Introduction

Fuel cells powered by liquid hydrogen are a promising propulsion technology to reduce environmentally harmful emissions such as CO2 and NOx because the only emission from a fuel cell is its product water. Low-temperature proton-exchange membrane fuel cells (LT-PEMFCs) are considered suitable for aviation application, as they provide good efficiency (40 % to 60 %) and a reliable operation due to a high technology readiness level compared to other fuel cell types (Kazula et al., 2023). Manufacturers claim a high specific stack power of 1.5 kW∕kg (ZeroAvia Inc, 2023).

Besides control, transient behavior and degradation the thermal management is one of the key challenges which have to be overcome by engineers to establish fuel cells as a competitive propulsion technology in aviation. In contrast to gas turbines or piston engines, fuel cells release only 10% to 20% of their waste heat by their exhaust flow (Berger, 2009). With the exception of a small system power up to approximately 3 kW, fuel cell stacks must be cooled directly with a cooling fluid (Barbir, 2013). As the efficiency of the fuel cell system is about 50%, approximately the same amount of power the fuel cell provides as electric power has to be released by the thermal management. From a heat exchange perspective, the low operating temperature range of 60 °C to 90 °C of a LT-PEMFC poses an additional challenge. For hot day conditions (ISA+25) the available temperature difference between the hot cooling fluid and the ambient air is only about 20 K to 40 K.

The large amount of waste heat and the small temperature difference result in large heat exchanger surfaces. The additional drag and weight of the heat exchanger is particularly disadvantageous for an aviation application. The challenge of cooling a fuel cell is also apparent in flying testbeds, which are equipped with large cooling air ducts that contain the heat exchangers. To either reduce the necessary heat exchanger surface by increasing the cooling air velocity or to compensate the loss of momentum of the cooling air flow, an additional cooling fan can be installed. However, it is important to note that such a cooling fan requires a significant amount of electric power, which must also be provided by the fuel cell.

Early publications on the design of fuel cell systems for aircraft propulsion have often simplified the thermal management to a function of the fuel cell power in terms of mass and power demand (Moffitt et al., 2006; Thirkell et al., 2017; Kadyk et al., 2018, 2019; Nicolay et al., 2021; Palladino et al., 2021). The additional drag due to the heat exchanger frontal area was completely neglected. Recent publications have focused on the detailed design of the thermal management system and evaluated its impact on the overall propulsion system. Kožulović (2020) has designed a heat exchanger for a mid-size airliner based on a counterflow liquid-air heat exchanger with corrugated fins. The heat exchanger is installed within a cowling with a diffusor and nozzle but without an additional fan. His analysis states that the propulsion power requirement increases by 27.3% during cruise phase due to the heat exchanger. The design is most efficient when reducing the air velocity prior to the heat exchanger to 15% of the freestream velocity. A subsequent study by Juschus (2021) is based on this approach. Hintermayr and Kazula (2023) optimized the air duct inlet of a 300 kW fuel cell system in terms of performance and sizing. They also considered an additional cooling fan to compensate the total pressure loss of the inlet section. In their studies, the fan had a power of about 20% to 95% of the fuel cell power, showing a strong dependency on the total pressure ratios of the inlet section and the heat exchanger. Hartmann et al. (2022) designed a thermal management for a fuel cell system that uses the liquid hydrogen as a heat sink. The remaining waste heat has to be dissipated by a heat exchanger with a fan. The used design approach does not rely on physics-based calculations to size the thermal management. Instead, scaling factors for the mass and the power demand by evaluating existing studies on aircraft heat exchangers have been used. Kellermann et al. (2021) designed a thermal management system using ram air and an additional cooling fan. The authors demonstrated that a fan can reduce the fuel burn for a turboelectric propulsion system and thereby increase its overall efficiency. Especially under hot conditions, the fan is beneficial in terms of reducing mass, drag, and fuel consumption. An architecture without a fan would need to be significantly larger to meet the same requirements. Eissele et al. (2023) used the results of Kellermann et al. (2021) to develop a scaling factor for the heat exchanger drag. They applied this scaling factor to a fuel cell propulsion system as part of an overall aircraft design but neglected the additional power demand.

Overall, the thermal management causes additional drag, weight and electric power demand in a relevant order of magnitude. The performance of the propulsion system is directly affected by the design of the heat exchanger and the cooling fan. Therefore, the thermal management design cannot be covered by simple scaling factors in the performance calculation of a fuel cell propulsion system but must be integrated into the design process.

This paper is structured as follows: The methodology for calculating the performance is presented first. This includes the definition of the cycle processes, the development of the applied component models and the design algorithm to solve the design problem. In the next section we conduct a design exploration study for typical design variables to demonstrate the benefits of the novel performance calculation approach. Finally, the results of the study for a reference propulsion system are presented and discussed.

Methodology

First, we give a brief introduction to the propulsion system under study. Then, we examine the cycle process of the propeller and the thermal management. By combining the energy conversion and the cycle processes, we derive general equations for the performance calculation of a fuel cell propulsion system. Similar to conventional propulsion systems we define thrust, efficiency and specific fuel consumption. To calculate the thermodynamic processes between the separate stations as well as the energy conversion of the fuel cell powertrain we develop component models. The methodology section concludes with a description of the iterative design calculation process that uses the component models to solve the cycle processes.

Performance calculation

This section describes the performance calculation of the fuel cell propulsion system. We first examine the energy conversion in the powertrain system from the hydrogen tank to the shaft power of the propeller and the resulting conversion losses. Next, we analyze the propeller and the thermal management by interpreting them as two independent cycle processes. The stations for each process are defined, and the state changes are sketched in the h,s-diagram. The derivation of thrust, power and efficiency is based on this diagram, following the conventional aircraft performance calculation method explained by Jeschke et al. (2024). The cycle processes and energy conversion by the powertrain are then merged to the overall propulsion system.

Fuel cell powertrain

The fuel cell powertrain is shown in Figure 1. A cryogenic tank supplies hydrogen with the power PH2 to the LT-PEMFC. The thermal insulation and vaporization of liquid hydrogen is not the subject of this publication. The fuel cell converts the electrochemically stored energy of the hydrogen into the electric power PFCS and provides it as direct current (DC). To decouple the fuel cell and the further electric components in terms of their operation voltage, a DC/DC converter transforms the fuel cell output power to the DC link voltage. The inverter transforms the DC link voltage into a three-phase alternating current (AC) for the electric motor. The electric motor converts the AC voltage power PIV into the mechanical shaft power PEM. A gearbox between the electric motor and the propeller enables an additional degree of freedom regarding the rotational speed of the electric motor. This allows the use of a high-speed and therefore power-dense electric motor. Finally, the propeller is driven by the mechanical shaft power PP.

Figure 1.

Architecture of a fuel cell propulsion system for aerospace application.

https://journal.gpps.global/f/fulltexts/213543/JGPPS-00257-2024-01.01_min.jpg

In addition to the powertrain path, the DC bus also supplies power to additional loads. This includes the power required by the cooling air fan, denoted as PC in this study. A battery is typically connected via a DC/DC converter and serves as a buffer to meet dynamic power requirements. However, since this study only examines stationary operating points, the battery is not considered in the following investigations. Following Figure 1, we establish the power balance around the DC bus by applying the efficiencies of the electrical components. The consumers are placed on the left-hand side of the equation, and the source is placed on the right-hand side to relate the power to the DC bus

(1)
PPηIVηEMηGB+PCηDCηEM,C=PH2ηFCSηDC.

During the numerous energy conversions, losses depending on the component efficiencies η occur. These losses are summarized in the power loss of the energy conversion system Q˙loss, which is transferred to the thermal management

(2)
Q˙loss=Q˙in,TM.

Cycle process of the propeller

Figure 2 shows the stations of the propeller cycle process (Figure 2a) and the thermodynamic state changes in the h,s-diagram (Figure 2b). In station 0, the propeller draws in air from the surrounding environment. The inlet flow tube contracts in front of the propeller, transitioning isentropically to station 12. Between stations 12 and 13, the propeller performs the specific propeller work aP, resulting in the propeller power

Figure 2.

Cycle process of the propeller of an aircraft fuel cell propulsion system. (a) Stations and (b) Thermodynamic changes in h,s-diagram.

https://journal.gpps.global/f/fulltexts/213543/JGPPS-00257-2024-01.02_min.jpg
(3)
PP=m˙PaP=m˙P(ht13−ht12)

with the propeller mass flow m˙P. The resulting increase in total pressure is expressed by the propeller total pressure ratio

(4)
πP=π12,13=pt13pt12.

However, the supplied power is not isentropically converted into a total pressure increase. Therefore, we define the isentropic propeller efficiency

(5)
ηP,s=ht13s−ht12ht13−ht12=ht13s−ht12aP.

Similarly, the isentropic nozzle efficiency ηN,s is defined for the change of state from 13 to 19. The usable output power of the cycle process is defined as

(6)
Pout,P=m˙P(c02−c1922),

which leads us to the thermal efficiency of the propeller with Equation 3

(7)
ηth,P=−Pout,PPP=−c02−c1922(ht13−ht12).

As the static pressures upstream and downstream of the propeller are equal (p0=p9), the propeller thrust is calculated by

(8)
FP=m˙P(c19−c0),

which leads us to the propulsion power

(9)
PF,P=FPc0.

With the equations above the cycle process of the propeller is completely defined.

Cycle process of the thermal management

Figure 3 presents the stations of the thermal management cycle process (Figure 3a) and the thermodynamic state changes in the h,s-diagram (Figure 3b). The illustration shows the schematic cowling of the heat exchanger and fan. The cowling is designed for low aerodynamic drag, as described by Drela (1996). From station 0 to 2 the ambient air is decelerated in a diffusor to increase the static pressure in front of the heat exchanger. The total pressure losses due to the expansion are considered by

Figure 3.

Cycle process of the thermal management of an aircraft fuel cell propulsion system. (a) Stations and (b) Thermodynamic changes in h,s-diagram.

https://journal.gpps.global/f/fulltexts/213543/JGPPS-00257-2024-01.03_min.jpg
(10)
π0,2=pt2pt0.

In the heat exchanger from station 2 to 3 the power loss of the energy conversion system Equation 2 is transferred to the cooling air mass flow m˙TM, leading to an increase in enthalpy

(11)
ht3−ht2=qin,TM=Q˙in,TMm˙TM.

Due to inner wall friction as well as expansion and compression of the cooling air, a total pressure loss occurs across the heat exchanger

(12)
Δpt2,3=pt3−pt2

that is a function of the geometry, fin design, air flow and fluid properties. To decouple the cross sections of the heat exchanger and the cooling fan, a transition duct from station 3 to 4 with the total pressure ratio

(13)
πt3,4=pt4pt3.

is assumed. Between station 4 and 5 a cooling fan with the total pressure ratio

(14)
πC=πt4,5=pt5pt4

and the isentropic efficiency ηC,s, see Equation 5, performs the specific cooling fan work aC, resulting in the cooling fan power

(15)
PC=m˙TMaC=m˙TM(ht5−ht4).

Figure 3b demonstrates that the air is perfectly compressed or expanded to ambient pressure (p0=p9) in an ideal nozzle from station 5 to 9, resulting in a loss of total pressure

(16)
πt5,9=pt9pt5.

For this cycle process, we define the power input and output. The usable output power of the cycle process is defined as

(17)
Pout,TM=m˙TM(c02−c922).

As there is a difference in velocity of the air between the inlet and outlet, the cooling air mass flow generates a force

(18)
FTM,int=m˙TM(c9−c0).

The cowling which covers heat exchanger and cooling fan creates an additional drag FTM,ext. As this force may account for a significant portion of the propeller’s thrust Equation 8 it must be included in the performance calculation. For the calculation of this force, refer to the section on component models and Equation 44. With the thrust of the thermal management

(19)
FTM=FTM,int+FTM,ext

we calculate its propulsion power

(20)
PF,TM=FTMc0.

Overall propulsion system

The energy conversion processes of the powertrain and propeller, along with the thermal management cycle, have been fully defined. The next step is to aggregate the equations of the three subsystems to calculate the power, thrust, and efficiency of the entire fuel cell propulsion system. The overall usable output power is calculated with Equations 6 and 17

(21)
Pout=Pout,P+Pout,TM=m˙P(c02−c1922)+m˙TM(c02−c922).

With Equation 21 and the supplied hydrogen power PH2, that we will derive later Equation 34, we get the thermal efficiency of the overall powertrain

(22)
ηth=−PoutPH2.

The total thrust of the fuel cell propulsion system consists of Equations 8 and 19

(23)
F=FP+FTM.

We also define the specific fuel consumption

(24)
SFC=m˙H2F

with the hydrogen mass flow m˙H2, which we introduce later Equation 33. The overall propulsion power is defined as sum of Equations 9 and 20

(25)
PF=PF,P+PF,TM=Fc0,

with which we calculate the propulsion efficiency

(26)
ηp=PF−Pout=21+c19c0+21+c9c0

and finally the overall efficiency of propulsion system

(27)
ηo=ηthηp=PFPH2.

Component models

Next, we develop component models which describe the energy conversion and thermodynamic changes of state.

Fuel cell system

As shown in the Figure 1, the fuel cell provides the net electrical power PFCS. A comprehensive model of the auxiliary electric consumers of the fuel cell like the air compressor, as described by Schmelcher and Häßy (2022), is omitted. Instead, the power demand is expressed via the factor faux. The gross power to be generated is then calculated as

(28)
PFCS,gr=PFCS1−faux.

The fuel cell system consists of multiple stacks, which in turn consist of multiple cells. The operating point of a cell is defined by its current density

(29)
icell=IcellAact,cell,

which relates the current Icell to the active area Aact,cell of a cell. The cell voltage Ucell is calculated by subtracting all losses from the theoretical voltage under standard conditions Uth0. It is assumed that the stack is operated at a constant pressure of pstack=3bar. The calculation of Ucell has been implemented according to Barbir (2013). The resulting polarization curve then provides Ucell as a function of icell and with

(30)
Pcell=UcellIcell=UcellicellAact,cell

we also get the electric power generated by a single cell. With Equation 28 we calculate the number of cells needed

(31)
ncell=PFCS,grPcell=PFCS1−fauxUcellicellAact,cell.

Having defined the operating point and the design of the fuel cell we now calculate the hydrogen consumption of the fuel cell system. The reaction equation of the fuel cell provides the charge number of hydrogen as zH2=2, see Appendix A. With the Faraday’s law, the Faraday constant F and the molar mass MH2 of hydrogen we get the stoichiometric hydrogen mass flow per cell

(32)
m˙H2,cell=IcellzH2FMH2

and for the fuel cell system with the number of cells from Equation 31

(33)
m˙H2=ncellm˙H2,cell.

The formula to calculate the hydrogen mass flow is derived in Appendix B. In real operation, more hydrogen is supplied than required for the stoichiometric ratio. In this study, we assume the use of a fuel cell with hydrogen recirculation. Any excess hydrogen that is not consumed is not considered in the fuel calculation as it remains within the system. With Equation 33 and the lower heating value of hydrogen LHVH2 we are able to calculate the supplied hydrogen power

(34)
PH2=m˙H2LHVH2

and the efficiency of the fuel cell system as

(35)
ηFCS=PFCSPH2=PFCSm˙H2LHVH2.

The fuel cell system’s total power loss is determined by

(36)
Q˙loss,FCS=PH2−PFCS.

A part of the supplied fuel power is released into the environment as waste heat via the exhaust gas flow expressed by the factor floss,ext=5%to10% (Berger, 2009). This reduces the amount of waste heat that actually needs to be cooled by the thermal management to

(37)
Q˙TM,FCS=Q˙loss,FCS−PH2floss,ext.

The mass of the fuel cell system

(38)
mFCS=pFCSPFCS

is calculated with the specific power pFCS which is a function of icell.

Heat exchanger

The heat exchanger is illustrated in Figure 3a from station 2 to 3. We assume a plate-fin heat exchanger with offset fins. This is a crossflow heat exchanger with thin fins attached to its plates to increase the heat exchange surface to the passing air. The fins do not run in a longitudinal direction through the entire depth of the heat exchanger. Instead, they end after a certain distance and are offset to the side. This design interrupts the boundary layer formation of the passing cooling air and thus increases the heat transfer. Depending on the heat exchanger’s design, the offsets may be repeated multiple times. This heat exchanger type is appropriate for transferring heat from liquid to gas. It is distinguished by a large heat transfer surface area per unit volume and high heat transfer coefficients at Reynolds numbers ranging from Re=500 to 10,000. Plate-fin heat exchangers with offset fins are commonly used in mobile applications, such as passenger vehicles and airplanes, due to their high specific power resulting from the thin-walled channel and fin structure (Shah and Sekulić, 2003). The heat flux transferred by the heat exchanger is calculated using the ε−NTU method described by Kays and London (2018) and Kakaç et al. (2012). The actually transferred heat power

(39)
Q˙TM,in=εQ˙max

is defined as the product of the heat exchanger effectiveness ε and the theoretical maximum transferable heat power Q˙max that depends on the fluid mass flows, their heat capacities and temperatures. ε is calculated using a correlation that depends on the flow arrangement and the number of transfer units NTU

(40)
NTU=UACmin.

Cmin is the minimum capacity heat rate. The product of the overall heat transfer coefficient U and the exchange surface A is broken down into three partial heat transfers

(41)
1UA=1ηahaAa⏟air \ side+δwλwAw⏟wall+1hfAf⏟coolant\ side.

A is the surface area and h is the heat transfer coefficient of the respective side. ηa is the surface efficiency of the air side with offset fins. Heat conduction in the walls is also taken into account. To calculate ηa, A, and h, respectively, we use correlations for plate-fin heat exchangers with offset fins and rectangular channels published by Manglik and Bergles (1995) and Shah and Sekulić (2003).

The pressure loss across the heat exchanger defined in Equation 12 is comprised as

(42)
Δp2,3=ΔpHEX=Δpin+Δpcore−Δpout,

consisting of three parts for the inflow into the heat exchanger, the friction in the core and the outflow according to Shah and Sekulić (2003). The core loss accounts for the largest share

(43)
Δpcore=G22ρ2(2(ρ2ρ3−1)+fdHEXrhydρ2ρ23¯)

significantly influenced by the Fanning friction factor f. The friction factor for offset fin heat exchangers is a function of Re and the fin geometry as stated by Manglik and Bergles (1995). The design calculation maintains constant geometric ratios of the fins, which have been calibrated using a real aviation heat exchanger (Rotax, 2021). The heat exchanger is scaled only via its cross-sectional area AHEX, with a constant height-to-side ratio, and its depth dHEX. The geometric constants of the fin, AHEX and dHEX, are also used to determine the wet mass of the heat exchanger mHEX, assuming aluminum as the material. The mass flow of the coolant is proportionally adjusted based on m˙TM using a constant ratio. The coolant side of the thermal management is not taken into account in the power balance, as the power demand is negligible compared to the air side (Kellermann et al., 2021).

Cowling

The external drag of the cowling is calculated using a drag coefficient cD,TM based on the shape and installation of the cowling, the effective frontal area of the heat exchanger AHEX,fr, and ambient air data (ρ0,c0)

(44)
FTM,ext=−12cD,TMAHEX,frρ0c02.

Thrust is considered positive when the force acts in the direction of flight. Therefore, it is necessary to include a negative sign. Hoerner (1965) gives typical values for drag coefficients of belly-type radiator installations and therefore we define cD,TM=0.06. The wall thickness of the cowling is neglected and the frontal area of the heat exchanger is assumed to be the frontal area of the cowling. To reduce the frontal area and, because of Equation 44, also FTM,ext, the heat exchanger is installed under an inclination angle αHEX as shown in Figure 3a. This installation reduces the effective frontal area to

(45)
AHEX,fr=sin⁡(αHEX)AHEX

Since the air always flows perpendicular to AHEX, the cooling air mass flow must be deflected by the angle αHEX before and after the heat exchanger. The discharge coefficient to calculate the total pressure loss of the inlet and outlet deflection is estimated according to Bohl and Elmendorf (2013).

Further propulsion system components

This study does not focus on the powertrain components, such as the electric motor, inverter, and DC/DC converter. Therefore, constant efficiencies and power densities are assumed in the design process. The data utilized in this study are presented in Appendix F. The mass of the gearbox is calculated using a correlation from Brown et al. (2005). A correlation by Chapman et al. (2020) is used for the mass of the cooling fan. The propeller mass was calculated using a correlation from LTH (2022).

Design calculation process

The flowchart of the design process is shown in Appendix C. It is important to note that some of the variables to be calculated are interdependent. For instance, the power of the cooling air fan PC is influenced by m˙TM, see Equation 15, which affects PFCS and thus Q˙TM,FCS. Q˙TM,FCS in turn has an influence on the required m˙TM. Therefore, the problem must be solved iteratively. At the start of the process, the requirements, design variables, boundary conditions, and estimated initial values are established as input data. This data is employed for the initial design calculations of the propeller from stations 0 to 19 and the thermal management system from stations 0 to 9. Subsequently, the remaining powertrain components and the fuel cell system are designed. Next, the actual power loss Q˙loss, which was initially estimated, and the total thrust of the propulsion system F are calculated. The cooling air mass flow m˙TM is iterated until the power loss of the propulsion system Q˙loss is equal to the heat output transferred by the heat exchanger Q˙TM,in according to Equation 2. To fairly compare designs and sensitivities, the resulting total thrust F must be constant for all parameter combinations. Because the design of the thermal management affects F, see Equation 23, the design calculation is embedded in another loop that iteratively sizes the propeller until the required thrust F is achieved.

Results and discussion

The design methodology described in this paper is applied to a reference propulsion system. The sensitivities in relation to the thermal management and the overall propulsion system are then discussed by varying three exemplary design variables.

Reference propulsion system

A small four-seater aircraft is used as reference application. Table 1 summarizes the design requirements and environmental conditions for the selected design point during cruise flight. The requirements are derived from typical general aviation aircraft and are otherwise arbitrarily defined. We assume here, that the fuel cell system is designed for the cruise operation point, while a battery provides additional power for take-off and climb. An exemplary design that fulfills the requirements of Table 1 is presented in Table 2. The data utilized for the design of the fuel cell are listed in Appendix D. The resulting polarization curve is presented in Appendix E. The remaining parameters for the powertrain components, which were assumed to be constant for the reference design and the design exploration study, are listed in Appendix F. We now apply the design methodology described and the reference values from Table 2 to the performance requirements and boundary conditions during cruise flight from Table 1. Thereby we obtain the performance data of our reference design as shown in Table 3 that serves as a reference for the following studies.

Table 1.

Performance requirements and boundary conditions during cruise flight.

ParameterValue
Thrust F1,000 N
Altitude ALT3,000 m
Ambient conditionISA + 15 K
Airspeed c085 m∕s
Table 2.

Design variables and their reference values.

ParameterValue
Cooling fan total pressure ratio πC1.04
Heat exchanger cross section AHEX0.90 m2
Heat exchanger depth dHEX0.15 m
Heat exchanger inclination angle αHEX20°
Fuel cell current density icell1.40 A∕cm2
Table 3.

Performance data of the reference propulsion system.

ParameterValue
Overall efficiency ηo22.5%
Propulsive efficiency ηp91.3%
Thermal efficiency ηth24.6%
Specific fuel consumption SFC3.15 g∕(kNs)
Cooling fan power PC22.8 kW
Total mass m196.6 kg
Thermal management mass mTM78.5 kg

Design space exploration

By exemplarily varying the design variables πC, AHEX, and icell, the sensitivities on the thermal management and the resulting deviations of the performance data from the reference design (Table 3) are discussed.

Total pressure ratio of the cooling fan πC

The results of varying πC are shown in Figure 4 for the thermal management and in Figure 5 for the overall system. Since the external thermal management drag FTM,ext is not a function of πC according to Equation 44, it remains constant. Due to losses in the cooling air duct and heat exchanger FTM,int is negative for πC<1.04. As πC increases, a higher total pressure is available downstream of the fan to be converted into thrust in the nozzle. Initially, this only compensates for the internal total pressure loss. At high values of πC>1.05, FTM,ext is fully compensated. From this total pressure ratio and above, the thermal management generates positive thrust FTM. It is evident that both FTM,int and FTM,ext contribute significantly to the required thrust of F=1,000N (Table 1). Therefore, it is justified to include the thermal management in the performance calculation.

Figure 4.

Plot of m˙TM, PC, FTM,ext, FTM,ext and mTM over πC; values of the variables in the left legend are displayed on the left ordinate axes and vice versa.

https://journal.gpps.global/f/fulltexts/213543/JGPPS-00257-2024-01.04_min.jpg
Figure 5.

Plot of the relative change from the reference design (Table 3) of ηo, ηp, ηth, SFC and m over πC.

https://journal.gpps.global/f/fulltexts/213543/JGPPS-00257-2024-01.05_min.jpg

Contrary to expectations, m˙TM does not increase as πC increases since the thrust nozzle is controlled to only pass the mass flow actually required for cooling. Therefore, m˙TM depends on the efficiency of the propulsion system, which is influenced by the πC, as we will discuss later. As m˙TM is almost constant, PC increases proportionally to πC. The thermal management system’s mass mTM increases only slightly with an increasing πC due to the larger fan because the unchanged heat exchanger accounts for the majority of mTM.

Figure 5 illustrates that ηp is highly dependent on πC. Initially, increasing πC to 1.04 leads to a rapid increase in ηp due to a significant reduction in the absolute value of FTM,int, as shown in Figure 4. This reduction causes a significant decrease in the additional thrust required by the propeller to compensate for drag, leading to a smaller dimensioned powertrain and thermal management. As ηth remains nearly constant, ηo follows the same trend as ηp. A fuel cell propulsion system without a cooling air fan (πC=1.00) would have an ηo which is 18.2% lower than the reference design. The fan’s increasing power PC leads to a snowball effect starting at πC=1.04: the fuel cell’s output power and loss both increase. The increased cooling power required results in a higher m˙TM (Figure 4), which in turn increases PC and because of Equation 1 also PFCS. Consequently, ηo decreases beyond a pressure ratio of πC=1.04. The specific fuel consumption SFC is inversely related to ηo. Therefore, it increases for small or large values of πC and also has a minimum at the reference design point.

As πC increases, the total mass m initially decreases. Figure 4 demonstrates that the fan compensates for the drag of the thermal management, resulting in smaller dimensions of the powertrain components and the fuel cell as already discussed. A fuel cell propulsion system without a fan would have a 17.3% higher total mass compared to the reference design. At πC=1.06, m reaches its minimum approximately 0.5% below the reference. Further increase in πC requires more power for the fan PC (see Figure 4), which must be provided by the fuel cell. Therefore, the mass of the fuel cell increases again from the reference design. This leads to a compensation for the mass reduction of the powertrain, resulting in a net increase of m from πC=1.06.

Cross section area of the heat exchanger AHEX

The variation of the heat exchanger area in Figure 6 starts at AHEX=0.6m2. This is the smallest possible value at which a sufficient cooling power is achieved. A small AHEX requires a higher m˙TM and PC to transfer the necessary cooling capacity due to high Reynolds numbers and a smaller heat transfer surface. As AHEX increases, the required m˙TM and PC decrease. From Equation 44 it is evident that FTM,ext increases as AHEX increases. mTM is mainly determined by the heat exchanger, which results in an almost linear increase despite the decreasing fan mass.

Figure 6.

Plot of m˙TM, PC, FTM,ext, FTM,ext and mTM over AHEX; values of the variables in the left legend are displayed on the left ordinate axes and vice versa.

https://journal.gpps.global/f/fulltexts/213543/JGPPS-00257-2024-01.06_min.jpg

To compensate for the increasing FTM,ext, the propeller must provide more thrust. While the power of the propeller increases with larger heat exchanger surfaces, the power demand for the thermal management increases with smaller heat exchangers. This leads to an optimum of ηo and total mass m as shown in Figure 7. The lowest possible m at AHEX=0.7m2 is achieved with a smaller heat exchanger surface compared to the optimum ηo at AHEX=1.1m2. Compared to the reference design, a thermal management system with the smallest possible heat exchanger has a 4.5% lower mass but a 10.3% lower ηo. The optimum ηo for our study is achieved at AHEX=1.1m2. For this heat exchanger size ηo is 0.7% higher and m is 7.2% higher compared to the reference design.

Figure 7.

Plot of the relative change from the reference design (Table 3) of ηo, ηp, ηth, SFC and m over AHEX.

https://journal.gpps.global/f/fulltexts/213543/JGPPS-00257-2024-01.07_min.jpg

Current density of the fuel cell system icell

The cell current density icell is varied to analyze its influence on the thermal management (Figure 8) and the overall system (Figure 9). The polarization curve of the designed fuel cell (Appendix E) indicates that the cell power Pcell initially increases with increasing icell, accompanied by an increase in losses. Therefore, a low icell corresponds to an efficient cell, while a high icell corresponds to a power-dense cell. The necessary m˙TM must also increase to achieve a sufficiently high cooling capacity. This results in an increase in PC and mTM (Figure 8), despite the heat exchanger accounting for a large portion of the thermal management mass. At a high current density (icell>1.4A/cm2), concentration polarization losses increase significantly, leading to a decrease in both efficiency and Pcell. As the current density increases, so does the thermal power transferred to the cooling air, resulting in an increase in FTM,int, which is known as the Meredith effect. However, at values of icell>1.4A/cm2, the nozzle must be opened wider to allow for the necessary m˙, which in turn leads to a lower c9 and a reduction in thrust as described by Equation 18. Increasing the load on the cell from 0.6 A∕cm2 to 1.4 A∕cm2 results in an increase in cooling air mass flow m˙TM by a factor of 2. The drag resistance FTM,ext remains constant due to the unchanged heat exchanger geometry (Figure 8).

Figure 8.

Plot of m˙TM, PC, FTM,ext, FTM,ext and mTM over icell; values of the variables in the left legend are displayed on the left ordinate axes and vice versa.

https://journal.gpps.global/f/fulltexts/213543/JGPPS-00257-2024-01.08_min.jpg
Figure 9.

Plot of the relative change from the reference design (Table 3) of ηo, ηp, ηth, SFC and m over icell.

https://journal.gpps.global/f/fulltexts/213543/JGPPS-00257-2024-01.09_min.jpg

Figure 9 illustrates that ηth decreases as icell increases due to the rising losses in the fuel cell. ηp remains almost constant, resulting in ηo following the same dependency as ηth on icell. Additionally, m decreases initially as the cell’s power density becomes higher. The sharp loss of power at high current densities, see Appendix E, must be compensated by a larger sized fuel cell system, so that m increases again compared to the reference design (Figure 9). Therefore, the cell should only be designed for icell<1.4A/cm2, as a higher icell leads to increased m and decreased ηo. Compared to the reference, a 33.8% higher ηo can be achieved with icell=0.8A/cm2 at an increase of 8.1% in m.

Conclusion

This paper illustrates the integration of the thermal management for a fuel cell propulsion system into the engine performance calculation. The thermal management air path is treated as a separate cycle, similar to conventional engines. Together with the propeller cycle process and the energy conversion from hydrogen to mechanical propeller power, key performance data of the engine performance calculation for the fuel cell powertrain are thus derived. Physically scalable models have been developed for the powertrain and the thermal management components. These models describe the changes in state of the cycle processes and the conversion of energy as a function of their design variables.

The capabilities of the presented method are demonstrated by a design space exploration. First, the fuel cell powertrain system and the thermal management are designed for a small aircraft as a reference application. The reference aircraft engine has an overall efficiency of ηo=22.5% and a mass of m=196.6kg, of which 78.5kg are accounted for by the thermal management system. Three exemplary design variables — cooling fan pressure ratio πC, heat exchanger surface AHEX and fuel cell current density icell — are varied. The sensitivities in relation to the thermal management and the overall aircraft engine are discussed. The thermal management causes high drag due to internal total pressure losses and external pressure drag of the cowling. To address this issue, the reference design includes an additional cooling air fan located behind the heat exchanger with a total pressure ratio πC=1.04. It was shown that the design of the thermal management has a major influence on the performance data of the propulsion system. A design lacking a fan (πC=1.00) has a lower overall efficiency ηo by 18.2% and higher total mass m by 17.3%. An optimal AHEX in terms of efficiency has also been identified. This is caused by increasing fan power PC for small heat exchangers and increasing propeller power PP to overcome the drag of a large heat exchanger. By varying icell, it was shown how an efficient cell influences the thermal management design compared to a power-dense cell. Increasing the load on the cell from 0.6 A∕cm2 to 1.4 A∕cm2 results in a two times higher cooling air mass flow m˙TM. With regard to the overall propulsion system, it is stated that at lower current densities, a trade-off between increasing efficiency and mass compared to the reference design must be considered, e.g. a 33.8% higher ηo versus a 8.1% higher m at icell=0.8A/cm2.

The presented method for calculating the performance of fuel cell thermal management systems will be used to analyze key components in more detail in the future. The heat exchanger has a significant impact on the drag, mass, and power demand of the thermal management system. While this study considered a conventional heat exchanger, future enhancements of the method will incorporate new heat exchanger geometries to assess their impact on engine performance. The same applies to the detailed design of the cooling air fan, the air intake, and two-phase cooling concepts. Further potential lies in the coupling of thermal management and hydrogen vaporization. The impact of the thermal management on overall propulsion performance is expected to be even more significant at higher airspeeds. We will therefore extend the method to larger aircraft for up to 50 passengers. The methodology presented thus enables the evaluation of innovative thermal management technologies for fuel cells in aviation.