Modelling and Simulation of a Propulsive Hybridisation for a Light Fixed-wing Aircraft Modellering och simulering av hybridisering av framdrivningssystem för ett lätt fastvingat ygplan

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Modelling and Simulation of a Propulsive

Hybridisation for a Light Fixed-wing

Aircraft

Modellering och simulering av hybridisering

av framdrivningssystem för ett lätt

fastvingat ygplan

By

Axel Yezeguelian

Master thesis in Second cycle Aeronautics, carried out at

Safran R&T Centre - Chateaufort

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Supervisor (KTH): Raaello Mariani KTH Royal Institute of Technology

Department of Aeronautical & Vehicle Engineering Teknikringen 8, 114 28 STOCKHOLM

Supervisor (Safran): Gaëtan Chesneau Etablissement Safran Paris-Saclay Rue des Jeunes Bois

Châteaufort CS80112

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Abstract

Propulsive hybridisation ts in with the sustainable development policies of many com-panies which are part of the transportation industry. Actually, it makes it possible either to reduce fuel consumption or to improve the aircraft performance at a xed fuel burn. However, the current technologies of batteries restrain a more regular use in light aviation. For this project this issue is conrmed as both the quasi-static perfor-mance assessment and the dynamic studies show that the endurance objective cannot be improved with Li/Ion batteries. However, it is possible to act directly on the en-gine performance by placing a thermal energy recovery system on exhaust gas pipes to take advantage of their high temperatures, greatly boosting the aircraft performance in cruise.

Sammanfattning

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Acknowledgements

First of all, I would like to thank Mr Chesneau, my tutor at Safran, for his good supervision and his patient guidance. My grateful thanks are extended to the whole E&P sta at Safran. I would also like to thank Mr Mariani from KTH for his supervision and his assistance.

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List of Figures

1.1 Typical mission [6] . . . 13

1.2 Pacelab interface (Structure, Properties and 3D views) . . . 14

1.3 Project specic Pacelab operation [9] . . . 15

1.4 Example of Amesim model for a four-cylinder engine [10] . . . 16

2.1 Serial hybrid architecture [6] in motor (left) and generator (right) modes 18 2.2 Parallel hybrid architecture [6] in motor (left) and generator (right) modes 19 2.3 Serial-parallel hybrid architecture [6] in motor (left) and generator (right) modes . . . 19

3.1 Comparison of the durations per ight phase for the two software version models (v3.5 and v6.2) . . . 23

3.2 PaceLab APD mission prole for the hybrid Studied Light Aircraft . . 27

3.3 PaceLab APD graphical result . . . 29

3.4 PaceLab APD processed matching constraints graph . . . 30

3.5 Routine of the adapted Raymer's method . . . 32

3.6 Take-o notation as dened by Gudmundsson [17] . . . 32

3.7 Dierent graphical results retrieved from the optimisation algorithm . . 38

3.8 PaceLab APD graphical result for e = 200 Wh/kg (left) and e = 500 Wh/kg (right) . . . 39

3.9 Evolution of relative endurance variation (with respect to conventional Studied Light Aircraft) with battery energy density . . . 40

4.1 Amesim model of a Mean Value Engine (based on [10]) . . . 42

4.2 Simplied block diagrams for throttle setting (left) and elevator setting (right) [10] . . . 43

4.3 Specic fuel consumption network curves for a gasoline engine [21] . . . 44

4.4 Sketch of an Organic Rankine Cycle [22] . . . 46

4.5 Chosen architecture for the Organic Rankine Cycle . . . 46

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List of Tables

2.1 Characteristics of the components in the Energy Propulsion Chain [6] . 21 3.1 PaceLab APD trade study result . . . 28 3.2 Solution of the adapted Raymer's method . . . 35 3.3 Python numerical results . . . 38 3.4 Relative deviation of endurance between the conventional and hybrid

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Nomenclature

EpropCL Propulsive energy at climb (J)

EpropT O Propulsive energy at take-o (J)

PpropCL Propulsive power at climb (W)

PpropT O Propulsive power at take-o (W)

¯· Mean value

δe Elevator setting (rad)

˙

Ebat Battery energy ow (W)

˙

mF uel Fuel mass rate (kg/s)

ηp Propulsive eciency

ηICE Eciency of the internal combustion engine

ηm Eciency of the electric motor / generator

γ Proportion of additional mechanical power provided by the ORC µ Runway friction coecient

ρ Air density (kg/m3)

σICE Throttle setting of the ICE

σm Throttle setting of the electric motor

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CD Drag coecient

CL Lift coecient

CD,0 Zero-lift drag coecient

CLT O Lift coecient at take-o

D Drag force (N)

d Electric motor specic power density (W/kg) dcooling Power density of the cooling system (W)

e Battery specic energy density (Wh/kg or J/kg) EBat Energy of the charged batteries (J)

EElec Electric energy consumed for propulsion (J)

EF uel Fuel energy consumed for propulsion (J)

eF uel Specic energy density of fuel (J/kg)

g Gravitational acceleration (m/s2₎

h Altitude (m)

HE Degree of energy hybridisation

HP Degree of power hybridisation

hCruise Cruise altitude (m)

ICE Internal combustion engine K Lift-induced drag factor L Lift force (N)

mBattery→energy Mass of the battery pack considering energy requirements (kg)

mBattery→power Mass of the battery pack considering power requirements (kg)

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mcooling Mass of the cooling system (kg)

mEM Electric motor mass (kg)

mfmax Fuel tank capacity (kg)

mF uelClimb Fuel mass required for climb (kg)

mF uel Fuel mass (kg)

M T OW Maximum take-o weight (N)

p Battery specic power density (W/kg) Pr Required propulsive power (W)

Pdeicing Electrical power necessary to use the de-icing system (W)

Pextra Mean additional power needed at climb to fulll the constraints when

taking o at MTOW (W)

pORC Power density of the ORC (W/kg)

Prec Recharge power of the batteries (W)

Pshaf tEM Shaft power of the electric motor (W)

Pshaf tICE Shaft power of the internal combustion engine (W)

Pthermal Thermal power coming from the electric motor Joule eect (W)

R Prescribed range (m) S Wing reference area (m2) srun Rolling distance (m)

SOCmax Maximum permitted state of charge (%)

SOCmin Minimum permitted state of charge (%)

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T T C Time to climb (s)

V Aircraft true air speed (m/s) V2 Take-o safety speed (m/s)

VV Rate of climb (m/s)

VCruise Cruise true air speed (m/s)

VLOF Lift-o speed (m/s)

VStall Stall speed (m/s)

W0 Take-o weight (N)

We Empty weight (N)

Wf Fuel weight (N)

Wbatref Battery weight reference, given in PaceLab APD (N)

Wbat Battery weight (N)

Wcooling Weight of the cooling system (N)

Wdeicing Weight of the de-icing system (N)

WEMref Electric motor weight reference, given in PaceLab APD (N)

WEM Electric motor weight (N)

Wreinf orcement Weight of the structural reinforcement at MTOW (N)

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Chapter 1 Introduction

1.1 Background

In a world in which environmental concerns have become a global challenge, it is more and more important to consider alternative technologies for aircraft propulsion. Actually, although the emission of greenhouse gases due to industrial activities has dropped by 14 % in the U.S. between 1990 and 2016 [1], the air pollution due to transportation has conversely increased by 20 % during the same period, largely because of the increase in number of ights [1]. In addition, air trac is responsible for 2 % of global greenhouse emissions [2].

Therefore, hybridisation technologies based on combustion and electrical propulsion have become a strong R&D eld for numerous aerospace companies. In fact, electric propulsion can be used to improve the performance of an aircraft, for instance its range, endurance, or rate of climb, at a xed fuel consumption.

The French engine-maker Safran is particularly interested in hybridisation, as it could favourably aect its future projects, by providing a signicant positive environ-mental impact from the aerospace world.

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1.2 Objectives

The objective of this project is to study the feasibility and the benets brought by a hybridisation of a light xed-wing aircraft, in collaboration with Safran SA. This aircraft is referred to as SLA (Studied Light Aircraft) throughout the report.

1.3 Design & performance requirements

The main objective of the aircraft manufacturer is to maximise the endurance of the SLA [6]. To do so, the fuel tanks should ideally be full at take-o. However, both the manufacturer and the regulations impose certain take-o and climb requirements, e.g. take-o rolling distance and climb rate, and the sole SLA conventional engine cannot provide enough power to fulll these constraints when taking-o at full fuel tanks, because the aircraft is too heavy. The aircraft endurance capability is therefore limited by the maximum allowed amount of fuel, which is a percentage of the full amount.

Two alterations can be performed to the conventional version of the SLA to overcome this issue, knowing that the geometry of the aircraft cannot be modied:

Change the internal combustion engine (ICE) to a more powerful one Add an electrical system (batteries/electric motor)

At a given additional power, the mass change due to the new ICE is obviously lower than the one due to the electrical system, mainly due to the current low energy densities of batteries compared to fuel. However, the electric system enables additional features: In case of engine failure, the available electric energy can be used as a back-up power source to increase the range of the aircraft so that it can reach a safe landing eld. It means that the batteries should be recharged as quickly as possible, as soon as the electric motor is turned o. If the batteries are empty, no power source is available and the descent rate is xed by the lift-to-drag ratio.

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In light of these features, Safran has favoured the electric hybridisation for improve-ment of the aircraft's performance. However, due to the disproportion between fuel and battery energy densities, the electric motor should be used as little as possible. Intuitively, in order to fulll the ground roll distance and time-to-climb constraints, it is necessary to "boost" the ICE with the electric motor during take-o and part of the climb. The challenge is then to properly choose the shaft power of the electric motor and the altitude at which the boost function is turned o during climb. The added system sizing is limited by the MTOW, which cannot be increased by more than 8.5 % [6] to keep the structural integrity of the landing gears.

Fig 1.1 is a sketch of the typical mission:

Figure 1.1: Typical mission [6]

An additional constraint is the requirement for the batteries to be recharged dur-ing ight, in order to avoid the necessity of external equipment for rechargdur-ing on the ground. This process can be achieved in reversing the electric motor so that it generates electricity. The unboosted part of the climb segment requires a full utilisation of the ICE, and there is no extra power to recharge the batteries. Therefore, as soon as the aircraft begins its cruise section of ight, the batteries are recharged at the maximum generator power so that the electrical consumers can be supplied for most of the cruise phase.

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is xed as well [6]. In these conditions, longer is equivalent to further: maximising endurance amounts to maximising range.

The nal constricting parameter is in the impossibility of altering the structure or the conguration of the SLA, which would impact its aerodynamic performance.

1.4 General steps

1.4.1 Performance evaluation

Endurance objective is the dening specication of the whole study: a typical sat-isfactory improvement would be of around +40 %. The quasi-static study outcome is a sizing of the added system elements, namely the electric motor and battery, so that the endurance is maximised and the manufacturer and regulation constraints are fullled.

In order to carry out the performance evaluation, PaceLab Aircraft Preliminary Design (APD) software was used. This platform is developed by TXTGroup, and enables a pseudo quasi-static assessment of the performance of a given aircraft, as dened by geometry, aerodynamic performance, and propulsion among others, and is based on the design approach by Torenbeek [7] in conjunction with that proposed by Raymer [8].

Fig 1.2 shows a screenshot of the PaceLab interface.

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Based on a set of known inputs, PaceLab provides outputs related to the ight envelope, payload vs range, specic air range as a function of altitude, speed and weight, mass budget, ight mission schedule, as well as take-o and landing performance.

Figure 1.3: Project specic Pacelab operation [9] In order to complete the analysis, the following procedure is applied:

Retrieve a le containing the model of the conventional SLA (geometry, aerody-namics, propulsion...) created on an obsolete version of PaceLab APD.

Import the model into the latest version, and redening all the input parameters such as fuselage and lifting surfaces shapes, nacelles, polars, thrust data, design missions and many others.

Implement the hybrid system using the latest PaceLab APD model. Analyse the results of the simulation.

Find an optimal design of the hybrid system, using the trade study functionality of the software.

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Safran had already carried out a study to assess the endurance enhancement when electrically boosting the SLA, but without any constraint consideration [6]. Indeed, the previous study was done on a previous version of PaceLab APD, which did not include any electric motor feature, preventing one from carrying out a quantitative study.

1.4.2 Energy optimisation

The second step in the process is to rene the model considering transient perfor-mance associated to hybridisation, where the sizing output obtained with the quasi-static approach becomes an input of the dynamic modelling. It should be noted that there is no sizing possibility in a dynamic dierential equation solver. As a result, a multiphysics simulation software called Amesim, developed by Siemens, was used. This simulation software is similar to Matlab/Simulink, but is more intuitive and adapted to multiphysics modelling, whereas Simulink is more adapted to signal processing. Indeed, it contains dierent libraries with native components, whose behavioural equations are already coded. Each library refers to a type of physics, such as Signals, Mechanics, Aerospace, Fluids, all of which are necessary for this study. An example of Amesim model is shown in g 1.4.

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Chapter 2 Hybrid propulsion

Hybridisation consists in merging two dierent techniques, in the current case com-bustion and electricity, into a propulsive system, with the aim of achieving either better fuel economy or better performance [11].

2.1 Arrangement of the propulsive subsystems

Depending on the vehicle, it is necessary to select an appropriate architecture of the hybrid system, focusing on the way the components of both the electric and heat-engine systems are linked together. The three main architectures are described in subsections 2.1.1 to 2.1.3 [5].

2.1.1 Hybrid electric serial architecture

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Figure 2.1: Serial hybrid architecture [6] in motor (left) and generator (right) modes

2.1.2 Hybrid electric parallel architecture

Unlike the serial architecture described in subsection 2.1.1, the mechanical power comes from both the electrical system and the internal combustion engine. The two systems are linked via a mechanical node, for instance a gearbox, which enables to nely control the amount of power coming from the engine with respect to the power provided by the electric motor. As a result, the propulsive system can deliver high power, but with a relatively low eciency.

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Figure 2.2: Parallel hybrid architecture [6] in motor (left) and generator (right) modes

2.1.3 Hybrid electric serial-parallel architecture

The serial-parallel architecture is a good trade-o between the two previously pre-sented, as it combines the advantages of each. Nonetheless, this kind of architecture is not suitable for aviation, as it requires complex control systems [5], which results in extra mass and additional risk in case of failure.

Nevertheless, this architecture is becoming more and more used in the car industry, as in the case of the Toyota hybrid vehicles [11].

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2.2 Architecture for the Studied Light Aircraft

Considering all the statements in section 2.1 and the capabilities of PaceLab APD, it was decided by the team working on the previous project to consider a parallel architecture to implement in the SLA.

2.3 Battery technologies

The battery technology is the main limiting factor as far as the propulsive system eciency is concerned. Indeed, it is a component that currently has very low gravimetric specic energy, also known as energy density.

Nowadays, the best available technology is the Lithium/Ion battery system, but its gravimetric specic energy hardly exceeds 250 Wh/kg, with a gravimetric specic power of around 2000 W/kg [4] [5]. New technologies that could reach higher energy densi-ties are currently under development [12]. Two examples can be cited, both retaining lithium anodes: Lithium/Sulphur and Lithium/Air.

The Lithium/Sulphur technology appears to be closer to being available on the market, as Sony announced a model for 2020 [13]. This technology has a double-advantage:

it has been demonstrated that it can reach a specic energy of 500 Wh/kg the use of sulphur makes it relatively cheap

Lithium/Air battery is a more long-term alternative, but it is expected to reach a specic energy of 1000 Wh/kg [5], hence four times higher than Li-ion. However, this technology is expected to be ready for 2050 [14].

2.4 Electric motor/generator

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2.5 Power management and distribution system (PMAD)

This device is mainly composed of cables, inverters and controllers. It enables the conversion of direct current to alternative current, which is generally required to run an electric motor, and can also be used to control the amount of power coming from the engine with respect to the amount provided by the electrical system [5].

2.6 Selection of components for the Studied Light

Air-craft

The technical specications discussed in sections 2.3 to 2.5 have been considered in relation to the values chosen for the rst project associated to the SLA, and which were used for comparison purposes.

The mass of the battery pack corresponds to the mass satisfying both the energy and power needs [5], as shown in eq 2.1.

mBattery = max(mBattery→energy, mBattery→power) (2.1)

Component Specic Power Specic Energy Eciency Battery (Li/Ion

base) 1000 W/kg 200 Wh/kg (cell) -110 Wh/kg (pack, with power man-agement & armour-ing)

70 % (limits of state of charge: 20 % to 90 %)

Electric motor 1600 W/kg / 85 %

Table 2.1: Characteristics of the components in the Energy Propulsion Chain [6]

2.7 Degree of hybridisation

Some typical parameters are used to size the level of hybridisation of a propul-sive system, and are dened as "degrees of hybridisation", based on energy or power considerations [15]. They are dened in eq 2.2 and 2.3.

HP =

Pshaf tEM

Pshaf tEM + Pshaf tICE

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HE =

EElec

EElec+ EF uel

(2.3)

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Chapter 3 Quasi-static sizing approach

3.1 PaceLab APD

3.1.1 Migration

The Energy & Propulsion team within Safran worked previously on a PaceLab model of the considered non-hybrid SLA. The main issue was that this model was built on an obsolete version of the software. Requiring the migration of this model to the latest version of the software and due to issues with the built-in migration option, it was decided to build a new model on the latest version of the software based on the former model. All the parameters were dened accordingly.

After completing the rebuild, the new model was validated against results obtained with the old one using a pre-determined set of inputs. The comparison of these two models is shown in g 3.1.

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A comparison of the outputs of the two models shows a large relative dierence in terms of duration or fuel consumed during the landing phase, which may be attributed to the phase modelling upgrade done by the software. However, landing is very short and negligible in terms of fuel consumption compared to other phases. Moreover, this phase is not studied in this project. All the other segments and the total values are less than 1 % dierent in absolute values. The new model is thus considered accurate enough to legitimate the further results.

3.1.2 Empty weight redenition

The empty weight of the hybrid SLA is greater than that of the conventional SLA. Indeed, the following increments should be considered [6]:

the de-icing system weight, whose value together with the power consumption were assessed in Chesneau [6]. It was decided to install the de-icing system on the hybrid version wings, so that the issue of ight cancellation is removed. In this case, if necessary, it is activated in cruise. For all the results presented in this chapter, it is installed -mass impact- but not activated -no power impact-. a resizing increment: the new MTOW requires a reinforcement of the aircraft

structure, especially for the wings. The value of this reinforcement was assessed in Chesneau [6].

a cooling system that has two functions: cooling down of the electric motor when boosting, and recovering thermal Joule eect energy from the generator to supply power to the de-icing system. A density dcooling, in units of kilogram per evacuated

thermal kilowatt, for the cooling system was assessed in Chesneau [6]. As a result, the mass of the cooling system can be dened as:

mcooling = dcooling· Pthermal = dcooling·

1 − ηm

ηm

· Pshaf tEM (3.1)

3.1.3 Hybridisation: parallel architecture

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to a propeller and one block associated to an electric motor linked to a propeller. As it stands, it is not possible to split the propeller from the engine. However, it is possible to superimpose the two blocks at the same location to model the hybrid system, and set calibration factor to 50 % on both propellers in order to simulate the model as a single propeller aircraft.

PaceLab APD imports thrust tables to assess the performance of the engines for dierent Mach numbers, altitudes and temperatures. Each thrust table characterises one engine, which means that two of them are necessary for the hybrid system:

The thrust table for the conventional engine block was previously designed by Safran so that it ts the considered reciprocal engine of the SLA -power and fuel ow data retrieved and adapted from the engine-maker-.

The thrust table for the electrical motor + propeller system is straightforward. The electrical boost function has to be used during take-o and part of the climb. The normalised available thrust is therefore 1/TAS for take-o and climb -the multiplying factor is the electric motor reference power-, and 0 for the other segments, corresponding to idle motor conditions. It means that, as far as the electric motor is concerned, its power is assumed to be constant with speed and altitude, and it is therefore not aected by incoming air ow as in the case of the combustion engines.

It is then possible to add a battery block to the aircraft equipment mass breakdown. This block retrieves the required electric power and electric energy for the considered mission and it sizes the mass of the battery pack depending on the densities of the chosen technology.

Then, a trade study is run to size the hybrid system. This feature permits the variation of some design parameters to retrieve, for each design, specic outputs related to the aircraft's performance, and visualise if the constraints are fullled or not.

In compliance with the specications for the project, the constraints are to keep unchanged the rolling distance and the time to climb of the conventional SLA. The fuel mass that can be carried is limited by the MTOW. The performance related output is the endurance of the mission. The design variables are the duration of the boost and the shaft power of the electric motor.

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to idle within the climb phase, as required. The issue can be resolved, as the software includes a feature that makes it possible to modify the calculation methods, by adding a patch-code from C#. Therefore, for this study, it is possible to concatenate two climb segments, and modify the methods so that the electric motor is in driving mode for the rst segment, and in idle mode for the second. A boolean parameter was included in the climb phase in order to allow or discard the electric boost.

Another drawback of the software is that the battery block is only considered as a mass breakdown, i.e. there is no state of charge account. To overcome this issue, acknowledging that it is not fully accurate, a calibration factor for the battery mass was set, depending on the limits of SOC. As stated in section 2.6, the battery SOC limits are set to 20 % (lower bound) and 90 % (upper bound). This range corresponds to the optimal operating conditions of the battery, in terms of voltage and current [6]. The calibration factor is dened in eq 3.2, and the new battery mass formula is eq 3.3

α = 1

SOCmax− SOCmin

(3.2)

mBattery = α · max(mBattery→energy, mBattery→power) (3.3)

Some problem, which is linked to this statement, appears: it is most likely dicult to model recharge without SOC consideration. Thankfully, there is a "Refueling" segment which is modelled in PaceLab APD. This segment can be set in "Providing" mode, which means that some fuel is transferred from the modelled aircraft to another. Basically, the battery recharge can be modelled as a fuel leakage: some shaft power converted to electricity is used to recharge the battery, which causes an increase of fuel ow in the ICE. The transferred fuel mass and mass rate are respectively proportional to the battery energy to recharge and the generator power, as shown in eq 3.4 and 3.5.

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Figure 3.2: PaceLab APD mission prole for the hybrid Studied Light Aircraft

3.2 Results

A trade study has been conducted, with the following input variables:

Sizing parameters: boost nal altitude, which corresponds to the altitude at which the "rst" climb segment is nished and the "second" one starts; and reference shaft power of the electric motor.

Optimisation variable: endurance

Constraints: rolling distance, time to climb

PaceLab APD does not proceed like a constrained algorithm: the constraints are not an input for the sizing process. However, for each tested point, a deviation with respect to the constraints is displayed. It is necessary to manually nd the point for which the deviations for the two constraints are positive, representing the case for which the constraints are fullled, and which gives the maximum endurance.

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Table 3.1: PaceLab APD trade study result

It can be observed from table 3.1 that it is not possible to reach the conventional SLA endurance value, as indicated in the " ∆Endurance

Conv LSA Endurance" column. It means that

the hybrid system does not increase the endurance of the SLA although it is its primary goal. This is possibly caused by the additional mass corresponding to the hybrid system, which does not allow carrying enough fuel for improving the endurance.

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Figure 3.3: PaceLab APD graphical result

Note: The background curves are typical results retrieved from the former study [6]. The optimal point corresponding to point 185 in table 3.1 is the blue dot on the graph in g 3.3. It is easy to see that it is the point that is the most up-left in the "accessible area", represented by the white zone. This point is below the x-axis, which means that the endurance is not increased with respect to the conventional SLA. The hybrid system is not useful for increasing endurance, as the hybrid system makes it possible to carry more fuel, but it is consumed more rapidly. However it can still be used as an electric supply for the de-icing system, which is installed on the wings, with its mass considered in the empty weight, but not activated in the mission performance assessment, therefore it does not consume electric power. Moreover, in case of engine failure, the electric motor can be used as a backup propulsive power source.

3.3 Matching constraints diagram

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area" in the graph, for which all the constraints are fullled, is the area underneath the curves of all segments.

Therefore, another trade study is run using the conventional SLA model, with the following parameters:

Design Parameters: reference thrust & take-o weight Objective Variable: weight over propulsive power (W/P )

Constraints: either take-o rolling distance, time to climb or endurance; respec-tively for take-o, climb and cruise

These trade studies allow one to retrieve the corresponding points for each curve in g 3.4.

Figure 3.4: PaceLab APD processed matching constraints graph

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power without bringing extra mass, e.g. a more powerful but not heavier engine. The extra relative power need would be approximately +9 %, which is obviously smaller than the +14 % needed for the battery/electric motor propulsive chain.

At this point, and in order to legitimate all the results retrieved from PaceLab APD, it was decided to explore other methods to size the hybrid system and assess the performance of the hybrid version of the SLA.

3.4 Theoretical sizing methods

3.4.1 Adapted Raymer's method

Daniel Raymer created a pre-sizing method for aircrafts, based on an initial estimate of the TOW [8]. Given this estimate, the following values are computed:

We

W0: based on statistical data, an empirical expression was found by Raymer

We

W0

= A · W₀B (3.6)

where A and B depend on the aircraft category (UAV, general aviation, freighter. . . ) Wf

W0: based on Breguet equation [16] (R is the prescribed range)

Wf W0 = 1 − e−R·c0·gL/D (3.7) W0 = Wpayload 1−Wf W0− We W0

The solution is obtained when the initial estimate coincides with the nal computed value.

This method is only applicable for conventional aircrafts, because:

it only considers fuel-based propulsive chain, through the Breguet equation: it implies a mass change, which is inadequate for electric power.

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The Raymer's method can be modied to consider the hybrid system sizing for the SLA. The empty weight increment for the hybrid version is xed, therefore no statistical data are needed for the structure. However, the additional mass due to the hybrid system can be sized considering the constraints to be fullled.

Fig 3.5 depicts the routine that enables the sizing of the hybrid system:

Figure 3.5: Routine of the adapted Raymer's method

The given constraints associated to a new MTOW cause an increase of propulsive power and energy compared to the conventional version.

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Actually, the most accurate srun equation is a complex integral, which is the follow-ing [7]: srun = 1 2 · g · Z V_LOF2 0 dV2 T (V ) W0 − µ − (CD − µ · CL) · 1 2·ρ·V2·S W0 (3.9) However, this integral is not analytically solvable. It is thus approximated at VT O = VLOF_√

2 to get the sizing equation 3.8.

srun is xed

VLOF = 1.1 · VStall, as dened in regulations [18].

µ0 _{= 0.02 + 0.01 · C}

LT O, as assessed empirically by Torenbeek [7].

CLT O is retrieved from PaceLab

Therefore, ¯T can be computed. Then,

Pprop_{hybT O} = ¯T · VLOF → ∆PpropT O = Pprop_{hybT O} − PpropconvT O (3.10)

Eprop_{hybT O} = Pprop_{hybT O} ·

srun VT O = Pprop_{hybT O} · srun 0.7 · VLOF (3.11) ∆EpropT O = Eprop_{hybT O} − EpropconvT O (3.12)

For climb, the sizing equation is [19]: Pr = VV · W + ( 1 2· ρ · S · V 3_{· C} D,0+ K · W2 1 2 · ρ · S · V ) (3.13) VV is the rate of climb. Even if it is not accurate, for this algorithm, Pr should

be constant, as no time inuence is permitted whatsoever: it is only a matter of mass budget. Therefore, average values of VV, V and W are taken, as follows:

¯

V = V2 + VCruise

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¯ VV = hCruise T T C (3.15) ¯ W = W0 (3.16)

Then, the additional power and energy can be computed:

∆PpropCL = Pr(W = ¯Whyb) − Pr(W = ¯Wconv) (3.17)

∆EpropCL = ∆PpropCL · T T C (3.18)

The hybrid system is sized as follows: mBattery =

1

ηp · ηm· (SOCmax− SOCmin)

·

max(max(∆PpropT O; ∆PpropCL)

p ;

∆EpropT O + ∆EpropCL

e ) (3.19)

mEM =

max(∆PpropT O; ∆PpropCL)

ηp· d

(3.20) Finally, all the design weights are computed:

We = Weconv + Wdeicing+ Wreinf orcement+ Wcooling

Wf

W0 is given by the Breguet equation

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A solution is obtained when the initial estimate matches the nal computed value. W0/M T OW 99.9 % We/Weconv 104.0 % Wbat/W0 3.2 % WEM/W0 0.8 % Wf/W0 16.6 % Endurance change 0.64 %

Table 3.2: Solution of the adapted Raymer's method

It can be observed in table 3.2 that, for the considered battery technology, at 200 Wh/kg per cell, 110 Wh/kg for the pack [6], the additional mass required for the hybrid system only makes it possible to improve the initial endurance to an inconsiderable extent.

This adapted Raymer's method only considers mean values of each state variable. It is much simpler than the PaceLab operation, but the result is inevitably less accurate. It is however interesting to compare the two methods, as presented in subsection 3.4.3.

3.4.2 Optimisation algorithm

The main issue with PaceLab APD is that some toolboxes are dicult to evaluate. At this point, it was decided to implement a constrained optimisation algorithm in Python in order to try to retrieve the PaceLab results, with a time-dependent model, adapted from Riboldi [19]. To do so, the PaceLab methods to assess take-o and climb performance were evaluated and complied with in the algorithm. They are not developed in this paper, but are mainly based on Torenbeek's theory [7], hence the same type of equations for take-o and climb as in subsection 3.4.1.

At each time step, all the variables describing the state of the aircraft are computed, often with integral calculation. The following parameters have been considered [19], among others:

The required power

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The remaining fuel

Wf = Wf0 −

Z t

t0

σICE· Pshaf tICE · g

eF uel· ηICE

dτ (3.22)

The current total weight

W = W0− Wf (3.23)

The recharge power of the batteries

Prec = σICE· Pshaf tICE + σm· Pshaf tEM −

Pr

ηp (3.24)

The battery energy ow ˙

Ebat = ηC · Prec−

σm· Pshaf tEM

ηm

(3.25) The remaining energy in the batteries

EBat= EBat0 +

Z t t0

˙

Ebatdτ (3.26)

The current altitude

h = h0+

Z t

t0

VVdτ (3.27)

The current speed

V = T AS(h) (3.28)

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The reference values correspond to the PaceLab sizing. Thus, the algorithm min-imises, for a given nal altitude of boost, the weight of the hybrid system hence its power. It is not a problem to x the nal altitude of boost, because it appears in PaceLab that, for every tested energy density, for which a trade study is presented in subsection 3.5, the optimal power of the electric motor is always the same. Conse-quently its nal altitude of boost is the same as well: the sizing problem can be correctly constrained.

Moreover, the two only variables are the battery and the electric motor weights: the throttle settings of all the systems are set to 1 in take-o and climb, because it is intuitively not worth carrying an additional system if it is not used at its maximum capabilities.

As in PaceLab APD, the fuel mass is determined with the missing mass to reach MTOW, which is equivalent to maximising endurance/range.

The advantages of this algorithm compared to PaceLab APD are:

Unlike PaceLab APD, the algorithm does consider a state of charge of the batteries The optimisation is time-dependent

The analysis of the results is more direct and less labour intensive than the Pace-Lab trade studies

The algorithm minimises the on-board mass for a given performance The drawbacks are the following:

The boost altitude must be xed, otherwise the problem is under-constrained. However, it seems like 65 % of cruise altitude is always the optimal value, as observed in subsection 3.5.

The model is not fully Pacelab-independent, as the reference used in the cost function corresponds to the PaceLab sizing results

The thrust tables cannot be directly used: regression functions of ICE shaft power and eciency are applied, with respect to altitude

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Table 3.3 and g 3.7 present an extract of the results obtained through the algorithm. Parameter Value

Endurance variation -2.97 % WEM/WEMref 0.99 %

Wbat/Wbatref 1.03 %

Hybridisation factor 13.84 % Table 3.3: Python numerical results

(a) Evolution of required power ratio (ICE,

EM and total) (b) Evolution of battery SOC (between 20% and 90 %)

Figure 3.7: Dierent graphical results retrieved from the optimisation algorithm

3.4.3 Comparison of the dierent sizing methods

It can be observed from table 3.4 that, for the considered mean values of engine performance and state variables, the adapted Raymer's method is the most optimistic in terms of endurance variation. Nevertheless, it is worth noting that it gives remarkably good results compared to more complex algorithms.

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Methods ∆ Endurance PaceLab APD -1.66 % Adapted Raymer's method +0.64 % Optimisation Algorithm -2.97 %

Table 3.4: Relative deviation of endurance between the conventional and hybrid Studied Light Aircraft, for dierent methods

3.5 Evolution of endurance with battery energy

den-sity

It can be interesting at this point to analyse the evolution of endurance with battery energy density, mainly to nd which battery density is necessary to reach a maximum endurance. It is also a way to compare once again the PaceLab and optimisation algorithm results.

Fig 3.8 shows graphically the results obtained in PaceLab APD for e = 200 Wh/kg and e = 500 Wh/kg:

Figure 3.8: PaceLab APD graphical result for e = 200 Wh/kg (left) and e = 500 Wh/kg (right)

From g 3.8, it can be observed that 65 % of cruise altitude seems to be the optimal nal boost altitude, whatever the energy density of the batteries.

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Figure 3.9: Evolution of relative endurance variation (with respect to conventional Studied Light Aircraft) with battery energy density

Fig 3.9 indicates that 300 Wh/kg are needed to reach +17.5 % of endurance. In-creasing it any higher is not necessary, as the added system weight would be limited by the battery power density. The absolute maximum value of endurance enhancement is achieved at +23 %, where the propulsive system does not bring any extra mass. 300 Wh/kg at battery pack level means approximately 600 Wh/kg at cell level: it is out of the capabilities of current technologies, but could be reachable in the foreseeable future. It is once again worth noting that the results retrieved from the two dierent meth-ods are relatively close to one another.

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Chapter 4 Energy paths dynamic approach

The quasi-static study has the capability to give an optimal sizing of the added systems in order to maximise a given objective variable, such as endurance. Amesim, which is a dynamic simulation software, does not include such feature, and the com-plexity of calculations prevents the iteration of many simulations in order to manually nd an optimal value. However, it allows to validate that the sizing works at each time step, and that the given mission, which is assumed to be followed by the aircraft in quasi-static studies, is eectively reachable in terms of ight controls. Moreover, other architectures that cannot be modelled in quasi-static approaches, such as ther-mal energy recovery devices, because hugely depending on transient behaviour, can be implemented in dynamic models. This kind of devices could improve the ICE fuel ow so that the +23 % upper bound of endurance enhancement could be overcome, hopefully to reach at least the desired +40 %.

4.1 Modelling the conventional Studied Light Aircraft

Unlike for PaceLab APD, there is no model of SLA built on Amesim, requiring the denition of the conventional version before modelling the hybrid system itself.

A predened aerospace library within Amesim was used to model some key compo-nents for the denition of the SLA, including its inertia, aerodynamic properties or the atmosphere characterisation.

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The model of landing gear in Amesim is very poor, because subjected to algebraic loops. Therefore, take-o is not studied and the only mission constraint is climb rate. The two phases of the mission are climb and cruise. Actually, the climb rate constraint is the most important, because it must be fullled for the aircraft to be certied. The constraint about take-o only restrains the possible landing runways.

4.1.1 The internal combustion engine

To assess the aircraft performance, one of the key elements is to model the recipro-cating engine from existing Amesim components. In fact, the Aerospace library includes blocks for turbofan and turbojet engines, but not for reciprocating engines, that are usually more utilised for cars, linked to a propeller. There are some ICE components for car performance, however they do not integrate all the needed constraints, especially fuel consumption calculation. Therefore, a model is retrieved and adapted [10], using the mechanics and IFP Engine libraries, developed by l'Institut Francais du Petrole -Energies Nouvelles.

The IFP Engine library includes a component called "Mean Value Engine Model" (MVEM), which seeks to "predict the mean values of the gross external engine variables (e.g. crank shaft speed and manifold pressure) and the gross internal engine variables (e.g. thermal and volumetric eciency) dynamically in time" [20]. This is a component that is not usable in itself, it has to be connected to manifolds and fuel injection models that can be retrieved from Amesim demos [10]. The two main advantages of the MVEM are that it models a variation of shaft power with air density, hence with altitude, and it calculates fuel consumption. However, unlike other models in Amesim, the power and fuel ow tables should have many inputs, e.g. manifold pressure, temperature, and some of them are not easy to extract from the engine-maker data.

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4.1.2 PID controller for the throttle and elevator settings

A controller is needed in order to be sure that the altitude and speed schedules are respected with regard to the constraints. This controller basically replaces the pilot operations. At each time step, a PID controller gives:

The conventional engine throttle setting required to match the speed schedule; the electric motor torque is developed in section 4.2.

The elevator setting required to match the altitude schedule.

Fig 4.2 shows the simplied block diagrams for throttle setting (left) and elevator setting (right):

Figure 4.2: Simplied block diagrams for throttle setting (left) and elevator setting (right) [10]

4.1.3 Validation of the model

In order to validate the newly created Amesim model of the SLA, it was decided to compare the variation with time of parameters such as thrust, lift coecient, throttle and elevator settings among others, retrieved from Amesim, with simulation outcomes provided by the aircraft maker. The model was then improved to be more accurate with respect to the known data. The endurance given by the Amesim simulation is underestimated of 4 %.

Once validated, the conventional SLA model can be made more complex to include the hybrid system elements. Apart from the elements themselves, it is also necessary to implement a power sharing controller to operate the dierent propulsive units.

4.2 Power sharing controller for the hybrid model

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respect to the power coming from the electric motor, optimal amount corresponding to the one giving the best trade-o between fuel consumption and electric propulsive system weight.

The controller could for instance use a fuel ow network, from which an optimal torque with respect to rotational speed can be retrieved for the conventional engine, as shown in g 4.3.

Figure 4.3: Specic fuel consumption network curves for a gasoline engine [21] In a general case, this curve implies a continuously variable transmission. However the SLA has a xed gear ratio. Therefore, for a given rotational speed, the torque, and hence the fuel consumption, are xed and cannot be fully optimised. Both are increasing functions with respect to the rotational speed. Thus, an optimisation problem could be to nd a minimal value for the rotational speed. However, it means that the batteries have to provide the remaining power needed to fulll the constraints, resulting in extra weight carried by the aircraft.

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fuel mass is assessed with the fuel consumption with respect to rotational speed curve, and the mass of battery is calculated with the remaining mean power to be provided at climb.

Table 4.1 shows a result of the optimisation:

Throttle setting Power ratio Fuel ow ratio mBattery + mF uelClimb

0.5 13.51 % 23.08 % 455.06 % 0.6 20.27 % 26.92 % 426.80 % 0.7 33.78 % 34.62 % 370.28 % 0.8 51.35 % 53.85 % 299.03 % 0.9 72.97 % 73.08 % 210.26 % 1 100.00 % 100.00 % 100.00 %

Table 4.1: Optimisation of the engine throttle setting

It is optimal to use the engine at its maximum power in order to have a small battery, due to battery low energy density. This remains true as long as e < 1300 Wh/kg at pack level or 2400 Wh/kg at cell level, which is currently largely unreachable.

Therefore, the control strategy can be implemented based on the optimisation result. During climb, the throttle setting retrieved from the PID controller controls the engine buttery valve, which limits the air intake, and as soon as the PID saturates, which means that the sole engine cannot fulll the speed schedule, a torque command is sent to the electric motor.

As far as cruise is concerned, the throttle setting of the ICE is chosen in order to maintain a level ight at the desired speed. Part of the generated torque is used to recharge the batteries. A PID checks the error between the actual state of charge of the batteries and its maximum reachable value (90 %) and sends a power command to the generator accordingly, with a limitation corresponding to the generator maximum power. Finally, the elevator setting is still controlled to match the altitude schedule.

4.3 Thermal energy recovery

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line, as exhaust gases can reach temperatures of several hundred degrees centigrades. One of the most mature technologies that could be used in aviation and car industry, is the so-called Organic Rankine Cycle (ORC), Organic referring to the nature of the working uid. It is basically a cycle which contains a pump, a boiler, a turbine and a condenser. Fig 4.4 sketches a simple model of Rankine cycle:

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Contrary to what g 4.5 depicts, the ORC mechanical power could be converted into electricity through a generator for it to be reinjected in the propulsive electric system, but the eciency would be worse in case of motor mode, as the eciency of the motor/generator would be applied twice.

A model of ORC in Amesim is sketched in g 4.6:

Figure 4.6: Amesim model of ORC (based on [10])

The turbine is mechanically linked to the engine so that it rotates at its speed, in order to retrieve a torque from it. Both can for instance be linked via a clutch. The generated torque is mechanically transferred to the shaft driving the propeller. The main advantage of this apparatus compared to the electric boost is that the torque can be extracted throughout the whole ight, without any mass impact, which means that the fuel consumption of the ICE can be lessened i.e. the maximum endurance computed in the quasi-static study can be in theory overcome.

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uid mass ow rate must decrease with time for it to recover enough thermal energy through the evaporator.

The turbine by-pass valve is controlled with respect to the turbine upstream pressure and superheating temperature, in order to get vapour only inside the turbine. If a high torque is required, the upstream pressure must be high, but the working uid should carry this pressure, or the associated temperature, without model failure. Therefore, the working uid must be chosen appropriately.

4.3.1 Choice of the working uid

Depending on the mechanical power that one wants to recover from the ORC and considering safety issues, a suitable working uid has to be chosen.

In fact, for the cycle to be ecient, the critical temperature of the uid should be as close to the heat source temperature as possible, which often means as high as possible in case of very hot boiling temperature [23]. Despite the O standing for Organic, the main molecule of the uid does not have to be organic, i.e. containing carbon atoms, for the cycle to work properly. Actually, water is often used for safety and environmental reasons. Moreover, it has a high critical temperature compared to organic uids (374 °C [23]). However, it expands when freezing, hence its rest pressure inside the pipes should be high enough to prevent it from freezing and damaging the pipes, during winter or at high altitudes. This can be done with an expansion vessel, which is a piston linked to a compressed air tank. Another solution is to automatically drain the water to a tank as soon as the uid is no more heated up.

In regard to all its advantages, and especially because the heat source temperature is around 1200 K, water is chosen as a working uid for the ORC.

4.3.2 ORC sizing with a mass budget approach

From the quasi-static study, it was concluded that in case of a take-o at MTOW, an extra 18 % of mechanical power was needed during part of the climb. At this point, it is necessary to assess the optimal power sharing between the ORC and the electric propulsive system, so that they provide this extra 18 % of shaft power together.

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γ can be dened as the proportion of the + 18 % mechanical power coming from the ORC. Thus, mORC = γ · Pextra pORC (4.1) mBattery = (1 − γ) · max( Pextra· tBoost ηm· e ;Pextra ηm· p ) (4.2) mEM = max((1 − γ) · Pextra d ; Pdeicing ηm· d ) (4.3)

It should be noted that the electric motor / generator should be able to provide at least the power required to use the de-icing system if needed, therefore it is sized accordingly.

Then,

ZF W = We+ Wpayload+ mORC· g + mBattery · g + mEM · g (4.4)

Wf = min(M T OW − ZF W ; mfmax · g) (4.5)

W0 = ZF W + Wf (4.6)

The mean fuel ow is impacted by the ORC, because it can be used in cruise, unlike the electric boost system. Therefore, using the Breguet equation [16]:

R = − L/D

c0_{(γ) · g} · log(1 −

Wf

W0

) (4.7)

where, in light of the engine data,

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Figure 4.7: Evolution of relative endurance variation with γ

It can be observed that, as expected, the more power coming from the ORC, the better in terms of endurance enhancement.

4.3.3 Optimal cycle crossing points

In order to retrieve the maximal power out of the turbine, it is necessary to properly choose the temperatures of evaporation and condensation, as well as the pump mass ow and the superheating after evaporation.

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Water is a wet uid, it means that an isentropic pressure drop, e.g. inside a turbine, can cause condensation, as shown in the step 3 to 4 in g 4.8. It is taken into account in the sizing portion, as it is optimal to have a two-phase ow at vapor saturation downstream the turbine, i.e. point 4 on the blue curve x = 1.

An iterative routine developed at Safran allows one to recover an optimal cycle in terms of mechanical power generation. It is not developed here, but table 4.2 shows the optimal state change temperatures of the water.

Step Temperature Evaporation 324 °C Condensation 100 °C

Table 4.2: Optimal crossing points at evaporation and condensation

It is supposed to give a mechanical power extracted from the turbine of 20 % of the engine nominal power in climb.

4.3.4 Sizing of the heat exchangers

In order to eectively have the crossing points of the optimal cycle in the T-s di-agram, it is necessary to properly size the heat exchangers. The exhaust gases are very hot, around 1200 K, therefore the convective exchange area of the boiler should be small, otherwise both the working uid and the conductive plate material would be overheated. Three exchangers are placed one after the other: the rst one is used at liquid state, the second one at two-phase state, the third one at vapor state.

Using trial-and-error in the Amesim model and considering the constraints cited above, the heat exchangers are sized to get the crossing points.

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Sizing parameter Boiler Condenser

Working uid Water Water

Heating/Cooling source Exhaust gases Air Pipe length over Pipe

di-ameter ratio 150 1300

Exchange area gain on heating/cooling source side with respect to uid side

5.8 -added ns- 1

Table 4.3: Sizing of the dierent components of the boiler and the condenser Therefore, the following T-s diagram is extracted from Amesim:

Figure 4.9: T-s diagram extracted from Amesim during climb

When running the Amesim model, it gives a mean value of generated extra mechan-ical power of 17 % of shaft power in cruise.

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4.3.5 Results

Some simulations have been run, with dierent congurations: ORC on/o, de-icing on/o in cruise. Table 4.4 sums up the endurance gains or losses depending on the conguration, always taking-o at MTOW:

De-icing (rows) and ORC

(columns) ON OFF

ON +10 % −15%

ON THE WINGS BUT OFF

+48 % +12 %

OFF THE WINGS +53 % +14 %

Table 4.4: Endurance enhancement for dierent congurations

The combination of fuel consumption enhancement and extra fuel compared to reference gives a maximum gain of +53 % in endurance, i.e. with ORC on and de-icing feature o the wings.

Fig 4.10 is a graph showing the remaining fuel over time for three dierent cong-urations: conventional SLA, hybrid SLA with de-icing OFF / ORC OFF and hybrid SLA with de-icing OFF / ORC ON:

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It can be observed that, although the hybrid version without ORC makes it possible to carry more fuel than the version with ORC, its high fuel ow in cruise reduces the achievable endurance. It is worth noting that the ORC enables a similar fuel ow compared to the conventional version, as the blue and orange curves are roughly parallel. Therefore, the increase of 8.5 % in TOW does not impact the fuel ow of the ICE.

To conclude, the ORC is very advantageous in terms of performance when connected to a piston engine. Indeed, unlike turbofans, the impact of exhaust gases loss of energy on the performance, dened as generated thrust, is negligible, and the heat source is very hot, up to 1000 degrees centigrades.

4.4 Limitations

The relative enhancement of endurance reaches values that greatly surpass the ex-pectations. However, considering the assumptions that were made to build the Amesim model, the results should be treated as indicative, notably for the following reasons:

The ORC weight was assessed, it could be higher.

No drag impact of the condenser air inlet was considered. However, the Meredith eect, which proves that some thrust can be generated by heated air in inlet ducts, can almost cancel out or even exceed this drag [26].

No impact of the exhaust gases loss of energy on the engine performance was modelled. Actually, the engine must theoretically increase its intake mass ow rate, hence its fuel ow, to counteract the pressure loss. There is a similar eect with turbochargers.

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Chapter 5 Conclusion and perspectives

Throughout this study, it has been demonstrated that a regular hybrid architecture cannot currently enable an enhancement of endurance, mostly because the fuel ow increase due to the take-o weight change counterbalances the extra fuel that can be carried. Consequently, two approaches were explored to address the problem:

Look to the future, preemptively relying on the alleged upcoming technologies of batteries. In this case, the endurance enhancement would plateau at +19 %. Consider a fairly new thermal energy recovery apparatus, the Organic Rankine

Cycle, that allows one in the end not only to take more fuel when upgrading the MTOW, but also to lessen the fuel ow: some mechanical torque is obtained in cruise for no mass penalty, because the system is sized with power, not energy. The endurance enhancement, to be taken as indicative based on the assumptions made, can reach +53 % if no de-icing is used: the initial objective can theoretically be achieved.

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Modelling and Simulation of a Propulsive Hybridisation for a Light Fixed-wing Aircraft Modellering och simulering av hybridisering av framdrivningssystem för ett lätt fastvingat ygplan