Adopting Exergy Analysis for use in Aerospace
David Hayes1 , Mudassir Lone2, James F Whidborne,3
Cranfield University, Cranfield, MK43 0AL, United Kingdom
José Camberos4
U.S. Air Force Research Laboratory, Wright Patterson Air Force Base, Ohio 45433
Etienne Coetzee5
Airbus Operations, Bristol, BS99 7AR, United Kingdom
Abstract
Thermodynamic analysis methods, based on an exergy metric, have been developed to improve system efficiency
of traditional heat driven systems such as ground based power plants and aircraft propulsion systems. However, in
more recent years interest in the topic has broadened to include applying these second law methods to the field of
aerodynamics and complete aerospace vehicles. Work to date is based on highly simplified structures, but such a
method could be shown to have benefit to the highly conservative and risk averse commercial aerospace sector. This
review justifies how thermodynamic exergy analysis has the potential to facilitate a breakthrough in the optimization of
aerospace vehicles based on a system of energy systems, through studying the exergybased multidisciplinary design
of future flight vehicles.
Keywords: Exergy, Thermodynamics, Multi Disciplinary Optimisation
1. Introduction
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10
15
Future commercial aircraft are likely to become more complex and highly integrated systems. As such, the powerplant, aerodynamics, stucture and aircraft subsystems must be designed in a more holistic manner, where a common
comparison metric is used for optimisation purposes. This paper proposes an extension to classic energy analysis,
known as exergy analysis which is conducted by the coupling of the first and second law of thermodynamics. A
general introduction to the use of exergy within aerospace systems can be found in Doty [39, 40] as well as the
published textbook by Camberos and Moorhouse [31], where the primary focus is that of military and hypersonic
systems. This paper reviews additional published work, with insights being derived for how this method can be used
specifically for the commercial aerospace industry, but with relevance to all aeronautics disciplines.
This review is written to advocate an alternative systems engineering approach to developing future commercial
aircraft, where entropy and energy are united to provide additional design insight where traditional methods are
restricted.
There is relatively little use of exergy analysis outside the thermodynamically dominant process of power generation in propulsion systems, where exergy is only applied at subsystem level and not as a unifying metric. This has
left the method widely unknown within the aerospace community. A thought upheld by Nixon in saying [74]
1 Research
Student, Centre for Aeronautics, d.hayes@cranfield.ac.uk
Centre for Aeronautics, m.m.lone@cranfield.ac.uk
3 Reader, Centre for Aeronautics, j.f.whidborne@cranfield.ac.uk
4 Aerospace Engineer, Aerospace Systems Directorate, jose.camberos@us.af.mil
5 Future Projects Engineer, Airbus Operations, etienne.coetzee@airbus.com
2 Lecturer,
Preprint submitted to Progress in Aerospace Sciences
July 17, 2017
Nomenclature
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ηa
Aerodynamic efficiency ()
g
Gravity ( sm2 )
ηp
Propulsion efficiency ()
H
Enthalpy (J)
ηs
Structural efficiency ()
L
Lift force (N)
γ
Ratio of specific heats ()
M
Mach number ()
3
V
Volume (m )
m
Mass (kg)
W0
Final aircraft weight (kg)
p
Pressure (Pa)
W1
Initial aircraft weight (kg)
Q
Heat (energy transfer) (J)
ψ
Flow exergy (J)
R
Range (m)
ρ
Air
S
Entropy ( KJ )
A
density( mkg3 )
2
Area (m )
T
Temperature (K)
t
Time (s)
g
)
( s.kN
cT
Thrust specific fuel consumption
D
Drag force (N)
U
Internal energy (J)
E
Energy (J)
V
Velocity( ms )
Ex
Exergy (J)
v∞
Free stream velocity ( ms )
F
Helmholtz free energy (J)
W
Work (energy transfer) (J)
G
Gibbs free energy (J)
wn
Velocity vector ( ms )
“Aeronautics is generally thought to be a mature discipline with little extra benefit to be obtained from further specialized research ... The only way that the science of aerodynamics can be made fertile again is to change the building
blocks of knowledge”
Thus this review challenges the traditional force balance approaches of design, and propose an alternative global
viewpoint of energy balance, by tracking the exergy flow and entropy generation in the system. This aims to lay the
foundations for a novel physics based MultiDisciplinary Optimisation (MDO) method to enable the development and
realisation of next generation commercial aircraft and technologies, where systems are highly coupled.
To achieve this, the state of the art in the aerospace industry is discussed in Section 2, including a study of aircraft
design and future trends, and assessing why an energy based approach may be applicable. Section 3 provides an
overview of the mathematics behind exergy analysis, and provides additional references for those interested in a more
indepth understanding. Section 4 reviews how exergy analysis has been widely applied in the fields of propulsion and
hypersonic systems, where conclusions are derived on the limitations of this analysis. Section 5 begins the debate on
the wider application of exergy analysis to commercial aircraft and looks at how other authors have justified the use of
exergy for aerospace applications. Sections 6 and 7 then review how exergy has been applied to date in aerodynamics
and multidisciplinary optimisation. The review concludes with some thoughts of how exergy could be applied in the
future of aerospace systems and the impediments to adoption in Section 8 and 9.
2. Design and Analysis of Commercial Aerospace Systems
Traditional development splits the aircraft into various disciplines, examples being propulsion, aerodynamics and
structures. Each of these aim to individually optimise discipline specific performance metrics, which are then nondimensionalised using contrasting methods to provide a comparison to other disciplines of an aircraft, as seen in the
Breguet Range Equation. Jupp [60] and Lee [61] cite the use of the Breguet Range Equation [10], where the product
2
(a) Traditional discipline specific optimisation
(b) Holistic system based optimisation
Figure 1: System Optimisation derived from Camberos [29]
of three nondimensionalised relationships, the propulsion efficiency6 η p , the aerodynamic efficiency7 (ηa ) and the
structural efficiency8 (η s ), are optimised to maximise the aircraft range (R) as
R=
W1
v∞ 1
L
ln
g cT {z}
D
W0
{z}
 {z }
ηa
ηp
35
40
45
(1)
ηs
In traditional design, and as a consequence of practicalities and difficulties in designing complex aerospace systems, there has been a historical segregation of component and subsystem design and analysis. This methodology has
proved successful for conventional swept wing aircraft configurations, as the subsystem disciplines are only loosely
integrated with one another. In addition, as a fallout of practicalities and work share in designing aerospace systems,
there is a historical segregation of component and subsystem design and analysis. This means disciplines have individually developed performance, loss metrics and optimization at subsystem level and and are not clearly linked
to the overall system performance metric or objective. So, when bought together to form the top level aircraft, as
shown in Fig. 1a, it can be argued that eventhough the system is optimised to a degree possible in terms of some
systemlevel traditional performance metric as the interactions between these subsystems has not been optimised the
top level system will thus not be optimal.
From a systems engineer’s perspective, their role at top level system design is to make trades between competing
disciplines and sources of loss to arrive at a vehicle design with the least possible cost9 . Thus the systems engineer
has a need for a loss accounting method that enables systematic analysis of loss where system wide consequences of
design trades can be evaluated. This premise led to the development of generalized models for vehicle thermodynamic
loss management by Roth and Mavris [94], where differential loss models can be built of all aircraft subsystems (Fig.
2), and the sources of work can be modelled against the vehicle losses under a unifying metric.
6 Function
of thrust specific fuel consumption (cT )
of aircraft Lift (L) and total Drag (D)
8 Function of initial aircraft weight (W ) and final post fuel burn weight (W )
1
0
9
Typically inflight fuel burn for a commercial aircraft
7 Function
3
Figure 2: Typical contributers used in loss management model construction [94]
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60
65
70
75
The question still remains though, of what unifying metric should be used in these loss models? The two universal
properties proposed from thermodynamics are energy from the first law of thermodynamics and entropy from the
second law of thermodynamics. Both energy and entropy are recognised as important in all natural processes including
physicsbased machines. Thus, using either of these metrics would provide the sought after integrated approach,
as all aircraft systems operate using energy from a common fuel source and will generate entropy through their
inefficiencies.
Any system design evolution works on the theory of allowing energy to transfer through a sub system more
easily, by minimising the entropy production. Throughout the history of thermodynamics, the focus has been on heat
engines and power generation technology with the aim to reducing the gap between actual operation and operation in
the reversible cycle.
Current applications of thermodynamic analysis go well beyond power generation to near enough any system,
with emphasis placed on identifying the mechanisms and system components that are responsible for thermodynamic
losses (irreversibilities), through entropy generation. With this understanding, and the knowledge of the theoretical
ideal operating conditions in a given environment, the concept of available work became the focus of academic study
for thermodynamic optimisation, establishing the theoretical performance limit and maximum achievable efficiency
of any system and process.
Thermodynamics is often misinterpreted in aeronautics as only being relevant to heat driven propulsion systems.
However, given thermodynamics is the study of energy content and transfer, and all systems and processes use energy
in some form, thermodynamic analysis provides a holistic approach to aircraft optimisation, suitable for all disciplines.
Recall the four laws of thermodynamics [33]:
0. Zeroth Law If two bodies are in thermal equilibrium wih a third body, they are also in thermal equilibrium with
each other
1. First Law Energy can be neither created of destroyed during a process; it can only change forms (principle of
conservation of energy)
2. Second Law It is impossible for any device that operates on a cycle to receive heat from a single reservoir and
produce a net amount of work (KelvinPlanck statement)
3. Third Law The entropy of a pure crystalline substance at absolute zero temperature is zero, since there is no
uncertainty about the state of the molecules at that instant
Thermodynamic exergy analysis, the method of this review, is the simultaneous application of the first and second
laws.
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Figure 3: Sign convention for heat, work and mass transfer into a system [17]
3. Thermodynamic Analysis for Commercial Aerospace Systems
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3.1. First Law of Thermodynamics
The first law of thermodynamics for a closed system allows energy to be transfered via work(W) and heat (Q),
defined by the notation of Fig. 3, as
Z
Z
∆E sys =
Qdt − Wdt
(2)
which is derived by defining the Joule proportionality constant as the equivalence of work and heat, with the total sum
of the energy remaining constant, such that energy is never created nor destroyed
Ė sys = Ėin − Ėout
(3)
However, for an energy study of a system such as an aircraft, the conversion of energy from one form to another
is not only of interest, but also the conditions, limitations and direction of such a conversion. This is where the
application of the second law of thermodynamics, the concept of entropy, can provide beneficial insight; as to whether
the achieved final solution is near the optimal case or whether the solution is in fact feasible.
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3.2. Second Law of Thermodynamics
Entropy is a useful state property in thermodynamics. If the process undergoes a thermodynamic transfer the
entropy will either increase or remain the same. The latter case is known as a reversible process, where energy is
transferred along a defined thermodynamic path cyclically such that the system returns to its initial state without any
change, the socalled Carnot cycle for a frictionless heat engine. However a reversible process is an ideal case, as all
real processes have irreversibilities, be it friction, expansion of gas, chemical reaction, diffusion of gases etc. Clausius’
second law of thermodynamics, states that real processes are irreversible and proceed only in one particular sense.
The directionality of a process can be defined in terms of the positive entropy generation, S gen as a function of the
systems pre, S 1 , and post, S 2 , entropy state, and that generated through heat transfer, Q, at a given temperature, T
Z
δQ
≥0
(4)
S gen = S 2 − S 1 −
T
Thus, even though energy can be transferred via work and heat, entropy generation is only associated with heat
transfer. In effect the concept of entropy defines the limits of efficient energy transfer in the form of heat (heat
engines). A systems total entropy, S sys , can be defined as
Ṡ sys = Ṡ in − Ṡ out + Ṡ gen
.
5
(5)
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95
100
3.3. Available Energy: The Synthesis of Energy and Entropy
It can be postulated that when applied individually energy or entropy analysis are incomplete. Undertaking a
first or second law analysis in isolation provides insight into the thermodynamic process behaviour, however neither
describe the system processes completely. The application of the first and second law together, outside propulsion, is
sometimes considered an abstract concept as energy and entropy are thought to be separate state properties. However,
the contrary is true, where a synthesised application allows the energy transfers of a system to be described with the
first law, and the second law providing insight into the feasibility, directionality and the losses of useful energy with
each of these energy transfers.
To clarify the understanding of a synthesised application take the coffee cup thought experiment. If a hot cup of
coffee is placed in a cooler room environment, the first law of thermodynamics states that energy can be transferred
via heat from the coffee cup to the environment, until the point at which the coffee and environment are in thermal
equilibrium. However, the opposite also obeys the first law, where the environment transfers energy via heat to the
coffee increasing the coffee temperature. When the second law is applied to this problem, and the definition that
entropy transfer must always be positive, it is understood that the first transfer is the only feasible concept where
energy is transferred from a hot to cold source.
The first mathematical synthesis of the first and second laws of thermodynamics was defined as available energy
which was posed by Gibbs in 1873, a concept revised from a thermodynamic optimisation viewpoint by Gaggioli
[49], [48]. Gibbs defined the term enthalpy
H = U + pV
(6)
as a measure of the total energy of a system, the sum of the internal energy (U) and the product of pressure (p) and
volume (V). The Gibbs Free Energy (G) is a theoretical value that defines the maximum work that can be obtained
from a closed system undergoing a reversible, isothermal (constant temperature) and isobaric (constant pressure)
process
(7)
TS
G = U + pV − {z}
 {z }
First Law
Second Law
A similar formulation is that of Helmholtz free energy (F), which defines the maximum work that can be obtained
from a closed system reversibly through a isothermal and isochoric (constant volume) process.
F = U − TS
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(8)
3.3.1. Exergy
Exergy can be viewed as an extension of Gibbs and Helmholtz Free Energy where the available energy is not
dependent on whether or not it is an isothermal, isobaric or isochoric process, however it is dependent on the unconstrained environment in which it resides. Ayres [15] highlights the similarity and difference of exergy to these two
forms of free energy, as:
“The most general of all thermodynamic potentials of course is exergy, defined as the maximum amount
of work that can be extracted from a system without any constraints on volume, pressure, temperature or
composition.”[15]
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120
Understanding the two fundamental principles of thermodynamics, a combined definition from Sciubba [97],
Bejan [19], Naterer [73] and Ayres [15] can propose a synthesised statement of the first and second laws.
“The maximum theoretical useful work obtained if a system is brought into thermodynamic equilibrium
with the environment by means of processes in which the system interacts only with this environment. As
such, exergy is a measure of the departure of the given state from the environmental state (distance from
thermodynamic equilibrium), the larger the departure, the greater the potential for doing work. It is not
a conserved quantity (like energy) but it is possible to construct an exergy balance for any energy or
materials transformation process, accounting for inputs, process losses, useful products and wastes.”
Thus analysis using the simultaneous application of the first and second law within a defined environment is
defined as thermodynamic exergy analysis and its optimization component, entropy generation minimization (EGM).
Bejan [19] comments that it is the premier method of thermodynamic analysis in engineering and it is now sweeping
every aspect of engineering practice, including aerospace applications, emphasized by Camberos’ statement that
6
“Such capability [of exergy analysis] may allow the development of new and innovative concepts that do
not just marginally improve performance but may enable the realization of entire new regimes of performance and operability, especially for highspeed aerospace vehicles” [30]
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For additional information on the basic premise of exergy, the reader is directed to Edwards [42] who provides an
uncomplicated thought experiment.
4. Thermodynamic Analysis Coupling the First and Second Law
This section outlines the general mathematics for use in exergy analysis, based on the previous definition.
4.1. Environmental Definition
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135
The environment in which a system resides is more commonly known as a reference state, which is defined by
thermodynamic variables of reference temperature (T 0 ), reference pressure (P0 ) and reference chemical potential of
species ’k’ (µk0 ). In practice an environment is defined by the baseline levels of any value, be it a temperature, pressure,
velocity, chemical composition, altitude etc. However whilst all are required for exergy analysis the temperature is the
most important as thermal energy transferred via heat is the least available form of energy, and the transfer associated
with entropy generation.
4.2. Physical (System) Exergy
The exergy or available energy of an independent system residing in a given environment is defined by the systems
physical exergy (Ex ph ). This can be easier understood by subdividing the total physical exergy into contributing parts,
the terminology of which varies between authors, but for consistency with the rest of this body of work we shall view
physical exergy as:
Ex ph = ExU + ExT + ExV + ExC
(9)
With the subexergies being defined as:
• Thermal exergy (ExU )
140
– Internal exergy (closed system)
– Enthalpy exergy (open system)
• Kinetic Exergy (ExT )
– Mechanical (objects in motion)
– Radiant (electromagnetic)
– Sound
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150
• Potential Exergy (ExV )
–
–
–
–
–
Gravitational
Stored mechanical (elastic)
Nuclear
Electrical
Magnetic
• Chemical Exergy (ExC )
Whilst chemical exergy is a form of potential exergy, it shall be discussed separately below due to the contrasting ideal
conversion definition of potential exergy.
7
4.2.1. Thermodynamic exergy
The thermodynamic exergy is defined as the work obtainable by taking the system through a process such as
compression, expansion or heat exchange, to the temperature and pressure states of the environment [15]. For a
closed system (non mass transfer) the thermodynamic exergy can be simplified to the internal exergy of the system
ExU = (U − U0 ) + P0 (V − V0 ) − T 0 (S − S 0 )
(10)
where the maximum work that can be output is a function of the internal energy (U), volume V, entropy (S ) and
the environment temperature (T 0 ) and pressure (P0 ). However in an open system, the exergy of mass flow must be
accounted for, as given in the enthalpy exergy
ExU = (U + PV) − (U0 + P0 V0 ) −T 0 (S − S 0 )

{z
}
(11)
(h−h0 )
155
where a clear resemblance to Gibbs Free Energy (equation 7) can be seen, however in this case for a fully defined
unconstrained environment.
4.2.2. Kinetic exergy
The kinetic exergy is defined as the work obtainable from movement, be it the motion of waves, electronics, atoms,
molecules or substances.
1
(12)
ExT = m (V − V0 )2
2 {z }

Mechanical
4.2.3. Potential exergy
The potential exergy is defined as the work obtainable from system state (e.g. position, chemical composition,
etc.), where the system has a disparity in some form to its environment which enables it to do or receive work.
k (x − x0 )2 VE(ǫ − ǫ0 )2 C(Υ − Υ0 )2
ExV = mg (z − z0 ) +
+
+ M(B − B0 )
 {z }
 {z }  2
2
2
{z
}  {z
}
Magnetic
Gravitational
Stored mechanical
160
(13)
Electrical (capacitor)
In practice kinetic and potential exergy are both perfect forms of exergy, in that they can be completely converted
to work, given a null reference state.
4.2.4. Chemical exergy
The chemical exergy is defined as the maximum amount of work obtainable by taking a system reversibly to the
same chemical composition as the environment, with environmental temperature and pressure conditions. Camberos
[31] formulates a mass derived chemical exergy (equal to the mole derived function) as given by
ExC =
n
X
yi µi1 − µi0
i
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(14)
where the exergy is a function of the chemical potential (µk ) and mass ratio (yi ) as opposed to alternative stoichiometric
mole ratio (vi, j /v j ) relationships of Simpson [98].
Whilst this is a form of potential exergy, it is not a mechanical exergy, and thus not all of the energy can be
converted to work. In addition to the exergy losses through heat generation (entropy production) found in reactions
such as combustion, irreversibility is generated as environmental species are released to the environment at their
environmental dead state chemical potential.
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180
4.3. Exergy Transfer Equation
Exergy (as with energy) can be transferred into and removed from a systems control volume though three means;
mass flow, heat and work. Considering a closed system, exergy can only be transferred by heat or work.
The flow exergy can be used to define the exergy of the mass flow into and out of the system, as the exergy, energy
and entropy contents of a system are proportional to mass.
The second law tells us that the maximum work that can be obtained from energy transfer between a system
temperature, T , and environment temperature, T 0 , is through the Carnot cycle heat engine. As such the Carnot
efficiency describes the fraction of heat that can be transferred, and ultimately the total amount of useful work, known
as the exergy transfer by heat.
Exergy transferred by work is equal to the work input or output itself. However in the case where work is done by
or on surrounding atmospheric pressure we must account for this as a loss in useful work output. Take a weightless
and frictionless piston as an example, work must be done on the atmospheric air to move it aside as work is input into
the system and the pressure rises.
The exergy balance is used to identify the change in exergy of a system given a specific exergy transfer. Coupling
the equations for mass transfer, heat transfer and work transfer with the decrease of exergy principle leads to an
expression for the balance of exergy equation representing a synthesis of the first and second laws as a rate change in
system exergy:
) X
(
!
X
X
dVcv
T0
˙ des = dExcv
+
ṁψ −
ṁψ −Ex
(15)
Q̇k − Ẇ − P0
1−
Tk
dt
dt
out
{z
} in

{z
} 
{z
}
HeatT rans f er
WorkT rans f er
MassT rans f er
˙ ph = Ex
˙ U + Ex
˙ T + Ex
˙ V + Ex
˙ C
Where ψ = Ex
4.4. Entropy Generation and Exergy Destruction
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Independently from Gibbs’ findings (equation 7), Gouy [54] and Stodola [102] defined the expression for useful energy in 1889 and 1898 respectively, as the difference between the enthalpy and the product of envionement
temperature and entropy change. The principle of the increase of entropy is stated by Stodola as [102]:
“The sum of the entropies of all the bodies taking part in any [real] process whatever is at the end of the
process greater than at its beginning”
The relationship stating entropy in terms of exergy destruction is important, as a value is generated in Joules, which
allows losses due to entropy generation to be more easily understood. This is defined formally as the GuoyStodola
theorem for exergy destruction (Exdes ∝ S gen )
Exdes = T 0 S gen
(16)
Defined by Stodola [102] as:
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195
“For irreversible processes of any nature (also chemical), the useful work suffers a reduction equal to the
product of the resulting increase of entropy in all the bodies taking part in the process and the temperature
of the heatabstracting reservoir, that is, the environment.”
Bejan [17] proposes the name Entropy Generation Minimisation (EGM) for the process of multidisciplinary
optimistion using the exergy and exergy destruction metric. Unlike the first law range maximisation analysis in the
Breguet equation (equation 1) exergy analysis and EGM are minimisation methods for exergy destruction and total
exergy use. However it is worth noting a finite amount of friction (or some other entropy generation) is generally
required for systems to operate. Consider ice skating in an ideal frictionless world, without friction with the ice there
would be no way of propelling forward, thus no movement would happen.
5. Performance Assessment
The second law therefore provides additional insight to the first law analysis, in the following areas:
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205
• Feasibility. The second law states a system moves to become more disordered and that entropy, a measure of
disorder, can only ever increase in a real system, thus can only be positive when energy is transferred between
a hot to a cool source. This is an important distinction, because the first law does not distinguish between heat
and work transfer [19].
• Irreversibility. The wastes or losses can be quantified by entropy generation. The increasing entropy in a system
marks the approach to thermodynamic equilibrium, which marks the point of maximum entropy.
• Availability. For the coffee cup thought experiment the energy quality can be seen as the absolute inverse of the
Carnot efficiency (ǫ) an expression for the maximum amount of work that can be taken from the coffee cup as a
function of the coffee temperature, T 1 , and the room environment temperature, T 0 (shown graphically in Figure
4).
Energy Quality =
T1 − T0
1
=
ǫ
T1
An interesting implication is that the exergy of a very cold body far exceeds its low energy content as heat is
taken from the environment. Thus, the amount of available work is high, as work is done on the body.
• Optimal Efficiency. If we take internal combustion engines as an example, the standard first law efficiency of
such an engine is usually around 20% [15]. This first law efficiency (ηI ) can be calculated as
ηI =
Wout − Win
Qhot
The idealized (Carnot) process provides us with the tools to provide a more accurate obtainable efficiency. A
reversible process never occurs in nature, but can still be used in thought experiments to provide a theoretical
upper limit for the performance of a device, through a second law efficiency which informs how well the process
could ever do compared to the reversible cycle efficiency (ηReversible )
ηII =
(ηI )Irreversible
ηReversible
6. Applying Exergy Analysis to Aerospace Systems
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225
Exergy analysis results can be obtained by simply understanding how the components and their interactions are
connected. Detailed information on the performance of a subsystem is not typically required, making it a useful
tool from the preliminary design phase and through production. Exergy analysis provides “a consistent framework
within which losses can be compared within machines, between machines of different types for the same job and with
perfection in the form of the completely reversible machine” [34].
Thus it is achievable to formulate a set of vehicle design requirements stated in terms of the total energy use
of the system, as an alternative view to that of discipline specific optimisation (see Fig. 1b). All systems over the
flight mission can therefore be modelled in terms of the fuel energy used and exergy destruction losses. One of the
convenient properties of exergy analysis is that exergy is easier interpreted than entropy, as exergy has the same units
as energy (Joules), and as such in an economic analysis (also referred to as thermoeconomics in texts [18], [83] [84])
as a monetary value can be assigned to the loss of exergy in terms of energy cost, based on the cost of fuel per Joule
for example. Then a simple comparison of every system can be made under the metric of exergy destruction in terms
of fuel use.
All real world processes are irreversible. Auditing a design with the entropy approach will highlight where available energy is being used throughout the system, showing areas of unavoidable irreversibilities such as combustion
losses as well as those irreversibilities with avoidable waste, as to direct the designers attention to those areas. The
second law approach is focused on identifying irreversibilties where entropy is produced with the aim to optimize
the structure as to minimize this production. Some common examples of system generic irreversibilities are given as:
Smith [99]
10
300
Quality factor (%)
250
200
150
100
50
0
0
200
400
600
Temperature (K)
800
1000
1200
Figure 4: Energy Quality as a function of its temperature, modified from [15]
• Mixing objects or fluids
• Heat transfer (through a finite temperature difference)
230
• Friction as a result of relative motion of objects or fluids
• Chemical reactions
• Inelastic deformation of solids
• Electric resistance
• Drag (vortex and parasitic)
235
240
245
• Sudden compressions such as shock waves
The significance of exergy analysis research is shown by Giurgiutiu [52] who cites Moorhouse and his collaborators at the Air Force Research Laboratory (AFRL) studies into exergybased multidisciplinary design as one of eight
fundamental research projects for future flight structures. One of critical outputs from Moorhouse’s work is the suggestion of changing the “analysis/design paradigm from energybased to exergy based (specifically, minimum exergy
destruction). This shift in methodology is even more critical in exploratory research and development where previous
experience may not be available to provide guidance” [39]. Hence, leading to the conclusion that the exergybased
conceptual framework enables the design of truly energyefficient, integrated systems, subject to constraints.
Periannan [79, 80, 81] applied exergybased analysis and optimization methods to the synthesis/design and operation of aircraft systems to show the advantages of such a method over first law methods. This was done by comparing
different objective functions to the same design; minimizing takeoff gross weight, maximizing thrust efficiency, maximization of thermodynamic effectiveness, and minimizing exergy destruction. Periannan showed that:
“As long as the constraint space is the same, an energybased objective produces the same optimum as
that of the exergybased objective provided that they are equivalent forms of the same thing, for example,
fuel consumption”[79]
250
When this analysis was extended beyond propulsion and Environmental Control System (ECS) to include the
aerodynamics (by definition not an energy system in the traditional sense), Periannan showed the equivalence between
11
the energy and exergy objectives no longer holds. The need for a common currency points generally to the need for
exergy as the basis for both analysis and optimization [80].
Doty [39] [41] [40] takes a similar comparison exercise, in this case a complex turbojet engine is simplified
into interacting thermodynamic systems; the combustor as the energy source, the diffuser for energy transfer and the
turbine for energy conversion. The paper aims to compare the same system process fromm an energy based first law
method
Z
Z
∂
~ A
~
(e + pv) ρVd
Q̇ − Ẇ s − Ẇ shear − Wother =
(17)
eρdV +
∂t CV
CS
as previously given in equation 2 and an exergy based second law method
! Z
!
Z
T0
dVCV
~ dA
~ − Ex
˙ des = dExCV
ψρV
1−
+
δQ̇ − Ẇ − P0
Tk
dt
dt
CS
CS
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(18)
for the exergy transfer in an open system as in equation 15.
Three main conclusions are drawn from this comparison, which shows the advantages of the second law approach
over the traditional first law methods [39]
• Second Law analysis provides physical limits on performance that the first law analysis does not
• First law energy analysis yields operating conditions that are not feasible, thus cannot exist. In the body of work,
40 % of the results obtained from the first law analysis were not feasible.
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• The exergy destruction focus provides a consistent accounting for all forms of losses regardless of point of origin
These examples have shown exergy analysis to be an excellent tool for optimising individual sub systems, however
the true potential of exergy analysis in the integration of the different technical discipline, under a complete system of
energy systems [30]. Optimization based on minimum exergy destruction, presents a MultiDisciplinary Optimisation
technique required for the analysis of aerospace vehicles in terms of the efficient use of onboard energy [30]. This
style of analysis could be done at any stage of design on high or low fidelity models where the whole system is
modelled and mapped over the entire mission profile and all locations of exergy destruction highlighted.
6.1. Research Institutions focusing on Exergy
From 2001 to 2009, the Air Force Office of Scientific Research funded research with the task; exergy based
methods for aerospace vehicle design [52]. Camberos and Moorhouse have summarised much of this US Department
of Defense funded research in Exergy Analysis and Design Optimization for Aerospace Vehicles and Systems [31].
The international research community applying exergy analysis to aerospace systems appears to be quite small, with
Camberos and Moorhouse being involved (and leading) any US based research through various institutions including
University of Dayton, Virginia Polytechnic Institute, Clemson University and Missouri University of Science and
Technology, all of which have sizeable research groups working on exergy analysis. However there is plenty of interest
in the topic outside of the US, with ONERA in France [12, 13, 14, 11], Anadolu University in Turkey [105, 43, 101],
Canadian National Research Council [82],University of Sao Paulo in Brazil [35, 36, 51, 50], Cranfield University
[57, 58] and Bath University [23] in UK to name just a few.
7. Exergy Analysis application to Propulsion systems
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Thermodynamic methods, such as exergy analysis, can provide a means for accounting for resources and wastes
in a systematic uniform way. However application of these methods have been limited in application mainly to design
optimisation of classical thermodynamicsbased disciplines, thus have not seen much usage in other areas. Early exergy analyses were focused on extracting the maximum exergy from a hot gaseous stream which is discharged into the
environment, as in an aircraft engine [18]. One of the reasons exergy research has focused heavily on thermodynamic
dominant propulsion systems is the viewpoint that in comparison to exergy destroyed due to propulsion, all other
forms of irreversibility are essentially negligible, thus focus for reduction through optimisation is on the engine [91].
From an exergy perspective, conventional turbofan engines convert chemical exergy into mechanical and electrical
exergy tfor use by other aircraft systems. At the beginning of a flight the source of exergy for current passenger aircraft
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Figure 5: Chalmers University concepts, open rotor (left), pulse detonation core (right) [56]
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is defined by the quantity of fuel and the chemical exergy contained within. Chemical exergy arises when there is
a disequilibrium between the resource and environment leading to a chemical potential. This could be a potential
created by a concentration gradient of species freely available in the environment, such as oxygen, carbon dioxide and
methane, or exergy arises from a nonenvironmental species, fuels typically fall into this category. In both scenarios
work can be extracted as the resource and environment are bought into chemical equilibrium.
Applying exergy analysis to aerospace systems is not a novel concept, with work dating back to the 1970s. The
dominant field of interest in publications was applied to steady state propulsion systems, a clear extension to the
previous applications of exergy to thermodynamic systems such as power stations. Examples of this work can be
found in Sciubba [97], Glansdorff [53], Bauer [16], Maltry [65], Clarke & Horlock [34], Lewis [63], Li & Qiu
[64], all of which undertook early optimisation analysis of aeronautic propulsive systems. This area is still under
development today, with huge potential for improvement in efficiency of aircraft engines.
“In time, the engines of nature acquire configurations that flow more easily, and this means that they evolve
toward less entropy generation, and more production of motive power per unit of useful energy (exergy)
used.”[21]
More recent approaches to applying exergy principles to the optimisation of propulsion systems, include Dincer
[37], Clarke [34], Marley [68] and Ehyaei [43] in turbojet engines and Doty [41], Roth [93] [92] [95] and Riggins
[85][88][86] in turbofan engines for commercial aircraft.
Noticing the lack of diversity in exergy analysis application beyond turbojet and turbofan, Grönstedt [56] included other potential future engines, using an assumed future 2050 optimised turbofan configuration as the baseline.
Grönstedt performed an exergy analysis on an (futuristic) open rotor engine from Chalmers University, an intercooled
recuperated engine and an engine working with a pulse detonation combustion core, which are the three alternative
configurations he saw as the future of aircraft propulsion (see Fig. 5). Whilst Grönstedt showed the alternatives proposed provided a valid alternative to the turbofan configuration from an exergy perspective, what is more interesting
are the conclusions on the use of the exergy metric, which were:
“A striking strength of the analysis is that it establishes a common currency for comparing losses originating from very different physical sources of irreversibility. This substantially reduces the complexity of
analyzing and comparing losses in aero engines. In particular, the analysis sheds new light on how the intercooled recuperated engine establishes its performance benefits... As part of analyzing the computational
results it has become evident that exergy analysis is also quite rewarding when a comparative analysis of
different engine architectures is carried out.”[56]
An area exergy analysis may prove highly beneficial is in providing evidence for the integration of electric engines,
an area of research gaining increasing focus for future aircraft. Schmitz [96] initially shows the shortcomings of
traditional analysis methods, and then demonstrates how the unified figures of merit provided by exergy are useful in
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allowing for consistent comparisons between electric and conventional engines. Schmitz’s work is concluded with a
detailed comparison between a conventional turbofan, a parallelhybrid turbofan, a novel integratedhybrid turbofan
concept, and an entirely electrical fan concept [96].
One should be mindful that individual subsystems (such propulsion) optimised separately to the complete system
are unlikely to be an optimised system as different subsystems will have adverse effects on each other. So whilst
use of exergy methods has been used for propulsion sub system optimisation, unless the integration of these to the
complete system an optimised result will not be achieved. Justification for this top level systems approach can be seen
from the analyses and optimisation of hypersonic vehicles (ramjet and scramjet) through exergy analysis by Brilliant
[27], Markell [66] [67] and Tang [104]. What this work showed is that to fully realise the benefits of exergy analysis
we must extend past just modelling the propulsion system to include the full system being mapped for its exergy uses,
including application to the airframe and its losses through irreversibilities, providing a more holistic approach to the
design process [96].
8. Aerodynamic and Structural Optimisation using Exergy
Concepts such as heat and work transfer are easily read across to aircraft systems such as propulsion systems
or environmental control systems (ECS), however it is less clear how the second law analysis is used on purely
aerodynamic systems. Exergy is transferred throughout the system including the airframe, but what needs to be
identified are how the aerodynamics uses and converts exergy and the causes of entropy generation /exergy destruction.
Taking a crude view of an airframe it has two primary purposes; (a) the structure to house the payload and (b) the
aerodynamics to convert forward thrust to lift. It is common to take a forcebased approach to the aircraft where the
lift opposes the weight, and the drag opposed the thrust, giving the generalised coefficients
CL =
CD =
L
1
2
2 γPM A
D
1
2
2 γPM A
(19)
(20)
The force balance approach, which results in lift and drag is just a theoretical concept to explain the basic aerodynamics of how a body flies, yet drag is simply a proxy for the second law entropy generation. Thus, an alternative
theoretical concept viewpoint would be that of an energy approach where two key energies are calculated, that to
keep the aircraft in the air, and that to propel the aircraft through the defined medium, in this case air. The airframe
generated drag (contributions from vortex, parasitic and wave), accounts for a loss in useful energy. Whilst to minimise liftinduced drag, the vortex drag can be viewed as the entropy generation required to keep the aircraft in the
air and thus cannot equal zero, whilst the parasitic and wave drag theoretically can be optimised to zero. Camberos
derived the alternative exergy coefficient as a function of the entropy generation, comparable to that of the lift and
drag coefficients, presented in Equation 21 is the corrected version from that of Camberos [29]
C Ex =
T 0 Ṡ gen
γPM 2 vA
(21)
8.1. The Oswatitsch expression for drag as an integral of entropy flow
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Early work in gas dynamics created the framework for deriving the entropy production through drag, notably from
Oswatitsch. Oswatitsch [75] stated that drag was simply a generation of entropy, and thus the generation rate of such
entropy would be the rate of exergy destruction.
“The power required to move a body immersed in a fluid with the constant velocity u∞ is equal to the
temperature of the approach flow times the flow of entropy through an area which includes all entropy
changes caused by the body” [75]
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In this case no useful work is done, u∞ W corresponds to the lost energy and the increase of the entropy flow represents
the increase of entropy per unit time of the whole system [75], as
Z
Z
˙ = v∞ W = T ∞ (s − s∞ ) ρwn d f = T ∞
sρwn d f
(22)
Ex
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Note that in the case of formation flight work is extracted from the drag of aircraft, so Oswatitsch above assumption
may not be valid for multiple aircraft, unless the the aircraft group are considered a closed system and analyse the
total entropy generated due to drag. Oswatitsch’s statement is related to the GuoyStodola thermodynamic theorem
(see equation 16) which states that the decrease of useful work of a thermal machine is equal to the entropy change of
the system times the surrounding temperature.
Paulus [77] included the dead state velocity term as a method to account for the variable environment parameters
in exergy mapping as
~ −V
~0
˙ =F V
~ −V
~ 0 = (T − D) V
(23)
Ex
as well as continuing the work to develop an exergy definition for lift. An interesting application of Oswatitsch’s
integral of entropy flow was that of Greene [55], who showed through exergy methods that the ideal lift distribution
for minimum induced drag is a parabolic shape and not the widely credited elliptical shape. Greene did this using the
method as outlined by Oswatitsch [75], however his use of this method has been disputed and thus the result put into
question [47] [89].
Entropy generation or exergy destruction due to aircraft aerodynamics are typically over shadowed by the exergy
destruction within the propulsion system. This does not however mean there is no purpose to optimise aircraft aerodynamics, as it may be the case reducing exergy destruction due to drag is more cost effective than reducing total engine
exergy destruction. Exergy analysis also proves to be a useful tool for wing optimisation when the aerodynamics are
considered in isolation from the rest of the aircraft.
Significant resources have been put into optimising aerofoil shape and wing lift distribution to maximise lift to
drag ratio, with these activities continuing to date for all new aircraft. Exergy analysis can be of benefit in improving
the thermodynamic performance of the system by highlighting the mechanisms generating entropy and allowing the
designer to pinpoint areas for improvement, or help dump unwanted energy from the system in landing or gust events.
Given the wide adoption of Computational Fluid Dynamics (CFD) in the design of aerodynamic systems, integration of exergy analysis into CFD solvers or as a post processor is an important step to make exergy analysis
fully versatile. Where a Reynolds Averaging Naviour Stokes (RANS) approach is used to model the turbulent flow,
Adeyinka [1] has included the modelled entropy production into the NavierStokes equations. The constitutive form
of entropy generation, which is mathematically equivalent to the transport equation for entropy, is given by Alabi
[5, 6, 7, 9, 8] as
1 ∂ui
qk ∂T
Ṡ gen = τi j
−
(24)
T ∂x j T 2 ∂xk
which is used to calculate the entropy in the flow over the airframe subsystem aerodynamics (AFSA) of a Boeing
747200, cruising at Mach 0.855. Modelling both inviscid and viscous flow, Alabi concluded that for the inviscid
solver minimal artificial entropy is produced, and that the majority of entropy generation is due to turbulence, as the
viscous dissipation term in the entropy equation dominates compared to the heat transfer term. Examples of the output
entropy generation are given in Fig. 6. Alabi validated this work using PrandtlGlauret airfoil theory for a lumped
parameter model [5, 6].
Focusing on the Blended Wing Body NASA N3X configuration, Arntz [11, 13, 12], showed the same conclusion
as Alabi in that viscous dissipation dominates entropy generation in drag. Arntz’s work also investigated the exergy
analysis of a blended wing boundary layer ingestion (BLI) system, and identified components of recoverable exergy
in the wake/jet of the aircraft that could be recovered using BLI methods. This goes against the Oswatisch theory
where all drag is lost energy and thus destroyed exergy.
Using a FORTRAN Reynoldsaveraged Navier Stokes flow solution, Arntz [14] computed the entropy generation
around the NASA Common Research Model (CRM) configuration travelling at transonic speed, thus as well as the
parasitic and vortex drag components of entropy generation, Arntz was able to show the entropy generated in shock
waves. Replicating and extending the work of Arntz at ONERA [14] McGuire [69] used the NASA Common Research
Model (CRM) to calculate the entropy and exergy destruction in the induced, parasitic and wave drag, calculating the
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Figure 6: Entropy generation around the B747200 aircraft and wing locations 14% (upper) and 28% (lower) [6]
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power loss (exergy destruction rate) for the CRM cruising at transonic speeds. Some examples of the results from
McGuire are given in Fig. 7.
Memon [70] provides a more detailed study for the exergy destruction in vortex drag, through experiments in a
water tunnel at Institute of Aerospace Systems, focusing on the exergy distribution in the vortex for a variable angle
of attack. When considering aerodynamics in energy terms, the point of minimum exergy state would be assumed to
correspond to the maximum lifttodrag ratio angle of attack. What Memon showed in that this is not the case, and
that it is related to where the wingtip vortex changes from a wakelike to jetlike vortex. Thus Memon concludes that
“the exergy method holds promise as a metric for the improvement of aircraft performance through the reduction of
lift induced [drag]” [70].
Hayes [58] compared the use of implicit (the Breguet Range Equation) and second law explicit energy (Exergy
Analysis) analysis methods for the incorporation of span extended technologies into future aircraft configurations.
Hayes showed exergy analysis leads to a methodology that can support the design of the complete vehicle as a system
of systems in a common mathematical framework. A critical part of this is the development of a decomposition
strategy where all the subsystem components can be optimized to a systemlevel common metric. Critically, it was
shown that both the Breguet and the Exergy method provide the same output from the benefit analysis when comparing
different inflight morphing mechanisms under each methodology. This can be seen in Fig. 8 where the analysis
shows for an aspect ratio of 12.6 assuming the mass increase is less than 17% from the baseline 9.4 aspect ratio, an
improvement of 11.5% can be made in the range which is equivalent to a reduction of up to 5% of the total source
exergy (fuel) use. In addition, the exergy method provides a more detailed analysis method which allows energy losses
to be compared to any of the aircraft’s subsystems.
9. MultiDisciplinary Optimisation using the Exergy Metric
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Multidisciplinary integrated design is where we consider the system as the complete collection of subsystems
interacting with one another and the optimisation of this system. As previously commented, this removes the issues
with designing subsystems in isolation where a suboptimal design is usually the outcome.
Conventional MultiDisciplinary Optimisation uses normalized coefficients to local variable dimensions, as seen
in the Breguet equation (equation 1) with the aerodynamic, propulsion and structure nondimensionalised factors.
However, such a method cannot account for essential differences between the aerodynamic, propulsion and structural,
and the magnitude of sensitivities can mislead the direction of optimization. Riggins [31] summarised this thought as
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(a)
(b)
Figure 7: Entropy generation due to vortex, parasitic and wave drag [69]
Figure 8: Comparison of the exergy and Breguet results for folding wing tips of an aspect ratio 12.6 aircraft [58]
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“In current MultiDisciplinary Optimisation and Analysis efforts, the various components and subsystems
are still generally evaluated or analysed in terms of their traditional and unique loss and performance
metrics... the characteristic, property, or quantity being used as the metric for loss minimization at all
levels of system, subsystem, and component design/evaluation should be the same as or at least explicitly
related to the systemlevel performance objective itself”
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There is no end point with the evolution of aerospace vehicles where one would say we have a perfect design,
but what exergy offers is a tool to be used to highlight areas of designs that waste useful energy and thus could be
improved to as near optimisation as feasible, summarised by Bejan as:
“Thermodyanmic optimisation (or entropy generation minimisation) brings the design as closely as
permissible to the theoretical limit” [20]
Camberos defines some of the key advantages of the exergy true common currency objective function for MDO
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as:
• Sensitivities are normalized according to global dimensions
• The magnitude of these sensitivities will be a better indication as to best direction for system optimization
• Opens viable (excluding physically infeasible) possibilities for revolutionary design
• Provide a clear picture of total system integration
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By devising ways to avoid the destruction of exergy, better use can be made of fuels. By accounting for all the
exergy streams of the system it is possible to determine the second law (exergetic) efficiency. By performing exergy
accounting at higher and higher fidelities, a map can be drawn of how the destruction of exergy is distributed over
the engineering system of interest. In this way the components and mechanisms (processes) that destroy exergy the
most can be identified. It is then by repeating the exergy analysis on the improved system that one can evaluate the
thermodynamic improvements made due to the second law implementation.
9.1. Visualising Exergy Use
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Due to the complex nature of aircraft systems, many authors have commented on the difficulty in visualising
exergy flow through an entire system. Two method have been proposed, the use of exergy flow diagrams from the
work of Paulus [76] [77] and Grassman diagrams by De Oliveira [36] and Berg [22].
Fig. 9 shows an example exergy flow diagram from the work of Paulus. The diagram represents the interactions
between different sub systems through which exergy can flow. One concern with this style of diagram is that with
a more complex system such as a commercial aircraft (see Fig. 10) the diagram will quickly become cluttered with
multiple interactions, making it difficult to decipher.
It is also easy to visualise the exergy flow through a system, using a similer graph to that of a Sankey Diagram,
known as a Grassmann diagram, where the exergy source (typically fuel) is mapped throughout the flight mission to
highlight areas of exergy destruction. The same exergy flow as in Fig. 10 can be shown for an A340 as an entropy flow
diagram in Fig. 11 (equivalent to Fig. 9) and a Grassmann diagram in Fig. 12, where the horizontal arrow represents
the flow of exergy, and the vertical arrows represent entropy production or exergy destroyed through various energy
conversion processes, such as combustion, the Environmental Control System (ECS) and in the generation of drag
[39].
9.2. Full Vehicle Exergy Analysis
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Complete aircraft optimisation is the process of performing an exergy analysis over the complete flight profile
and assessing the exergy flow and use throughout the system, to the point of total exergy destruction. A widely
published and referenced body of work detailing an application complete aircraft exergy analysis is the morphing wing
optimisation of a future advanced air to air fighter (AAF) [106, 100, 99, 79, 80, 81, 28, 26, 82, 83, 84, 66, 72, 71, 78].
This is an example of a widely applied application of exergy analysis where it is coupled with largescale optimisation
of a system, the principles of which are the same as discussed in previous sections.
The initial study into the AAF by Von Spakovsky [106] simplified the AAF into two subsystems, the propulsion
and airframe. The aim of the study, based on the DARPA morphing aircraft structures programme, was to perform
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Figure 9: Exergy Flow Diagram of a light aircraft [76] [77]
Figure 10: Exergy Flow through a generic commercial aircraft
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Figure 11: Exergy Flow Diagram of a generic commercial aircraft, derived from Camberos [29]
Figure 12: Grassmann diagram for the exergy flow through an aircraft, highlighting irreversibility locations
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Figure 13: Sensitivity analysis of morphing wing effectiveness, Butt [28]
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optimisation studies on the AAF airframe at different flight phases where the wing sweep, length, root chord length and
tip chord length were the parameters to be optimised. An empirical exergy analysis was undertaken on these different
configurations by Butt [28] with fuel consumption as the comparable output. A standard fixed wing fighter jet was
also included for comparison. The model does not include actual morphing technologies, just the geometries they
would create. Therefore to account for the additional components Butt [28] applies fuel and wing weight penalties as
shown in Fig. 13.
The conclusion to this work was that if the morphing technology had a weight and fuel usage that lay in the shaded
region of Fig. 13 the morphing wing provided a benefit in terms of total fuel consumption, as derived from an exergy
perspective.
This work was extended by another masters student of Von Spakovsky, Smith [99], who took the same model
of the AAF propulsion and airframe, but increased the complexity by including other exergy using devices such as
the ECS, fuel loop system, vapour compression loop system, electrical systems, central hydraulics systems, oil loop
system and flight control systems.
10. Improvement and Optimization Studies
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An example of multidisciplinary integrated design with the use of an empirical exergy model, Doty [38] showed
a surrogate model for a wing and turbofan engine, provided benefits from an exergy destruction point of view when
compared to individually optimised subsystems. Doty also compared the results of a first law analysis against that of
a second law exergy analysis, commenting that the second law approach showed which optimisations were actually
feasible (the concept of building directionality into the method).
The conclusions made by Doty [38] regarding the optimisation of integrated systems, echo those of Riggins [89]
[90] who performed integrated system exergy analysis mainly on hypersonic vehicles. Riggins was also involved with
the work of Marley [68] who took a lumped parameter model of a singlespool turbojet engine. The work highlighted
under what conditions the steady exergy analysis methods can be applied to the transient operation of a turbojet
engine. Marley [68] concluded that steady exergy analysis calculated engine thrust does track the actual thrust during
transient manoeuvres, through two analysis on a full aircraft and engine in different control volumes as seen in Fig.
14.
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Figure 14: Control volume definition for Marley study into entropy generation regions [68]
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Riggins’ [87] work on hypersonics is also documented in Camberos’ textbook [31], where Riggins discusses how
exergy analysis and optimisation provides significant advances in aerospace vehicle design, especially of hypersonic
flight, where there is a demand for a thorough and systematic integration of all subsystems. In this work, Riggins
compared the output of two entropy based optimisation routines for the vehicle against a known set of design variables
that yielded a maximum vehicle performance. The two entropy based method were (1) inclusive of the vehicle only
availability and (2) included (1) but with the far field wake entropy generation. Riggins showed using a simple
academic example (Fig. 15) that for hypersonic vehicles the wake entropy generation can be three to five times larger
than entropy generation associated with the vehicle itself (see Fig. 16), thus the farfield volume must always be
included in analysis.
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11. Mapping Exergy over the Variable Flight Envelope
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Ground based systems, such as power stations, which are typical subjects of exergy analysis have a relatively
consistent external environment, so can be assumed to have a constant reference state. The majority of exergy analysis
applied to aerospace vehicles makes the same assumption, whether this be a ground based propulsion system or
assuming the complete vehicle operates only in the dominant cruise phase of flight. It is accepted that the maximum
thrust obtainable from combustion is dependent on the composition of the environment in which the system operates,
exergy analysis broadens this to any transfer of heat or work being dependent on the environment. In such a way,
when exergy analysis is extended for use in aerospace applications it is evident that the external environment should
be far from constant through the mission profile. The thermodynamic variables of temperature and pressure will
significantly vary at sea level when compared to aircraft cruising altitude.
The reference state difficulty associated with aerospace exergy analysis has been studied by both Dincer [37] and
Berg [22] [23] [24].
At a more fundamental level, Sciubba [97] states in relation to chemical exergy selecting a set of reference substances and determining their average concentration in the earths crust. These reference substances are the basis
for the calculation of the exergy of the individual chemicals. The problem of how to identify a convenient ”average
composition” of the lito hydro and lower atmosphere was debated. Small differences in the reference elements produce substantial differences in the exergy values for most practical metals and fuels. At present, in practice all exergy
calculations are based on the reference environment published by Szargut [103]
Gandolfi [50] mapped a complete flight mission of a commercial aircraft, identifying exergy destruction at different
phases of flight. Fig. 17 are the results Gandolfi found for the distribution of irreversibilities among flight phases,
where whilst cruise (assumed to be 40 minutes) is the largest destroyer of exergy, it does not overshadow the other
phases as to make them negligible. A development of Gandolfi’s work would be to study the actual flight missions of
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Figure 15: Global control volume showing constituent vehicle, freestream, and wake control volumes by Riggins [87]
Figure 16: Detailed breakdown of instantaneous exergy losses at beginning of mission [87]
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Figure 17: Distribution of losses as a percentage of exergy in different phases of flight as stated by Gandolfi [50]
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Figure 18: (a) Turbojet cumulative rational efficiency for various reference states [37]
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airlines, as each aircraft can be used for a variety of different missions, often being used for missions the aircraft was
not primarily designed for.
Dincer [37] adapted the work of Clarke [34] on theoretical analysis of aircraft turbojet power plants, to include a
variable reference state, which Dincer compared against constant reference states at sea level and cruise altitude. The
chosen comparison metric was cumulative rational efficiency (Equation 25) a function of the thrust power extracted,
PT and the input exergy from fuel, Xin . Dincer defined this as found that irregularities in the instantaneous efficiencies
with flight distance are put into better perspective in terms of their impact on engine efficiency over an entire flight by
weighting them by this ratio. Thus, short phases of flight such as take off, where the turbojet is running at a higher
efficiency does not cloud the dominant phase of cruise flight.
Rt
PT (t) dt
ψcum = R 0t
(25)
X (t) dt
0 in
Fig. 18 displays the compared variable reference state and two constant states at sea level and cruise altitude.
The sea level reference state can be seen to over estimate the efficiency of the turbojet when compared to the variable
model, as well as having an inverse increase in efficiency during climb. This increase of efficiency during climb is
an illusion of negative exergy in the incoming airflow, which occurs due to the growing discrepancy between the
modelled sea level state and the actual state at altitude. The cruise altitude reference state creates a positive illusion
of exergy during the climb phase, starting from a fictitiously low engine efficiency. However as the flight mission is
dominated by cruise the plateau efficiency is close to that of the variable reference environment. Dincer [37] concludes
that the variable reference state should be used for aerospace power unit applications, with a cruise altitude constant
reference state only being used where the complexity of the variable reference state is not feasible.
Dincer modelled a flight mission dominated by the cruise phase of flight, which may be suitable for commercial
flights. For a military flight mission there is typically no dominating flight phase as such the only option would be to
use a variable reference state, or else errors in both numerical accuracy and predicted trends would be more evident
with the constant state model.
Etele [44] conducted a similar analysis to Dincer on varying reference states (T 0 ,P0 ) by taking a turbojet engine
and modelling the sensitivity of exergy efficiencies to the reference environment. Comparing analysis using reference
states based on ground level, cruise altitude and one that varies the conditions based on flight phase. In contrast to
the conclusions of Dincer, Etele was able to show that the exergy efficiency of a simplistic approach (ground level or
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Figure 19: Variance of fuel chemical exergy with environment temperature [58]
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cruise reference) gave a similar result to that of the complex variable reference state. However, the work of Berg [22]
[24] on timevariant exergy analysis concluded that for a complete system mapping the vehicle exergy must allow
for time variant analysis. Such an analysis allows for temporary storage of exergy. Berg undertakes a timevariant
analysis in a similar method to that of Gandolfi [50] [51], where the phases of flight are broken down, and reference
environment parameters are obtained for each of the broken down phases. Unlike Gandolfi, Berg is able to validate
his results against a simple UAV model [22] and then through a more complex commercial aircraft mapping [24].
The initial exergy reserves are calculated by the exergy of the jet fuel and/or batteries on board the aircraft. The
exergy of these sources is then mapped through each conversion process with the exergy destruction highlighted at
each stage, to the point of complete exergy destruction.
Hayes [58] noted that assuming a constant enthalpy of formation and standard molar entropy with pressure variation, the chemical exergy of the fuel changes with altitude (variable temperature) as shown in Fig. 19, where the sea
level chemical exergy content (at 298K) and cruise flight exergy content (at 217K) are highlighted. This relationship
suggests a decrease in propulsion efficiency with increasing altitude, where in cruise the exergy available is 98% that
available at sea level. A trend that is comparable to that seen with in use turbofan engine efficiencies.
The combustion of standard commercial aircraft fuel, Jet A (C12 H23 ), is given as follows:
C12 H23 + 17.75O2 → 12CO2 + 11.5H2 O
(26)
Assuming environment of T 0 = 298K and P0 = 100kPa standard composition of air for xk , the exergy released in
combustion of Jet A can be obtained using equation 14
Exc = µC12 H23 ,T M + 17.75µO2,0 − 12µCO2 ,0 − 11.5µH2 O,0 = 44.34MJ/kg
(27)
12. Developing Exergy for Future Aerospace Application
Since the development of the de Havilland Comet (the first commercial jet liner) in 1949, the energy intensity10
for each aircraft evolution has reduced, see Fig. 20. The Advisory Council for Aviation Research and Innovation in
10 Energy
Intensity is a measure of aircraft fuel economy, stating the amount of energy required to move one passenger one kilometre
26
Figure 20: Evolution of aircraft energy intensity [59]
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Europe (ACARE) [2] attributes this reduction to five major challenges for every future aircraft; (1) to meet market and
societal needs, (2) to maintain and extend industrial leadership, (3) to protect the environment and the energy supply,
(4) to ensure safety and security and (5) to prioritise research, test capabilities and education.
To protect the environment and the energy supply11 , the European Commission has outlined an acceptable pace for
emissions reduction in Flightpath 2050 [45]. In response, ACARE have laid out a set of targets12 that will enable the
aims of Flightpath 2050 to be achieved. One of these targets states that relative to the capabilities in 2000, by 2050;
“CO2 emissions per passenger kilometre [are to be] reduced by 75%, NOx emissions by 90% and perceived noise
by 65%” [2]. However, air transport is currently experiencing the fastest growth of any mode of transport [62], and
by 2035 it is estimated the required number of passenger aircraft will increase by 109% from 2015 levels [4]. Thus,
to meet the environmental targets original equipment manufacturers (OEMs) need to commit to keeping the trend in
efficiency improvements that is evident in the latest generation of aircraft.
The market driven needs of airlines are also pushing for lower energy intensity aircraft, as a reduction either means
lower more competitive air fares or a higher profit margin as a result of the lower fuel costs.
Recent improvements in propulsion efficiency are evident in the Airbus A320 NEO (New Engine Option) where
the development of Geared Turbofan (GTF) engines offers a 15% reduction in fuel burn [60]. The enhancement of
the aerodynamic efficiency was the driver for the introduction of span extension technologies on the folding wingtips
on the Boeing 777X. Advances in structural efficiency are noticeable in the proliferation of composite materials
technology which has increased from roughly 15% at the end of the 20th century to the Boeing 787 and Airbus A350
XWB where approximately 50% of the structure weight is composite [60].
27
Figure 21: Predictions of measures to be taken to reduce carbon emissions [3]
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12.1. How to Meet the Requirements for Future Aircraft?
These examples of evolutionary improvements to conventional configurations have contributed to aircraft now
being 70% more fuel efficient per seat kilometre than the de Havilland Comet [3]. A trend echoed by the European
Environment Agency who note “the environmental performance of European transport is slowly improving, but there
is still some way to go in decreasing oil consumption in transport” [46].
Thus the ACARE climate targets seem feasible, assuming technological developments continue at a similar rate.
However, the International Energy Agency [59] has highlighted a trend that conventional aircraft configurations are
near optimised, demonstrated by the plateauing improvements in energy intensity seen in Fig. 20.
Giurgiutiu [52] anticipates that research issues for future aircraft will be focused on “disruptive new and revolutionary structural concepts and unprecedented flight configurations”. This premise is verified by ATAG [3] with
the forecast that evolutionary improvements to current technology will account for less than 10% of the reduction in
carbon emissions (see Fig. 21), with the majority of reductions expected from biofuels and additional newgeneration
technology.
Hence aircraft manufacturers are researching technologies and configurations that may provide the required performance improvements. Propulsion efficiency improvements are expected from next generation turbofan development
as well as new concepts of open rotor engines and hybrid turbofanelectric propulsion as seen in the conceptual Airbus
EThrust aircraft. Future aerodynamic efficiencies move away from the conventional swept aircraft configuration to
High Aspect Ratio Wing (HARW)[25] and Prandtl box wing aircraft[32] to reduce vortex drag, blended wing body
concepts to minimise aircraft surface area and thus parasitic drag and also laminar flow wing technology seen in the
BLADE (Breakthrough Laminar Aircraft Demonstrator in Europe) project [60].
11 To
counter the contribution of aviation to global warming
worldwide with targets from the Air Transport Action Group (ATAG) [3].
12 Replicated
28
Figure 22: Airbus EThrust Concept (left) and NASA SUGAR Volt (right)
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12.2. Why an Energetics Based Approach is Applicable?
These revolutionary concepts need to be designed with no prior flight experience, thus requiring a more rigorous analytical process to supplement the lack of inservice performance information. This leads to the need for a
methodology that can support design of the complete vehicle as a system of subsystems in a common mathematical
framework [30]. The Breguet method (equation 1) has proved adequate for current practice where subsystems are
designed independently of the top level system, thus the propulsion, aerodynamic and structural efficiencies can all
be optimised separately. However, as commercial aircraft become more integrated vehicles, similar to what we see
in military and hypersonic design today, performance optimisation needs to be considered at the top level, in order
to account for the interactions between competing engineering disciplines, as failure to do so either places operating
limits on systems or cost large sums of money to correct.
The Breguet equation does not provide a systematic way to trade performance metrics across disciplines. Hence,
in order to facilitate highly integrated configurations, a new method of analysing the performance of an aircraft
is required that allows inefficiencies in processes to be tracked across the whole system and the development of a
decomposition strategy where all the components can be optimized to a systemlevel common metric. Such a holistic
approach would treat all systems and interactions under one universal property that quantifies performance.
As an example, the performance benefit of a battery driven electric engine is difficult to assess against the conventional fuel driven turbofan. Not only do the two technologies require different system configurations with a battery
storage requirement for electric propulsion (a mass that unlike jet fuel is not burnt off during flight), but the technologies have no common design metric.
12.3. The Slow Adoption of Exergy Analysis
Since the first use of the term available work by Gibbs [15], areas where exergy analysis has seen wide adoption
are those processes dominated by thermodynamics, such as heat engines and power generation technology (internal
combustion gas engines, steam power cycles, gas turbine cycles and renewable energy cycles), heat exchanges and
heat networking, air conditioning systems, cryogenics and chemical processes. Direct references for these are not
given as beyond the scope of this paper, but a comprehensive review of these technologies is provided by Sciubba [97]
and Ayres [15].
Much of the work in the aerospace sector on exergy analysis is subsystem specific, focused in the propulsion
community, given the traditional thermodynamic nature of the system, and as such read across from earlier uses of
exergy analysis. However in the aerospace community, outside of propulsion, there has been a slow adoption of
thermodynamic optimisation and the exergy method [97].
Ayres [15] gives the reason for the slow adoption of exergy being due to confusion and misunderstanding associated with thermodynamics, which essentially is generated due to many of the variables not being physical variables
people can measure, including entropy, enthalpy, internal energy, heat, Gibbs free energy and exergy, whilst these are
mathematically proven within the theory, they cannot be physically visualised. Noting the difficulty in explaining the
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concept of exergy, Zabihian [107] presented a paper purely focused on how to comprehend the concept of exergy and
teach it to students, focusing on a more global understanding of the methodology rather than to just one application
as many authors focus.
Edwards [42] argues the adoption of exergy methods has been slow in the field of combustion as exergies are
approximately equal to the respective lower heating values, thus providing little benefit in real calculations.
A further obstacle is a consistent definition of exergy, which is exacerbated by the fact different authors have
used various terms to refer to exergy and the term exergy for slight different purposes. Sciubba [97] and Ayres [15]
provide examples of this including; available energy, Arbeitsfähigkeit (translated from German as working capacity),
exergie (German), availability, available work, available useful work, useful energy, distinguishability and essergy
(an abbreviation of essence of energy). Sciubba [97] states the accepted terminology is now exergy (with a few
American authors still using the term availability). Justified by the definition of such work being based on energy
meaning internal work, from the Greek en and ergon, and then changing the prefix to the Greek ex suggesting external
application to work.
Working with an exergy metric would also require significant change to the design practice, as typically aircraft
subsystems are optimised for their individual requirements to the optimal operating conditions, irrespective to the top
level optimisation and efficiency of the complete system. A critical part of implementing an exergy based approach is
the development of a decomposition strategy where all the subsystem components can be optimized to a systemlevel
common metric. This would be no easy task, as major subsystems of aircraft are designed by different companies
and incorperated at a higher level, such as the Airbus and engine suppliers relationship.
12.4. Case Study  Next Generation Aircraft  High Aspect Ratio Morphing Wing
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To conclude the paper, below is a case study looking at how exergy analysis could be used for high aspect ratio
morphing wing aircraft, aiming to trigger the readers mind with possible applications of such a method.
The majority of the Flightpath 2050[45] carbon reduction targets are assumed to occur due to additional technologies [3], a term which refers to technologies to be incorporated into aerospace systems that are not currently present
and thus can’t be improved from a base state. One such technology being considered is that of a morphing wing,
where wing geometry is substantially changed in order to improve aircraft performance by either expanding the flight
envelope or replacing conventional control devices for improved aircraft control. In effect it aims to allow real time
vehicle adaptation, enabling optimal performance over this wider flight envelope. Morphing has been the subject of
numerous studies over the past years, however an inflight morphing device on an operational commercial aircraft is
yet to be seen.
Morphing wing has been receiving more attention in recent years, due to the develop of next generation High
Aspect Ratio Wing (HARW) commercial aircraft. As shown in Fig. 23 the trend is for higher aspect ratios for newer
aircraft, primarily due to the increase in size and also the improvements of the lift the drag ratio.
The reason why morphing has not seen fullscale application in aerospace is not just due to the conservative design
approach of the industry, but that changing the aerodynamic profile of a wing requires some form of actuation system,
which must be powered and adds weight to the aircraft. Thus, any performance benefit morphing provides must
outweigh the penalty due to additional weight and power. However, there is an absence of unifying metric that allows
accurate comparison of the wide range of performance characteristics and different morphing technologies.
Also, consider a morphing device that significantly changes the aspect ratio of the wing. In current research the
wing is treated as a rigid body [100], and the benefits of drag reduction are compared to the losses in morphing the
wing to this position. However, the aeroelastic properties of the wing have also been significantly altered. Whilst
affecting aircraft flight dynamics this also impacts structural dynamics including wing damping. Furthermore, any
twist in the wing changes the lift distribution, all of which has to be considered under a single metric.
However, for a next generation HARW aircraft there are two major issues, firstly longer wings means a larger
wing root bending moment under gust loading and secondly airports can only accommodate a limited wing span, a
limit HARW aircraft will exceed. To counter the issues raised here, morphing wing may allow some form of Load
Alleviation Devices (LAF) on the HARW to lower the wing root bending moment, and also allow wing folding at
airports to accommodate gate restrictions, such as with the Boeing 777X. Designs of such devices again need to be
considered under a single optimisation metric. It is therefore the authors opinion that exergy analysis and EGM may
provide a capability that allows the realisation of this type of aircraft.
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Figure 23: Aircraft Aspect Ratio against introduction year
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12.5. Future Work in Exergy Based Aircraft Design
The majority of exergy studies focus on steadystate performance analysis and adopt simplified models for flight
dynamics and morphing, and estimate the exergetic cost of such devices in global performance terms such as weight
and fuel burn penalties. As a result, the future direction for the development of exergy is the definition, calculation
and analysis of dynamic exergy for flexible aircraft; where the effects of variables such as wing flexibility on stored
strain energy and consequently exergy destruction will be explicitly studied. Developing a method for selecting the
appropriate reference state will be another area of interest. The selection of a reference state is straight forward for
steadystate analysis, however, in a dynamic scenario the exergetic content of the atmosphere over the course of a
timedomain simulation must be considered to accurately account for a varying reference frame.
One of the common themes throughout the review is the fact that the work has been completed within the academic
community on highly simplified examples. This is useful for proving the theoretical foundation of exergy analysis,
but unless the method can be proven for more complex real world systems it is unlikely to be adopted into industry.
Numerous studies have been conducted into optimisation of specific aircraft subsystems with exergy, such as the
Environmental Control System (ECS), propulsion and wing / aerofoil geometry. The concept of complete aircraft
mapping has been attempted by a few authors to show exergy destruction variation over different stages of aircraft
flight.
13. Conclusions
690
This review has discussed the previous applications of exergy analysis in the aerospace sector, focusing primarily
on commercial application. The limitations have been derived and discussed along with the potential benefits to
further proliferation of this second law method in the aerospace community. It has been shown how exergy analysis
and mapping exergy destruction provides:
• a consistent common currency to allow consistent accounting across sub systems
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• lossproducing mechanisms can be readily mapped at the system level
• analysis space provides physically possible/meaningful bounds
• provides foundation for robust and efficient optimization
• should produce same result regardless of technique utilised, and also match the results of first law implicit
methods, but providing additional insight on top of this
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• an understanding of how one system influences and interacts with other nondiscipline specific subsystems
Acknowledgements
This research is supported by an Engineering and Physical Sciences Research Council (EPSRC) Industrial Cooperative Award in Science & Technology (CASE) grant in collaboration with Airbus Group.
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