findings of the example OAT sensitivity analysis, a final optimization is run with a LT-PEMFC of temperature 80°C and water as the coolant.The final optimized fuel cell system and TMS characteristics are shown in Table 5, where it can be seen notably that there is a decrease in the TMS mass and fuel mass penalty.To account for the reduced mass, the  final design variables are shown in Table 6.Lower coolant and atmospheric air mass flows will reduce the heat exchanger sizes, drag produced by the air inlets, required pump power, etc.The corresponding payload is now 586 kg and results in an extra passenger onboard compared to the initial study.

Conclusions
In conclusion, a hybridization of such aircraft at 33% and the given design point is feasible with a reduction in payload.Furthermore, the FC stack and TMS design choices can have a significant impact on the aircraft as shown with the coolant and fuel cell stack temperature examples and should be implemented in the aircraft design loops.Limitations of the work includes the oversimplified models used to scale down the conventional propulsion system mass and approximately estimate the FC stack and other BoP components masses.In addition, the safety and redundancy of installing such system needs to be studied.Furthermore, as mentioned there is no consideration for the physical integration of implementing the FC stack, TMS and associated components.Future work will focus on developing a methodology to consider the volume allocation, performing a sensitivity analysis on the hybridization factor and also incorporating a high-temperature (HT) PEMFC.

Figure 1 :
Figure 1: Liquid-cooling thermal management system for fuel cells.

Figure 2 :
Figure 2: OEM breakdown for the reference aircraft.

Figure 3 :
Figure 3: OEM breakdown for the initial optimization of the hybrid aircraft.

Figure 7 :Figure 8 :
Figure 7: TMS total mass vs. coolant type with KFO as initial parameter.

Table 2 :
[7]iables to be studied in the OAT method where EG is a 50% water/ethylene glycol mix, PG a 50% water/propylene glycol mix.Fluid characeristics are obtained in[7].

Table 3 :
Initial optimization FC system and TMS characteristics.

Table 4 :
Mass breakdown between reference and hybrid aircraft, with an MTOM of 3625 kg.

Table 5 :
Final optimization FC system and TMS characteristics.

Table 6 :
Design variables values in initial and final optimizations