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CEAS Aeronautical Journal

https://doi.org/10.1007/s13272-023-00699-2

ORIGINAL PAPER

A method foranefficiency andweight‑optimised preliminary design

ofahydrogen‑powered fuel cell‑based hybrid‑electric propulsion

system foraviation purposes

MücahitAkkaya1 · NicolaiNeumann1· DieterPeitsch1

Received: 27 February 2023 / Revised: 13 September 2023 / Accepted: 7 November 2023

Abstract

There is a worldwide effort to advance the usage of zero-emission propulsion systems for aircraft. Due to their high ther-

modynamic efficiency and the fact that they produce no

CO2

and

NOx

emissions, hydrogen-powered fuel cells are becoming

increasingly popular for aviation purposes. However, fuel cell systems suffer from lower power density and higher cooling

requirements when compared to conventional propulsion systems. Harnessing the high potential requires an optimised design

of the whole propulsion system and its heat management system. This paper aims to present a method for the preliminary

design and dimensioning of a fuel cell-based hybrid-electric propulsion system, which respects the limits of the heat manage-

ment system and is weight and efficiency optimised. Thermodynamic models of the whole propulsion system are a crucial

element to enable further investigations. Such a model has been developed, which is suitable for unsteady simulations of

the propulsion and the heat management system performance of a short-range four-seater aircraft. A parameter study of

the design parameters has been performed to display their impact on the system mass, the overall efficiency and the total

hydrogen consumption. These results enable the identification of an overall optimised configuration. The study indicates

that fuel cell-only configurations with an oversized fuel cell stack are beneficial for the analysed aircraft and flight mission.

Keywords Hybrid electric aircraft· PEM fuel cell· Preliminary design· Optimisation Performance

List of symbols

A Area,

𝛼

Angle of attack,

◦

ALT

Altitudem

C Heat capacity rate,

W∕K

C Battery capacity,J

Drag coefficient–

Lift coefficient–

Power coefficient,–

Specific heat capacity,

J∕(kg K)

Thrust coefficient–

D Diameter,

D Drag force,

E Nernst voltage,

𝜖

Effectiveness,–

𝜂

Efficiency,%

𝛾

Flight path angle,

◦



Enthalpy change,

h Specific enthalpy,

J∕kg

h Heat transfer coefficient,

W∕(m2K)

Lower heating value,

J∕kg

I Current,

J Advance ratio–

𝜅

Ratio of specific heats–

𝜆

Stoichiometric factor–

L Lift force,

M Mass,

ΔmH2

Hydrogen consumption,

M Mach number of the aircraft–

m

Mass flow,

kg∕s

mred

Reduced mass flow,

ms√K

N Number of fuel cells in the stack–

N Shaft speed,

1∕s

NTU

Number of transfer units–

P Power

p Pressure

(Total) pressure ratio–

q Dynamic pressure,

* Mücahit Akkaya

m.akka[email protected]

1 Chair forAero Engines, Institute ofAeronautics

andAstronautics, Technische Universität Berlin,

Marchstraße 12-14, 10587Berlin, Germany

M.Akkaya et al.

1 3



Heat flow,

𝜌

Density,

kg∕m3

T Temperature,

t Time,

𝜃

Pitch angle,

◦

T Thrust,

TOM

Take-off mass,

U Heat transfer coefficient,

W∕(m2K)

v Velocity

m∕s

v

Rate of acceleration,

m∕s3

W Weight,

Subscript

Air

amb

Ambient

BAT

Battery

Compressor

Chemical

col

Coolant

Electric

est

Estimated

Fluid

H∕H2

Hydrogen

At component inlet

max

Maximum

min

Minimum

O∕O2

Oxygen

out

At component outlet

Overall

Prop

Propulsive

ref

Reference

req

Required

Surface

Shaft

stoich

Stoichiometric

Sys

System

util.

Utilised

Wing

x,z Referring to coordinate axis

Abbreviations

ACARE

Advisory Council for Aeronautics Research and

Inovation in Europe

ERDF

European Regional Development Fund

Fuel cell (stack)

HEX

Heat exchanger

IBB

Business Development Bank of the Federal

State of Berlin

PEM

Proton exchange membrane

1 Introduction

Sustainability is an important challenge that industries

across all sectors must address in order to reduce their

environmental footprint and thus their impact on the cli-

mate. The contribution of aviation to anthropogenic cli-

mate change is currently estimated at around 5% [1], which

is trending upwards as air passenger traffic grows at a rate

of 4% per year [2]. In the Flight Path 2050 document [3],

the Advisory Council for Aeronautics Research and Inno-

vation in Europe (ACARE) set a number of targets for

reducing pollutant emissions. For example,

CO2

emissions

are to be reduced by 75% per passenger-kilometre by 2050

compared to an aircraft in 2000. Research and develop-

ment and the continuous replacement of older aircraft are

leading to an increase in efficiency and thus a reduction

in specific fuel consumption, resulting in lower pollut-

ant emissions per passenger-kilometre. However, several

recent projections indicate that efficiency improvements

through further improvements in known technologies will

not meet the goals of the Flight Path 2050 document [4,

5]. Therefore, it is necessary to explore the use of alterna-

tive, more radical approaches that will enable to meet the

requirements.

The use of electric propulsion promises not only to pro-

vide energy conversion at a higher efficiency, but also to

directly eliminate

CO2

and

NOx

emissions during flight.

One possibility is the use of batteries as a power source.

Batteries have a major advantage due to their very high

efficiency of 90% [6], as their losses are low and less waste

heat is generated. However, batteries have a relatively low

gravimetric energy and power density, which would result

in a very high battery weight if used alone. In particular,

the low energy density has a strong impact on the range,

since range is directly correlated with available energy.

Another challenge with batteries as the main power source

is that they must either be replaced or recharged between

flights, which would result in very long turnaround times

given the current state of the art. An alternative electri-

cal power source are fuel cells. Hydrogen-powered pro-

ton exchange membrane (PEM) fuel cells, for example,

have a higher gravimetric power density than batteries,

and their tanks can be filled with either cryogenic or pres-

surised hydrogen in a relatively short time between flights.

Although fuel cells are relatively efficient compared to gas

turbines or internal combustion engines, their efficiency

is lower than batteries, resulting in higher losses and

thus more waste heat. Since fuel cells do not have a high

exhaust mass flow, as i.e. gas turbines, the heat generated

must be removed by a heat management system.

Hybridisation approaches that combine batteries and

fuel cells can create synergy effects. For example, one

A method foranefficiency andweight‑optimised preliminary design ofahydrogen‑powered fuel…

1 3

advantage is that batteries support the fuel cell stack in

high-performance phases, resulting in a lower required

maximum power of the fuel cell stack. Kadyk etal. [7]

conducted a design study of a hybrid propulsion unit for

an Airbus A320. They demonstrate that hybridisation ben-

efits depend on mission range. For a mid-range application

hybrid designs with a reduced fuel cell size yield a reduced

fuel consumption.

Alternatively, the fuel cell system could be kept constant

and would hence be oversized. Oversizing the fuel cell sys-

tem could be a valuable design strategy. There are at least

two strategies to benefit from an oversized fuel cell system

as proposed and described in the work of Kasim etal. [8].

Assuming a power requirement of

150 kW

provided by four

50 kW

stacks. The fuel cell stacks could be operated in a

daisy-chained mode. That means that during each flight,

one of the four fuel cell stacks is rotationally deactivated,

which preserves the lifetime of all four fuel cell stacks and

eliminates degradation without having to change the fuel cell

stacks between two flights. Alternatively, in order to achieve

the required power, the power output of each stack could be

reduced. In that case, the stacks are operated at part load,

which leads to a higher efficiency. Kasim etal. [8] estimate a

fuel burn reduction by 10% for a typical Cessna 208 Caravan

and a

350 km

flight mission.

Kadyk etal. [9] also stress that the fuel cell stack needs

to be designed in the context of the whole energy system.

They suggest that the fuel cell stack should always be at least

slightly oversized to avoid the efficiency penalty close to

maximum fuel cell stack power. Moreover, depending on the

application, further oversizing, i.e. investing in a larger and

heavier fuel cell stack in order to gain a more efficient pro-

cess, might be beneficial. They provide a performance cost-

benefit curve for a propulsion system for an Airbus A320.

According to them, the ratio of energy-to-power determines

the optimal oversize of the stack.

In [9], however, the aircraft was powered only by fuel

cells. The combination of fuel cells and a battery greatly

expands the design space. For example, the use of a stronger

battery increases the weight of the battery and thus the sys-

tem weight. On the other hand, a stronger battery leads to a

lower required maximum power of the fuel cell stack, so that

either the fuel cell stack can be shrunk, reducing the weight

of the fuel cell stack, or the fuel cell stack can remain at con-

stant dimensions but operated at a lower power, increasing

its efficiency. The consideration of both effects is of great

importance to find an efficiency and weight-optimised pro-

pulsion system design for an aircraft.

This paper presents a model based method for the effi-

ciency and weight-optimised sizing of a hydrogen-powered

fuel cell-based hybrid-electric aircraft respecting the limits

of a set heat management system. The process of this design

method is shown as flowchart in Fig.1. For this purpose, a

model of a four-seater hybrid-electric aircraft was created.

This model is then used to simulate the transient behaviour

of the propulsion system and its heat management system

during a typical flight mission. The simulations are con-

ducted for a number of different fuel cell stack and battery

configurations. Key parameters such as maximum stack

temperature, overall efficiency, total hydrogen consump-

tion, and system mass of the fuel cell stack and battery are

compared. A “sweet spot area” where an optimised overall

design would be possible is identified.

The field of fuel cell-based hybrid-electric aircraft pro-

pulsion systems is relatively new and thus there is a lack of

published data that can be utilised for the design. Hence, to

be able to build a model for the proposed design method,

besides published data, assumptions have to be made based

on industrial and academic experience. For that, an air-

craft manufacturer that researches hybrid-electric aircraft

was consulted. However, as this paper mainly describes the

method itself, as well as having preliminary design char-

acter, the proposed assumptions can be replaced if more

accurate assumptions can be made or more detailed data is

available.

2 Methods andmodels

This section covers the models and methods of this paper.

First, the aircraft, its propulsion system and its heat manage-

ment system will be described. Subsequently, the models for

the preliminary design methodology are introduced.

2.1 Concept aircraft

A preliminary design method of the propulsion system for a

hybrid-electric short-range four-seater aircraft shall be pre-

sented. It is assumed that the take-off mass, excluding the

battery and the fuel cell stack, remains at

2000 kg

independ-

ent from the actual power battery and fuel cell stack masses.

Fig. 1 Flowchart of the preliminary design methodology

M.Akkaya et al.

1 3

Thus, the impact of mass changes of individual components

on the aircraft’s structure is neglected. Furthermore, the

wing area

is estimated at

18 m2

. The assumptions of the

aircraft’s take-off mass as well as its wing area are in line

with aircraft of the same aircraft class [10–12]. Exemplary

diagrams for the lift and drag polars were used, provided by

an aircraft manufacturer.

2.2 Propulsion system

The architecture of the aircraft’s propulsion system is

depicted in Fig.2 for one side of the aircraft, as the propul-

sion system is completely symmetric. The required thrust

is generated by one propeller on each side of the aircraft,

which is driven by an electric motor. The electric motor is

supplied with electric power from the fuel cell stack during

lower power levels, or by the fuel cell stack and the bat-

tery during higher power levels. Additionally, as the battery

discharges during high power levels, it is charged during

lower power levels such as cruise. The propulsion system

also requires a compressor, as the fuel cell stack is operated

at a higher pressure than ambient pressure. Hence, a part of

the generated electric power is supplied to the compressor.

The power demand of secondary subsystems, i.e. coolant

pumps or aircraft electronics has been neglected, as their

power demand is very small relative to the primary compo-

nents of the propulsion system.

2.3 Heat management system

The heat management is one of the most crucial aspects

regarding the utilisation of fuel cells, therefore a proper heat

management system must be designed [13]. In this paper, the

fuel cell stack is actively cooled with a heat exchanger (FC-

HEX), using a liquid coolant, as demonstrated schematically

in Fig.3 for one side of the aircraft. After cooling the fuel

cell stack, coolant is pumped into a second heat exchanger,

in which it is cooled by air. The air intake is integrated into

the nacelle downstream of the propeller increasing the heat

exchanger’s driving pressure difference. The coolant is then

returned into the coolant tank, which supplies the coolant

fluid for the whole heat management cycle. As the fuel cell

stack also has a minimum temperature limit, a valve down-

stream of the FC-HEX allows to recirculate a portion of the

coolant. Thus, the coolant temperature at the entrance of the

FC-HEX increases, facilitating a faster warm up.

Although, other components such as the battery or the

electric motor also generate heat and must therefore be

cooled, they will not be further discussed within this paper.

The cooling requirement of the electric motor is relatively

independent of the investigated design parameters, as it

mainly depends on the motor efficiency. The battery how-

ever, is only used for a relatively short time and operates

with a very high efficiency. Therefore, relatively low waste

heat is generated for a relatively short time. It is therefore

decided, that the battery cooling is not within the scope of

this work, as the focus is on the fuel cell stack cooling. How-

ever, for future investigations, the heat management model

can be extended to also consider the cooling of further com-

ponents, i.e. the battery and the electric motor.

2.4 Models

The presented design method is based on an aircraft model

that simulates the transient behaviour of the aircraft’s pro-

pulsion system and heat management system. The general

structure of the aircraft model for the preliminary design

method is represented in Fig.4.

As shown, the model is split into four interacting sec-

tions. The first section, called atmosphere model, deter-

mines the atmospheric properties during flight. As the

temperature and pressure change with altitude, the atmos-

pheric properties must be determined at each time step.

The second section is the thrust demand model, which

determines the thrust demand at each time step. The

Fig. 2 Flowchart of the aircraft’s propulsion system (one side)

HEX

Tank

PEM Fuel cell stack

FC-HEX

Air

Propeller

Air

Fig. 3 Flowchart of the aircraft’s heat management system (one side)

A method foranefficiency andweight‑optimised preliminary design ofahydrogen‑powered fuel…

1 3

required thrust is computed for a constant flight mission

taking into account the aircraft weight, which in turn

depends on the sizes of the battery and the fuel cell stack.

The ambient air properties and the required thrust are

inputs into the two main sections: the performance model

which simulates the behaviour of all primary components

of the propulsion system and the heat management model

which simulates the behaviour of the heat management

system. On one hand, the heat management model requires

the generated heat, which results from the performance

model as it is able to determine the occurring losses. Fur-

thermore, the heat management model requires inputs

describing the propeller behaviour, as the air intake for the

air heat exchanger sits downstream of the propeller. On the

other hand, the performance of the fuel cell stack depends

on its temperature which is computed in the heat manage-

ment model. Therefore, the performance model and the

heat management model are in a continuous exchange of

information. The performance model also determines the

consumed hydrogen, which defines the change in mass

during flight.

Due to these interactions, the aircraft model is of a

highly iterative nature. Furthermore, due to transient

operation phases and due to its dynamic characteristics,

the model consists of a vast number of mathematical equa-

tions containing several differentials. Therefore, Matlab/

Simulink is used to set up and combine the models into the

overall aircraft model, as shown in Fig.4.

2.4.1 Thrust demand model

The flight mission defines the acceleration as well as all

velocity components of the aircraft. Furthermore, the alti-

tude of the aircraft is set within the flight mission. This

model determines the thrust demand to satisfy the require-

ments set by the flight mission. For that, the mass of the

aircraft is used as an input at each time step of the flight

mission.

To determine the required thrust, the aircraft dynamics

and therefore all forces that act on the aircraft during flight

must be considered. All assumptions, as well as approxima-

tions and definitions regarding aircraft dynamics are based

on Hull [14] and Yechout etal. [15]. The aircraft is viewed

as a point-mass, in which all forces are applied to the air-

craft’s center of gravity. Furthermore, the earth is approxi-

mated as a flat, non-rotating, inertial reference frame. It is

also assumed that the atmosphere does not move relative

to the earth. Additionally, only longitudinal and vertical

movements are considered, neglecting any lateral move-

ment. Therefore, the position of the aircraft is defined by

its x and z coordinates, as well as its pitch angle

𝜃

, which

describes the deviation of the aircraft’s axis to its reference

coordinate system. A second angle that can be defined is the

flight path angle

𝛾

, which describes the movement of the

aircraft within the coordinate system, defined in Eq.(1). A

windless operation is assumed, therefore, the angle of attack

𝛼

is defined as the deviation between the flight path angle

and the pitch angle.

During flight, the main forces are the weight W, the thrust

T, the drag D and the lift L as shown in Fig.5. The drag

force acts tangentially to the flight path angle, whilst the lift

(1)

tan

(𝛾)=

z

x

Fig. 4 Flowchart of the aircraft model

Fig. 5 Coordinate system for the force equations

M.Akkaya et al.

1 3

applies vertically. Assuming, that the propeller and the air-

craft are aligned, the thrust is always tangential to the pitch

angle. The weight always applies directly towards the nega-

tive z-axis of the reference system. The force equation can

be defined for each axis, which results in the Eqs.(2) and (3).

The aircraft velocity v, as well as the accelerations

vx

and

vz

are predefined by the flight mission. The mass is defined

by the configuration and the consumed hydrogen. The lift

coefficient

can be determined for the angle of attack

𝛼

the aircraft’s lift polar, whilst the drag coefficient

can be

determined by using the aircraft’s drag polar. As the angle

of attack directly correlates with the pitch angle, the only

two independent variables in this system of two equations

(Eqs.2, 3) are the pitch angle and the thrust. Therefore, the

system of equations can be solved iteratively to determine

the thrust demand.

2.4.2 Performance model

The propulsion system, as shown in Fig.2, consists of several

main components, which need to be modelled individually.

The modelling of the main components such as the fuel cell

stack, the battery, the compressor, the electric motor and the

propeller will be presented in this section.

Propeller The propeller model uses a propeller map, which

delivers the thrust coefficient

for a combination of advance

ratio

and power coefficient

(see Eqs.4, 5) [16, 17]. The

advance ratio and the power coefficient can be determined by

the shaft speed N, the propeller diameter D, the aircraft veloc-

ity v and the shaft power

PShaf t

, which are all inputs of the

propeller model.

The advance ratio and the power coefficient are then used to

interpolate the thrust coefficient by the propeller map, which

enables to determinate the generated thrust T by Eq.(6) [16,

17]. A PID-Controller is used to vary the shaft power, until

the thrust of the propeller model matches the required thrust

of the thrust demand model.

The thrust can then be used to determine the outlet veloc-

ity of the propeller

vout

by Eq.(7) [16], which enables to

(2)

⋅

vx=T

⋅

cos(𝜃)−L

⋅

sin(𝛾)−D

⋅

cos(𝛾)

(3)

⋅

vz=T

⋅

sin(𝜃)+L

⋅

cos(𝛾)−D

⋅

sin(𝛾)−W

(4)

D⋅N

(5)

Shaft

𝜌

⋅

3⋅

(6)

=CT⋅

𝜌

⋅N2

⋅D

compute the dynamic pressure at the outlet of the propeller

qout

by Eq.(8). It is assumed, that the dynamic pressure can

be utilised as the available pressure difference

Δp

for the air

flow in the air heat exchanger, which sits downstream of the

propeller.

Electric motor Electric motors are well known to operate at

a relatively constant efficiency over a broad operating enve-

lope. Hence, in this model, the electric motor efficiency

𝜂EM

is set constant at 95% [6], which is a conservative approach,

as modern electric motors operate at even higher efficien-

cies. The generated shaft power

PShaf t

of the electric motor

can therefore be determined by Eq.(9) based on the supplied

electric power

PEl

Battery Batteries are mostly described by two parameters,

the total capacity and the maximal electric power. Analogue

to the electric motor, the battery efficiency is assumed to

be constant, as batteries also operate at relatively constant

efficiencies. The battery efficiency

𝜂BAT

is assumed to be

90% [6] during both discharging and charging. During bat-

tery charging, the supplied electric power

PEl

is converted

into chemical power

Pch

as in Eq.(10). During discharge,

the chemical power is converted into electric power as in

Eq.(11).

The change in the capacity

ΔC

over a period of time

Δt

can

therefore be determined by Eq.(12).

Fuel cell stack As the fuel cell stack is the main power

source, its behaviour is modelled in more detail. The ther-

modynamic maximum output voltage E, that a single fuel

cell can deliver, can be determined in volts by the Nernst

equation, which is shown in Eq.(13) [18–20], consisting

of the fuel cell temperature

TFC

, and the partial pressures of

hydrogen

PH2

and oxygen

PO2

(7)

out =

√

T⋅8

𝜌

⋅

𝜋

⋅

2+v

(8)

out =

𝜌

out

(9)

PShaft =𝜂EM

⋅

PEl

(10)

Pch =𝜂BAT

⋅

PEl

(11)

ch =

𝜂

BAT

(12)

∫t+Δt

Pch d

A method foranefficiency andweight‑optimised preliminary design ofahydrogen‑powered fuel…

1 3

The real cell voltage V is implemented by a polarisation

curve, which depicts the cell voltage as a function of cur-

rent. The polarisation curve [21] describes the cell behaviour

for a defined cell temperature and pressure. The compressor

enables the fuel cell to be operated at exactly that pressure

for which the polarisation curve is displayed. The impact of

a temperature variation on the operation behaviour is not

implemented. However, the heat management system aims

to operate the fuel cell stack at a relatively narrow tempera-

ture range.

The power that is generated can therefore be determined for

a single cell by multiplying the cell voltage V and the current

I. In order to determine the total electric power of the fuel cell

stack

PStack

, the power of a single cell must be factorised by the

number of cells of the fuel cell stack N, resulting in Eq.(14).

The difference between ideal and real fuel cell performance

is due to losses, which are removed in terms of heat. Hence,

the heat for a single cell is determined by the difference

between the Nernst voltage E and the cell real voltage V

multiplied by the current I. This result is then multiplied

by the number of fuel cells in the stack to determine the

total heat generated in the fuel cell stack



QStack

, as shown

in Eq.(15) [13].

In order to determine the total hydrogen consumption, the

rate of hydrogen reacting in the fuel cell stack needs to be

obtained. For that, the current can be divided by the Fara-

day constant F, which results in the flow rate of electrons

per fuel cell. In order to get the flow rate of electrons of the

whole stack



Ne−

, this must be multiplied by the number of

fuel cells in the stack. Each reacting hydrogen atom supplies

one electron. Therefore, the flow rate of electrons equals

the reaction rate of hydrogen atoms



. This can be used to

determine the mass flow rate of hydrogen

mH2

, that is used

for the reaction, by multiplying the molar mass of hydrogen

, as demonstrated in Eq.(17) [22]. Assuming that no

hydrogen diffuses without being involved in the reaction, the

hydrogen consumption rate equals the mass flow rate of the

reacting hydrogen. By integrating this mass flow rate over

the whole flight, the total hydrogen consumption

ΔmH2

can

be determined, as shown in Eq.(18).

(13)

=1.229 −0.85 ⋅10

−3

⋅

(

TFC −298.15

)

+4.3085 ⋅10−5

⋅TFC ⋅

[

ln(PH2)+1

⋅ln(PO2)

]

(14)

PStack =N

⋅

(15)



QStack

=N⋅(E−V)⋅

(16)



N−

⋅

Analogue to that, the required air flow can be determined.

Two hydrogen atoms react with one oxygen atom. Therefore,

the reaction rate of oxygen atoms equals half of the reaction

rate of hydrogen atoms. This rate can then be multiplied

with the molar mass of oxygen

, in order to determine

the mass flow rate of oxygen that reacts in the fuel cell stack

mO2

. For dry air, oxygen only makes up 23.01% [23] of the

mass, thus the air flow that would be needed for a stoichi-

ometric reaction

mair,stoich

can be determined by Eq.(20).

However, this air flow would only satisfy if every oxygen

atom also reacts. As this is not to be assumed, surplus of

air needs to be supplied to satisfy the needs of the fuel cell

stack. In the literature, varying stoichiometric factors

𝜆

can

be found, which is assumed as 2 [20] for this paper. Hence,

the compressor needs to supply an air flow which is deter-

mined by Eq.(21) [22].

Compressor The compressor provides air to the fuel cell

stack at its required pressure. In this case, the air is com-

pressed to a pressure of 2 bar. The required power for the

compressor

can be determined by Eq.(22), in which

𝜂C

is the isentropic compressor efficiency,

is the specific heat

capacity of air,

is the total pressure ratio of the compres-

sor, and

𝜅

is the ratio of specific heats.

The total pressure ratio of the compressor is defined as the

ratio between the total pressure at the outlet of the compres-

sor to the total pressure at its inlet. When the outlet veloc-

ity of the compressor is neglected, assuming that the air

passes through the fuel cell slowly to enable a reaction, the

total pressure at the outlet can be set to the required operat-

ing pressure of 2 bar. Assuming a total pressure loss of 2%

within the air intake, the total pressure at the inlet of the

compressor can be determined by the total pressure at the

inlet of the air intake. Hence, the required total pressure ratio

(17)



NH⋅MH=

⋅

(18)

mH2

=∫

End

Start

N⋅I⋅MH

(19)



⋅MO=

N⋅I⋅MO

F⋅2

(20)



air,stoich =

m

0.2301

N⋅I⋅MO

F⋅2⋅0.2301

(21)



air =𝜆⋅mair,stoich =

⋅

O⋅

𝜆

F⋅2⋅0.2301

(22)

𝜂

⋅cp⋅mair ⋅

(

𝜅−1

)

M.Akkaya et al.

1 3

is determined by Eq.(23), in which

pamb

is the ambient static

pressure and M is the Mach number describing the aircraft

velocity.

2.4.3 Heat management model

The heat management system is depicted in Fig.3. The mod-

els of the fuel cell stack, the fuel cell stack heat exchanger,

the air heat exchanger and the tank are introduced next.

Fuel cell stack The fuel cell stack is modelled as a thermal

mass, which is characterised by its specific heat capacity

its mass

MFC

and its temperature

TFC

. To determine the tem-

perature of the fuel cell stack during the flight, the energy

balance considering all heat flows must be used. As men-

tioned earlier, heat is generated within the fuel cell stack,

which is represented by



QStack

. Furthermore, heat is removed

by the fuel cell heat exchanger denoted



QFC−HEX

. Other heat

transfer mechanisms such as radiation and heat transfer to

surrounding air have been neglected. Also, energy associ-

ated with incoming and outgoing fluids has been ignored.

Thus, the energy balance can be written as shown in Eq.(24)

[13, 22]:

Hence, to determine the temperature at each time step, the

temperature gradient

dTFC

must be determined. Therefore,

the heat which dissipates through the fuel cell stack heat

exchanger



QFC−HEX

is required.

Fuel cell stack heat exchanger The fuel cell stack heat

exchanger is modelled as a solid wall along which coolant is

passed. A general approach to describe the forced convective

heat flow between a surface and a fluid is shown in Eq.(25),

in which h is the heat transfer coefficient,

AHeat

is the heat

transfer area,

is the temperature of the surface area whilst

describes the temperature of the fluid [22, 24].

One main factor of the heat flow is the temperature differ-

ence, which is not constant over the whole heat transfer area,

hence Eq.(25) cannot be applied directly. Therefore, adjust-

ments have to take place in order to determine the heat flow

within the heat exchanger. It is assumed, that the heat trans-

fer coefficient is constant over the whole heat exchanger.

Furthermore, it is assumed that the surface temperature,

describing the fuel cell stack, is homogeneous whilst the

coolant temperature changes between the entrance and outlet

(23)

Π= 2 bar

0.98 ⋅

[

pamb ⋅

(

1+𝜅−1

2M2

)

𝜅

𝜅−1

]

(24)

p⋅MFC ⋅

=Σ



QStack −



FC−HEX

(25)



=h⋅A

Heat

⋅

(

−T

of the heat exchanger. The total heat transfer area

Aheat

split into infinitesimal small sections in which the coolant

temperature is assumed constant. Therefore, the Eq.(25) can

be applied for each section individually. However, the fluid

temperature of a section is determined by the heat flow and

the fluid temperature in the previous section. This method

leads to a differential equation, which when solved results

in Eq.(26). This equation can also be derived by utilising

the definition of the log mean temperature difference, as

the same approach is applied [25]. The Eq.(26) enables

to determine the coolant temperature at the FC-HEX outlet

Tcol,out

with the fuel cell stack temperature

TFC

, the coolant

flow

mcol

, the specific heat capacity of the coolant

and the

coolant temperature at the FC-HEX inlet

Tcol,in

. The total

heat flow in the FC-HEX



QFC−HEX

can hence be determined

by Eq.(27).

Air heat exchanger The heat is removed from the heat

management system by the air heat exchanger. The heat

exchanger is modelled as a cross heat exchanger. Data for

individual operating points was provided by the manufac-

turer, in order to describe the behaviour of the heat exchanger

correctly. The data points are used to derive characteristic

curves, which were cast into a model.

The air heat exchanger is modelled with the

𝜖

-NTU

method. First, the air mass flow must be determined.

For that, the characteristic curve in Fig.6 is used, which

describes the reduced air mass flow of the heat exchanger

mred

as a function with respect to the available pressure

ratio

. The values in Fig.6 are normalised by referring

(26)

Tcol,out

−

(

−T

col,in)

⋅e

−

⋅

AHeat

mcol⋅c

(27)



QFC−HEX

⋅m

col

⋅

(

col,out

−T

col,in)

Fig. 6 Characteristic curve describing the reduced air mass flow

mred

with respect to the available pressure ratio

A method foranefficiency andweight‑optimised preliminary design ofahydrogen‑powered fuel…

1 3

each absolute value to predefined reference values

mred,ref

and

Πref

The available pressure ratio is defined as shown in

Eq.(28) by the ambient pressure p and the available pres-

sure difference

Δp

at the propeller outlet. However, the

reduced air mass flow of the heat exchanger is defined by

the absolute air mass flow

mair

, the ambient pressure p and

the air temperature at outlet of the heat exchanger

Tair,out

To initiate the iteration, a proper outlet air temperature is

guessed to determine the air mass flow.

Once the air flow is determined, the heat capacity rate C

can be calculated for the coolant flow and the air flow, as

product of the mass flow

m

and the specific heat capacity

. The lower value defines the minimum heat capacity rate

CMin

and the higher value defines the maximum heat capac-

ity rate

CMax

. The air flow and the coolant flow are used for

the heat exchanger map in Fig.7, which is derived from a

set of characteristic curves. Each curve describes the product

of the heat transfer coefficient U and the heat transfer area A

over the air flow for a specific coolant flow. A linear inter-

polation is applied for deviating coolant flows. To normalise

the values in the heat exchanger map in Fig.7, each value is

divided by its corresponding reference value.

The product

U⋅A

can then be used to determine the

unitless characteristic value

NTU

, as shown in Eq.(30)

[24, 26]. Additionally, the second characteristic value,

generally referred as the heat capacity ratio

, can be

determined by Eq.(31) [24, 26].

(28)

Π= p

p+Δp

(29)



red =

mair ⋅

√

air,out

p+Δp

These two characteristic values can be applied to the cor-

relation in Eq.(32), which gives the effectiveness

𝜖

. The

minimum heat capacity rate and the inlet temperature of the

air and the coolant are used to determine the maximum heat

flow



QMax

as shown in Eq.(33) [24].

Once the effectiveness and the maximum heat flow are

determined, they can be used to calculate the real heat flow



QHEX

, as shown in Eq.(34). As the calculation is done based

on an estimation for the air outlet temperature

Tair,out

, the

determined heat flow can be used to calculate a new outlet

temperature, which starts the next iteration step, until the

temperature converges.

Tank The coolant within the tank is modelled as a homoge-

neous thermal mass, with the specific heat capacity of the

coolant

, the total tank capacity M, and the temperature of

the coolant within the tank

TTank

. Analogous to the fuel cell

stack, the energy balance is needed to determine the cool-

ant temperature. Therefore, the enthalpy of the incoming

and outgoing coolant must be considered. For the tank, it

is approximated that at each time step no mass is accumu-

lated. Hence, incoming and outgoing mass flow are identi-

cal. Additionally, it is assumed that the temperature of the

outgoing coolant flow equals the temperature of the coolant

within the tank. Therefore, the resulting energy balance is

shown in Eq.(35).

2.5 Model validation suggestions

The validation of a model, that simulates the operational

behaviour of a multi-component system and thus the interac-

tion of different components is equally challenging as it is

important for its reliability. In order to have a representative

model however, the most relevant components are modelled

based on the physical characterisation of the component’s

behaviour. Hence, it is assumed that the model accuracy is

sufficient and will thus be used for the proposed method in

(30)

NTU = U

⋅

Min

(31)

Min

CMax

(32)

𝜖=1−e

C−1

⋅NTU0.22

⋅

(

e−Cr⋅NTU0.78

−1

)

(33)



QMax

Min

⋅

(

col,in

−T

air,in)

(34)



QHEX

=𝜖⋅



Max

(35)

p⋅M⋅

Tank

=mcol ⋅cp⋅(Tin −TTank

)

Fig. 7 Heat exchanger map

M.Akkaya et al.

1 3

this paper, as the validation is out of the scope of this work.

However, suggestions regarding validation will be provided

for further investigations.

To validate the model for a certain configuration, all com-

ponents are needed. These components need to be utilised

for individual tests on component level, to derive the com-

ponent characteristics, which need to be implemented into

the model. For these tests, it is important to investigate the

component behaviour in its entire operational range. Addi-

tionally, besides steady-state tests, for some components,

it might be beneficial to add transient tests, to be able to

describe the component’s dynamic behaviour, i.e. limits for

acceleration and deceleration or its thermal inertia.

After providing the model with all derived characteris-

tics, either the whole system, or a subgroup of interacting

components can be built into a test-bed which needs suf-

ficient instrumentation. A test with a defined power curve

shall be performed on the test-bed and a simulation is to

be performed with the model at the same power settings

and the same ambient condition as in the test. Characteristic

parameters such as temperatures, pressures and electrical

as well as mechanical power, which are measured in the

test-bed, shall be compared to the simulation results. If the

difference between simulation and test is significant for cer-

tain parameters, the data must be used to derive physical

explanations for this error, which can then be quantified and

implemented into the model. Once there are no significant

errors, the model can be considered validated.

3 Parameter study

The presented model simulates the behaviour of the propul-

sion system and the heat management system over a defined

flight mission for different fuel cell stack and battery sizes.

This section gives insights of the performed parameter

studies.

3.1 Flight mission

A flight mission is defined with a cruise phase at an altitude

8000 ft

, a cruise velocity of

58.9 m∕s

and a cruise duration

. That yields a total mission range of

700 km

Figure8 shows the flight mission schematically with its

altitude over time, as well as the required electric power

PEl,req

for the propulsion system and the electric power

which is supplied by the fuel cell stack

PFC

. The deviation of

the required electric power and the supplied electric power

by the fuel cell stack defines the battery power. When the

required power is larger than the supplied electric power of

the fuel cell stack, the battery is discharged. When the sup-

plied power of the fuel cell stack is larger i.e. during cruise,

the surplus of power is utilised to charge the battery. Once

the battery is fully charged, the fuel cell stack load reduces

to match the required power of the propulsion system. As

the fuel cell stack can be oversized, the maximum available

power of the fuel cell stack

PFC,Max

does not have to match

its maximum utilised power.

3.2 Parameter variation

The parameter study varies the fuel cell stack and the bat-

tery. The dimension of each individual fuel cell of the stack

is assumed to remain constant. Therefore, only the number

of cells N within the stack is varied. An increasing number

of cells within the stack leads to an increasing maximum

power of the fuel cell stack. The P-Stack of the manufacturer

PowerCell is used as a reference. The datasheet [21] delivers

a polarisation curve, describing the cell behaviour. Further-

more, the maximum power, weight and geometry data are

available for several configurations with different fuel cell

counts in the stack. This data is used to derive a linear cor-

relation that describes the maximum power of the fuel cell

stack in kilowatts as a function with respect to the number

of fuel cells N, as shown in Eq.(36).

Furthermore, the data suggests that the fuel cell stack mass

does not increase exactly linearly with power. Therefore, the

two largest configurations are used as a reference, in order

to derive the correlation in Eq.(37) for the approximated

fuel cell stack mass

MFC

in kilogrammes with respect to the

number of fuel cells. These two configurations are within

the range required for this study.

(36)

PFC,Max =0.2772

⋅

N−1.0815

(37)

MFC =0.0556

⋅

N+16.722

Fig. 8 Power distribution during the flight mission

A method foranefficiency andweight‑optimised preliminary design ofahydrogen‑powered fuel…

1 3

Changes in fuel cell count are also considered in the fuel

cell stack heat exchanger model. It is assumed, that the heat

transfer coefficient h is constant, whilst the heat transfer area

AHeat

increases linearly with the number of fuel cells N. By

utilising an estimated value for one case, provided by an

aircraft manufacturer, the linear correlation in Eq.(38) was

derived, which describes the product

⋅

AHeat

in kilowatts

per kelvin with respect to the number of fuel cells.

By these approximations, all relevant characteristic param-

eters within the model are a function of the number of fuel

cells within the stack. Hence, the first parameter of the study

is the number of fuel cells N. The second component that

needs to be defined is the battery. In general, to approximate

the battery mass, the energy density or the power density

is utilised. For that, the battery mass is determined by the

required power and the power density and by the required

energy and the energy density. Whatever is more demanding

defines the mass of the required battery. For this paper, the

energy density of batteries is assumed to be

0.8 kW h∕kg

[7], whereas a power density of

0.5 kW h∕kg

is assumed.

However, neither the maximum required battery power, nor

the required total energy of the battery is defined before

the simulation is performed. Therefore, the battery power

or energy is not used as second parameter for the parameter

study. Rather, the maximum utilised power of the fuel cell

stack is used as the second parameter of this study. Based

on this power, a maximum power of the battery is estimated.

Initial simulations with the model presented in Sect.2.4

show, that the required peak power is about

170 kW

per side

of the aircraft. Hence, for the initial run, the battery mass is

determined by the estimated maximum power of the battery

PBAT,est

, which is determined in kilowatts by Eq.(39). This

power is then used to determine the estimated battery mass

MBAT,est

in kilogrammes by utilising the power density as

shown in Eq.(40).

The fuel cell stack mass as well as the battery mass are

then used to determine the maximum take-off mass, which

is utilised to set the configuration for the model. Hence,

the simulation can now be performed. The results of the

simulation deliver a maximum required battery power

PBAT

and a required total energy

CBAT

of the battery. This is then

utilised to determine the battery mass in kilogrammes as

shown in Eq.(41). This iteration is performed several times,

until the battery mass stabilised, hence the estimated battery

(38)

⋅

AHeat =0.02

⋅

(39)

PBAT,est =170 −PFC,max,util.

(40)

BAT,est =

BAT,est

0.5

mass before the simulation equals the battery mass after the

simulation.

Hence, the size of the battery can be changed by the varia-

tion of the maximum utilised power of the fuel cell stack. It

is therefore sufficient for the battery and the fuel cell stack

to vary the number of fuel cells N and the maximum utilised

power of the fuel cell stack

PFC,Max,util.

. For this study, the

number of fuel cells within the stack is varied between 400

and 800 in increments of 50, whereas the maximum utilised

electric power of the fuel cell stack is varied between

75 kW

and

180 kW

in increments of

15 kW

, leading to a total of 72

different configurations.

4 Results

The results of the performed parameter study will be ana-

lysed in this section. To ease the evaluation of the results, all

configurations are compared to a reference configuration. A

common approach for hybridisation would be to size the fuel

cell stack based on the required power in the climb phase.

Therefore, the battery is only required to aid the fuel cell

stack during the take-off phase. Furthermore, the available

power of this configuration still enables the fuel cell stack

to charge the battery during the cruise phase. Initial calcula-

tions show, that the climb phase requires approximately up

120 kW

electric power for the propulsion system. There-

fore, for the reference configuration, the maximum utilised

power of the fuel cell stack is kept at

120 kW

. However,

prior to this paper, the literature shows that oversizing might

be beneficial regarding efficiency whilst the mass increases.

Therefore, for the reference configuration, the fuel cell

stack will be slightly oversized with a maximum available

power of

130 kW

to increase the efficiency without increas-

ing the mass significantly. As the initial calculations also

showed a peak power demand of approximately

170 kW

, the

required battery power is estimated at

50 kW

for the refer-

ence configuration.

4.1 Maximum temperature ofthefuel cell stack

This paper aims to present a method to identify a configura-

tion that is efficiency and weight-optimised, whilst respect-

ing the limits of the heat management system. Therefore,

the first parameter that will be analysed is the maximum

fuel cell stack temperature during the flight, as this defines

whether the configuration can operate safely with the pre-

designed heat management system. The maximum limit for

the fuel cell stack temperature in this paper is defined as

(41)

BAT =max

([

PBAT

0.5 ,

CBAT

0.8

])

M.Akkaya et al.

1 3

87 ◦C

[27, 28]. The Fig.9 shows the maximum fuel cell

stack temperature over the whole flight across all configura-

tions. The maximum temperature is presented by isolines

with respect to the maximum available power of the fuel cell

stack

PFC,Max

on the y-axis and the battery power

PBAT

the x-axis. This format is kept along all analysed parameters.

It can be derived, that the maximum temperature of some

configurations exceed the limit of

87 ◦C

, therefore these con-

figurations are not to be considered further. These configura-

tions will be highlighted across all following result plots by

not applying a colour to these configurations.

The results show, that the reference configuration is one

of those, which exceed the maximum fuel cell stack tem-

perature limit. The figure also shows that increasing the bat-

tery size causes the maximum fuel cell stack temperature to

increase slightly at first, followed by a significant decrease

at a certain point. This decrease is related to the decreasing

maximum utilised power of the fuel cell stack, which results

in a lower generated heat.

Furthermore, it can be seen that the maximum tempera-

ture of the fuel cell stack decreases with increasing fuel cell

stack size despite constant battery power and thus almost

constant utilised power of the fuel cell stack. In addition to

the efficiency gain due to oversizing, which leads to lower

heat generation, the heat capacity of the fuel cell stack

increases. Since the generated heat correlates with the uti-

lised power of the fuel cell stack, the high heat generation

rate only applies during the relatively short take-off and

climb phase. Therefore, the increased heat capacity due to

the higher fuel cell stack mass mainly drives a reduction of

its maximum temperature by increasing its thermal inertia

and thus decreasing the change of temperature with respect

to time.

4.2 System mass

The aircraft weight mainly defines the power requirement

and is therefore one optimisation criteria. It is aimed to

minimise the aircraft weight by decreasing the aircraft’s

component masses. However, this paper assumes a constant

mass for all components except for the fuel cell stack and the

battery, as it presents a method for the preliminary design.

Therefore, a weight optimisation can only be achieved by

minimising the system mass

MSys

, which in this paper is

defined as the sum of the fuel cell stack and battery masses

for each side of the aircraft. Figure10 presents the system

mass for all analysed configurations, which highlights the

improvement of this proposed design method by displaying

the deviation of the actual system mass to the system mass

of the reference configuration.

It is shown, that the weight-optimised design is reached

for a fuel cell-only configuration with no oversizing. For

that configuration, a system mass reduction of up to approxi-

mately

90.15 kg

(63.04%) is determined. The Fig.10 also

shows, that increasing the battery power affects the system

mass more significantly than increasing the maximum fuel

cell stack power, which is due to the higher power density of

fuel cells. For instance, the fuel cell-only configuration with

Fig. 9 Maximum temperature of the fuel cell stack during the mission

◦C

with respect to the maximum fuel cell stack power and the bat-

tery power

Fig. 10 System mass per side of the aircraft as deviation to the refer-

ence configuration in kilogrammes with respect to the maximum fuel

cell stack power and the battery power

A method foranefficiency andweight‑optimised preliminary design ofahydrogen‑powered fuel…

1 3

the highest analysed oversizing would still lead to a system

mass reduction of

81.95 kg

(57.30%) compared to the refer-

ence configuration.

4.3 Overall efficiency

The primary purpose of the propulsion system is to supply

the demanded propulsive power by generating the required

thrust. Therefore, the output of the propulsion system over

the flight can be quantified by integrating the propulsive

power over the whole flight. As the battery is charged dur-

ing the mission, the total input can be quantified by the total

mission fuel consumption

ΔmH2

and the lower heat value of

hydrogen

Hu,H2

. The overall efficiency

𝜂Overall

over the flight

can therefore be determined by Eq.(42). The Fig.11 pre-

sents the overall efficiency in percent for the configurations

of the performed study.

Figure11 shows, that an increasing battery power at a con-

stant fuel cell stack size generally leads to a slightly decreas-

ing overall efficiency despite allowing the fuel cell stack

to operate at a more efficient part load during take-off and

climb. This is mainly due by the additional losses that occur

during discharging and charging the battery. However, the

figure also shows that increasing the maximum fuel cell

stack power improves the overall efficiency significantly.

The identified efficiency-optimised configuration is the fuel

(42)

𝜂

Overall =

∫t

End

tStart

PProp dt

Δm

⋅H

cell-only configuration with the highest analysed oversizing

at an overall efficiency of 43.49%. This leads to an efficiency

improvement of 3.15%-points as the reference configuration

operates at an overall efficiency of

40.34%

4.4 Mission fuel consumption

The main aim of improving the efficiency is to decrease

the mission fuel consumption. However, different configu-

rations lead to different total masses and thus to different

required propulsive powers. Hence, a higher efficiency does

not automatically lead a lower mission fuel consumption,

as an increased mass affects the mission fuel consumption

negatively. A weight decrease as well as an efficiency gain

are positively affecting the mission fuel consumption. As

this paper aims an optimisation in efficiency and weight,

the mission fuel burn is used as the objective function com-

bining both criteria into one parameter. Therefore, for this

analysis, the mission fuel consumption is separately evalu-

ated and even prioritised. The Fig.12 presents the mission

fuel consumption per side of the aircraft as deviation to the

reference configuration.

The reference configuration consumes approximately

9.88 kg

of hydrogen per side of the aircraft. Figure12 shows

that an oversized fuel cell-only configuration can lead to

a mission fuel consumption decrease of

1.10 kg

(11.17%).

As shown earlier, the oversized fuel cell-only configuration

is the most efficient one. As the system mass and thus the

take-off mass does not increase significantly by oversizing

Fig. 11 Overall efficiency over the flight mission in percent with

respect to the maximum fuel cell stack power and the battery power

Fig. 12 Mission fuel consumption per side of the aircraft as devia-

tion to the reference configuration in kilogrammes with respect to the

maximum fuel cell stack power and the battery power

M.Akkaya et al.

1 3

the fuel cell stack, the high efficiency by oversizing mainly

affects the fuel consumption so that the oversized fuel cell-

only configuration is the identified consumption-optimised

configuration.

4.5 Summary

The results show, that the optimised weight is reached for

the fuel cell-only configuration with no oversizing, which

enables a system mass reduction by

90.15 kg

(63.04%).

However, the efficiency and fuel consumption is optimised

for the fuel cell-only configuration with the maximum ana-

lysed oversizing. This configuration still yields a reduction

of the system mass by

81.95 kg

(57.30%), whilst enabling

an efficiency gain of 3.15%-points and a fuel consumption

decrease of

1.10 kg

(11.17%). The efficiency and fuel con-

sumption is prioritised over the system mass. Furthermore,

the efficiency and fuel consumption-optimised configuration

is only slightly heavier than the weight-optimised configura-

tion. Therefore, as the result of this paper, the fuel cell-only

configuration with the highest analysed oversizing is identi-

fied as the overall optimised configuration.

5 Conclusion andrecommendations

This paper demonstrated a model based preliminary design

method for an efficiency and weight-optimised hybrid-elec-

tric aircraft. For that, a transient model of an aircraft’s pro-

pulsion system and heat management system was developed.

This model has been used to conduct a parameter study to

determine characteristic parameters for different configu-

rations of fuel cell stack and battery sizes. These param-

eters have been analysed to identify an overall optimised

configuration.

The conducted study shows, that the dimensions of the

fuel cell stack and the battery have a significant impact on

the overall performance of the aircraft’s propulsion system.

The first main advantage of this design method is to identify

all configurations, which respect the limits of the heat man-

agement system and can therefore be utilised. The reference

configuration for instance was evaluated to exceed the maxi-

mum temperature limit and can therefore not be operated

without an improvement of the heat management system.

The overall optimised configuration in this paper is

identified to be the oversized fuel cell-only configuration

with a maximum power of the fuel cell stack of

220 kW

This leads to a system mass decrease of 57.30%, an effi-

ciency gain of 3.15%-points and a reduced fuel consump-

tion by 11.17% when compared to the reference configura-

tion, whilst respecting the limits of the heat management

system. However, for more detailed design phases, it is

recommended to analyse the whole “sweet spot area”,

which for the analysed aircraft and flight mission is iden-

tified as all fuel cell-only configurations or configurations

with relatively small batteries, given that the characteristic

parameter only deviate slightly in this area.

The decreased system mass leads to decreasing require-

ments on other components such as the structure. There-

fore, the more detailed, iterative design phases could

potentially show even higher benefits. Furthermore, it

was evaluated for the identified “sweet spot area”, that the

maximum temperature of the fuel cell stack has a big mar-

gin to the maximum temperature limit. Therefore, the heat

management system could be adjusted by using smaller

heat exchanger and air intakes, so that the aircraft weight

would decrease further and the drag could decrease, which

would even enable a further decreased fuel consumption.

The proposed method for the preliminary design can

also be applied in more advanced design phases by increas-

ing the level of detail in the model, which can be achieved

by the available data of more advanced design phases. For

instance, the component masses of more components such

as the compressor, the heat exchanger, structural compo-

nents etc. would also have to be adjusted for every con-

figuration. Additionally, the level of detail regarding the

component behaviour can be increased, as well as adding

components to the model which were neglected for the

preliminary design, such as the required power of small

components like pumps, or the heat management of the

batteries and the electric motor. Furthermore, additional

limits such as operational limits of components or physi-

cal limits regarding the integration can be implemented in

order to identify configurations that exceed limits and must

therefore be excluded.

Author contributions All authors contributed to the study conception

and design. The preparation of the used model, the data collection,

as well as the analysis were performed by MA. The first draft of the

manuscript was written by MA and NN and all authors commented on

previousversions of the manuscript. All authors read and approved

the final manuscript.

Funding Open Access funding enabled and organized by Projekt

DEAL. The authors would like to acknowledge the European Regional

Development Fund (ERDF) and the Business Development Bank of the

Federal State of Berlin (IBB) for their financial support of the research

project: flying with hydrogen as energy carrier.

Data availability The datasets generated and analysed during the cur-

rent study are available with restrictions from the corresponding author

on reasonable request.

Declarations

Conflict of interest The authors have no competing interests to declare

that are relevant to the content of this article.

A method foranefficiency andweight‑optimised preliminary design ofahydrogen‑powered fuel…

1 3

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copy of this licence, visit http://creativecommons.org/licenses/by/4.0/.

References

1. Grewe, V., Rao, A.G., Grönstedt, T., Xisto, C., Linke, F., Melkert,

J., Middel, J., Ohlenforst, B., Blakey, S., Christie, S., etal.: Evalu-

ating the climate impact of aviation emission scenarios towards

the paris agreement including COVID-19 effects. Nat. Commun.

12(1), 1–10 (2021)

2. International Air Transport Association-IATA.: 20 year passenger

forecast (2020)

3. Krein, A., Williams, G.: Flightpath 2050: Europe’s vision for aero-

nautics. Innovation for Sustainable Aviation in a Global Environ-

ment: Proceedings of the Sixth European Aeronautics Days, vol.

63 (2012). https:// doi. org/ 10. 2777/ 50266

4. IATA.: Aircraft technology roadmap to 2050. 05 (2020)

5. Cumpsty, N., Mavris, D., Kirby, M.: Aviation and the environ-

ment: outlook, Ch. 1 in ICAO: Environmental Report: Aviation

and Environment, p. 2019. Destination Green-The Next Chapter,

ICAO (2019)

6. Hoelzen, J., Liu, Y., Bensmann, B., Winnefeld, C., Elham, A.,

Friedrichs, J., Hanke-Rauschenbach, R.: Conceptual design of

operation strategies for hybrid electric aircraft. Energies (2018).

https:// doi. org/ 10. 3390/ en110 10217. (ISSN:1996-1073)

7. Kadyk, T., Schenkendorf, R., Hawner, S., Yildiz, B., Römer,

U.: Design of fuel cell systems for aviation: representative mis-

sion profiles and sensitivity analyses. Front. Energy Res. (2019).

https:// doi. org/ 10. 3389/ fenrg. 2019. 00035

8. Abu Kasim, A.F.B., Chan, M.S.C., Marek, E.J.: Performance

and failure analysis of a retrofitted cessna aircraft with a fuel cell

power system fuelled with liquid hydrogen. J. Power Sour. 521,

230987 (2022). https:// doi. org/ 10. 1016/j. jpows our. 2022. 230987

9. Kadyk, T., Winnefeld, C., Hanke-Rauschenbach, R., Krewer, U.:

Analysis and design of fuel cell systems for aviation. Energies

11(2), 375 (2018). https:// doi. org/ 10. 3390/ en110 20375

10. Piper Aircraft, Inc. TYPE-CERTIFICATE DATA SHEET Piper

Model PA-46 (2010). https:// uploa ds- ssl. webfl ow. com/ 6294e

c9350 22269 cdd66 e27c/ 62c69 68a15 59f5c 5fb1c 75d8_ Europ

ejski% 20Cer tyfik at% 20Typu% 20-% 20M350. pdf

11. Frey, J., Sell, F., Gillespy, R., Pfifer, H.: Aerodynamic design and

wind tunnel test of a laminar wing with split flap for a fuel cell

powered aircraft. Deutscher Luft- und Raumfahrtkongress 2022

published by Deutsche Gesellschaft für Luft- und Raumfahrt -

Lilienthal-Oberth e.V. (2023). https:// doi. org/ 10. 25967/ 570209

12. APUS Zero Emission. APUS i-2: The Zero Emission GA Air-

craft. https:// group. apus- aero. com/ wp- conte nt/ uploa ds/ 2021/ 09/

APUS_i- 2_ 20210 901. pdf

13. Bargal, M.H.S., Abdelkareem, M.A.A., Tao, Q., Li, J., Shi, J.,

Wang, Y.: Liquid cooling techniques in proton exchange mem-

brane fuel cell stacks: a detailed survey. Alex. Eng. J. 59(2),

635–655 (2020). https:// doi. org/ 10. 1016/j. aej. 2020. 02. 005.

(ISSN:1110-0168)

14. Davig, G.H.: Fundamentals of Airplane Flight Mechanics.

Springer, Berlin (2007). (ISBN:978-3-540-46571-3)

15. Yechout, T.R., Morris, S.L., Bossert, D.E., Hallgren, W.F.:

Introduction to Aircraft Flight Mechanics. American Insti-

tute of Aeronautics and Astronautics Inc, Providence (2003).

(ISBN:978-1-56347-577-1)

16. Manwell, J.F., McGowan, J.G., Rogers, A.L.: Wind Energy

Explained: Theory, Design and Application. Wiley, New York

(2010)

17. Aviv, R., Gur, O.: Propeller performance at low advance ratio. J.

Aircr. 42, 435–441, 03 (2005). https:// doi. org/ 10. 2514/1. 6564

18. Ansari, S.A., Khalid, M., Kamal, K., Ratlamwala, T.A.H., Hus-

sain, G., Alkahtani, M.: Modeling and simulation of a proton

exchange membrane fuel cell alongside a waste heat recovery

system based on the organic rankine cycle in matlab/simulink

environment. Sustainability 13(3), 96 (2021). https:// doi. org/ 10.

3390/ su130 31218. (ISSN:2071-1050)

19. Zhu, C., Li, X.: A new one dimensional steady state model

for pem fuel cell. World Electr. Veh. J. 4(3), 437–443 (2010).

(ISSN:2032-6653)

20. Hoeflinger, J., Hofmann, P.: Air mass flow and pressure optimi-

sation of a pem fuel cell range extender system. Int. J. Hydrogen

Energy 45(53), 29246–29258 (2020). https:// doi. org/ 10. 1016/j.

ijhyd ene. 2020. 07. 176. (ISSN:0360-3199)

21. PowerCellution-PowerCell Sweden AB.: P Stack. https:// www.

datoc ms- assets. com/ 36080/ 16360 22110-p- stack-v- 221. pdf.

Accessed Feb 2023

22. Liso, V., Nielsen, M.P., Kær, S.K., Mortensen, H.H.: Thermal

modeling and temperature control of a pem fuel cell system for

forklift applications. Int. J. Hydrogen Energy 39(16), 8410–

8420 (2014). https:// doi. org/ 10. 1016/j. ijhyd ene. 2014. 03. 175.

(ISSN:0360-3199)

23. Tschegg, E., Heindl, W., Sigmund, A.: Die Luft und ihre Zusam-

mensetzung, pp. 218–253. Springer, Vienna (1984). https:// doi.

org/ 10. 1007/ 978-3- 7091- 8771-5_ 18 . (ISBN:978-3-7091-8771-5)

24. Lechmann, A.: Modellierung von Wärmeübertragern in den

Gaswechselsystemen von Verbrennungsmotoren. Doctoral the-

sis, Technische Universität Berlin, Fakultät V-Verkehrs- und

Maschinensysteme, Berlin (2008). https:// doi. org/ 10. 14279/ depos

itonce- 1929

25. Rubenstein, D., Yin, W., Frame, M.: Mass transport and heat

transfer in the microcirculation. In: Biofluid Mechanics. Biomedi-

cal Engineering, 3rd edn., vol. 96, pp. 331–374. Academic Press

(2022). https:// doi. org/ 10. 1016/ B978-0- 12- 818034- 1. 00008-6

(ISBN:9780128180341)

26. Stieglitz, R., Heinzel, V.: Thermische Solarenergie Grundlagen.

Technologie, Anwendungen (2013) 978-3-642-29475-4. 32.23.01;

LK 01. Springer, Wiesbaden (2012)

27. Tang, X., Zhang, Y., Sichuan, X.: Temperature sensitivity char-

acteristics of pem fuel cell and output performance improvement

based on optimal active temperature control. Int. J. Heat Mass

Transf. 206, 123966 (2023). https:// doi. org/ 10. 1016/j. ijhea tmass

trans fer. 2023. 123966. (ISSN:0017-9310)

28. Tawalbeh, M., Alarab, S., Al-Othman, A., Javed, R.M.N.: The

operating parameters, structural composition, and fuel sustainabil-

ity aspects of pem fuel cells: a mini review. Fuels 3(3), 449–474

(2022). https:// doi. org/ 10. 3390/ fuels 30300 28. (ISSN:2673-3994)

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