Thierry Yj Druot
email: thierry.druot-ext@enac.fr.

Nicolas Peteilh

Pascal Roches

Nicolas Monrolin

Hydrogen Powered Airplanes, an exploration of possible architectures leveraging boundary layer ingestion and hybridization

This study addresses the design of tube-and-wing, turbofan, hydrogen powered passenger transport airplanes from a top-level conceptual approach. The integration of liquid hydrogen fuel systems in the airplane is modeled in a multidisciplinary framework in order to rank the different possible architectures according to overall technical feasibility and performances. If we exclude the Cryoplane layout [1] which has been already studied in the 2000s, we identified mainly three realistic possibilities to store important volume of hydrogen in a classical tubeand-wing layout : in the rear fuselage, within under-wing pods or within piggy-back tank. In this study, we assume that the piggy-back tank is a separated tapered shape attached on top of the fuselage for safety reasons. Adding external tanks to a tube-and-wing configuration also brings additional drag and weight. The possibility to recover some penalty by installing boundary layer ingesting pusher fans on the tail cones of the different tapered bodies of each configuration is analyzed in both contexts of pure thermal propulsive architecture or partial turbo-electric architecture. It appears that boundary layer ingestion is likely to improve significantly the performances in case of external tanks. The feasibility limit of each configuration is discussed according to geometrical constraints and its performances are compared with those of a classical kerosene airplane designed with the same requirements. Finally, a short sensitivity analysis illustrates the effect of technological parameters associated with liquid hydrogen storage and fuel cells integration.

II. Introduction

In the next decades, Aviation will probably face the most challenging evolution of its history. The necessity, for the whole society, to move towards sustainable behaviors and technologies will have a great impact on Air Transport business. With its energy consumption per user being among the highest of transport sector, Aviation has hardly any other choice but organizing itself its transformation towards non-fossil fuel utilization. Presently we have identified only three way to remove fossil fuel from the equation of the Aviation :

1) To use synthetic fuels in place of fossil kerosene. These fuels differ from bio fuels because their production processes just require CO2, water and energy to proceed. Their use in a sustainable scheme requires to capture CO2 from air which brings additional complexity and costs.

2) To use hydrogen in compressed or liquid form as fuel. This way requires lots of transformations in existing infrastructure, based on current technologies. Most of these transformations have to be scaled up.

3) To develop full electric propulsion powered by batteries or fuel cells. In this approach, scaling available technologies to the required level for medium and long-range airplanes will probably last decades.

It seems that there is no easy way to reach sustainability in Aviation. Considering the state of the art of different technologies, the above approaches number 1 and 2 seem to be more likely to offer midterm viable solutions.

The use of synthetic fuel allows to keep airplane unchanged, which is a great advantage. Additionally, the production of synthetic fuels relies on the capture of CO2, which can be done directly at the exhaust of the most polluting industries for example. By doing so, Aviation would avoid fossil fuel emissions, but globally it would not avoid CO2 emissions.

Furthermore, when the emissions of industries will decay to meet international climate change objectives, the CO2 will have to be extracted from the atmosphere which brings additional costs. As a conclusion, the use of synthetic fuel, in the long-term, is inevitably linked to atmospheric C02 capture.

The use of clean fuel such as hydrogen is probably the most robust choice regarding sustainability especially if we consider that the development of full electric terrestrial transports such as cars, buses or trains, powered with fuel cells may contribute to the demand of hydrogen. For Aviation, hydrogen is a big challenge because it does not only require huge infrastructures adaptation but also a critical evolution in airplane design.

The aim of this study is to present the most promising layouts to integrate a big hydrogen tank within turbo-machine powered tube-and-wing airplanes and to rank them according to their feasibility and performance. Opportunities of boundary layer ingestion and hybridization is also considered to reduce the impact of additional fuel tank volumes.

Each aircraft architecture is optimized according to a multidisciplinary process based on simple models thanks to the open source, Python-based library MARILib_2.0 available on Gitlab [START_REF] Druot | MARILib public v2.0, commit e259f023efea09ab5cf98c90bcdd1c9922ed80bb[END_REF]. A first version of this library was introduced in 2019 [START_REF] Druot | A Multidisciplinary Airplane Research Integrated Library With Applications To Partial Turboelectric Propulsion[END_REF].

In the first chapter, the main issues related to the use of hydrogen as fuel are presented and discussed. The second part presents the proposed architectures to store hydrogen on board in a liquid form together with a qualitative comparison between them. The third chapter shows the type of model that has been used for the unconventional components of the architectures. Finally, the fourth part presents the technological criteria that have been used to assess the feasibility of each aircraft layout and the quantitative results of the study.

III. H2 characteristics that matter

In this section, the physical specific features of the hydrogen are discussed in the perspective of hydrogen based propulsion system for aircraft.

From a technical point of view, kerosene is very efficient for Aviation. It has both a high energy-to-mass ratio and energy-to-volume ratio which makes it at the same time very powerful and easy to store into the airplane. Additionally, it is liquid on the Earth in the current condition of use and can be stored within existing structural parts of the airplane thanks to simple and light adaptations. In comparison, hydrogen seems to bring more drawbacks than advantages. It offers a higher energy-to-mass ratio but a much lower energy-to-volume ratio which makes it hard to store inside an aircraft. By adding their own weight, volume and complexity, hydrogen tanks are making the use of hydrogen even more challenging for aviation.

In principle, hydrogen can be stored either as a compressed gas or as a liquid if temperature is kept at -253°C (20.3K). For compressed H2 tanks, a maximum pressure of about 700 bars turns out to be the reference storage value for vehicles [START_REF] Rivard | Hydrogen Storage for Mobility: A Review[END_REF]. For liquid H2, the tank is required to provide excellent thermal insulation combined with either ambient pressure or, for hybrid tanks, pressurisation loads up to 5 bars. However, as liquid hydrogen density decreases when the pressure increases (+11% in volume at 4bars), it is better to have a maximum pressure as low as possible to minimize the size of the tank for a given hydrogen mass [START_REF] Winnefeld | Modelling and Designing Cryogenic Hydrogen Tanks for Future Aircraft Applications[END_REF]. This last capability is interesting as it first enables to retain, for a slightly longer period of time, the evaporated hydrogen that should otherwise be released, and second to improve the fuel flow control. This boil-off losses, caused by thermal leaks through the tank walls, strongly depend on the surface-to-volume ratio but is estimated to be less than 1% per day [START_REF] Züttel | Materials for hydrogen storage[END_REF]. In the context of aviation, tanks are filled just before the mission and fuel consumption will start just after and will mitigate pressure increase inside the tank.

Tables 1 and2 compare kerosene and hydrogen fuels and related tanks in terms of mass, volume and energy. The characteristics of the tanks depend on the type of fuel. The overall shell density represents the mass of the tank shell per unit of volume of the shell. This parameter is very important to model liquid hydrogen tanks where the shell has to provide thermal insulation features.

The most important results are summarized in Table 2.

Table 1 Comparison between kerosene and hydrogen storage characteristic when tank is included. The green cells correspond to input data and the blue ones to key results.

Table 2 Comparison between kerosene and hydrogen storage key characteristics in terms of energy density, with and without tank.

Both energy-to-mass ratio and energy-to-volume ratio are high for kerosene and the contribution of kerosene containers is negligible. The energy-to-mass ratio of 2 is about 3 times higher than for kerosene but its energyto-volume ratio reveals to be more than 4 times lower than kerosene if we include the container in the estimation.

Concerning the 700bar 2 both energy-to-mass ratio and energy-to-volume ratio are drastically reduced as the weight of the tank shell is very high. If compressed 2 may bring some advantages for very short-range airplanes due to the simplicity of its management but we can rule it out for medium and long ranges. In the rest of this paper, we concentrate on the use of 2 with hybrid vessels that are able to sustain an internal pressure of about 2 bars.

From these figures, we can predict several consequences for the overall design of a hydrogen powered airplane. First the poor energy-to-volume ratio of hydrogen will obviously necessitate to create specific volumes in the aircraft to host 2 containers. Additionally, to be efficient, these containers will need to be bulky, in order to mitigate thermal losses with a high volume-to-surface ratio. To illustrate this concept, we compare the tank efficiency in term of volume and mass for a thin volume similar to a wing structural box and for a cylindrical or spherical volume. In these estimations, the wall thickness is 80mm including pressure resistant shell and thermal insulation. Table 3 presents the numerical results for a similar volume and three different shapes (wing box, cylinder and sphere).

The volume efficiency is the ratio of the internal volume of the tank, that is the useful volume to store 2 , over the external volume that also includes the tank wall or shell volume. The mass efficiency is the ratio of the 2 mass over the 2 + container mass. We can see that both volume and mass efficiencies are correlated with the volume-to-area ratio of the container. Moreover, the efficiencies of a cylindrical container are very close to the corresponding efficiencies of a spherical one which is ideal. The most important result is that the mass efficiency of a cylindrical tank, with comparable size in length and diameter, is more than 2 times higher than for wing box like container. Of course, these figures are valid if the fuel is stored in one single volume in the tank. Splitting the fuel into several volume would necessarily decrease the efficiency of any type of container. Finally, we can conclude that, as long as the fuel can be stored in one volume (or at least a very few ones), compact shapes with comparable size in all dimensions are much more efficient than thin or tapered shapes.

The question is : where to find (or create) such volumes in a (reasonable) aircraft layout ? Considering the above remark about tank shapes, only 3 possibilities exists for a tube-and-wing basic architecture :

1) To dedicate a part of the fuselage internal volume to nest the tank.

2) To plug under-wing tank pods like military airplanes.

3) To install a piggyback tapered container over the fuselage.

Pros and cons of these 3 arrangements are discussed in Section IV.

The second consequence is related to the high energy-to-mass ratio of the hydrogen. Other things being equal otherwise, an hydrogen powered airplane will require less fuel mass than a kerosene airplane, its takeoff weight will be lower and the airplane may be globally more efficient provided the penalties due to 2 volume and management do not jeopardize the mass benefit. This can be approached using the Breguet equation ( 1) which gives the range as a function of the lift-over-drag ratio / , the specific fuel consumption , the flight velocity , the landing mass LDW and the fuel burnt .

= / log + (1)
which can be reversed to retrieve the fuel burnt for a given range as in Equation ( 2).

= / -1 (2)
The results are presented in Table 4 are obtained using the following assumptions:

1) / = 20 (a classical value for a modern airplane)

2) Kerosene fuel heat : 43 MJ/kg Table 4 Comparison between kerosene mass and expected hydrogen mass.

The reference aircraft is presented in the column 1. It is representative of a modern short-range airplane. The use of Hydrogen in place of kerosene is responsible for a decrease of 12583-4221 = 8362kg of the necessary fuel mass to fly the mission. But the hydrogen airplane will probably have a higher drag (columns 3 and 4 : -3 L/D counts), due to a longer fuselage for instance, and a higher mass (column 4 : +7 tons), due to the special tank and fuel system. The chosen penalties values brings again the TOW to the same mass level as the kerosene aircraft. This first guess for penalties is reasonable at this stage but needs to be confirmed.

As a result of reduced mass fuel on board, the displacement of the center of gravity due to fuel consumption will also reduce which may have positive consequences on the handling quality constraints management.

The third consequence is induced by the very low temperature of liquid hydrogen. Refueling an airplane will generate a great amount of hydrogen evaporation because of the necessity to bring the tanks themselves to about 21.2

Kelvins [START_REF] Züttel | Materials for hydrogen storage[END_REF]. This hydrogen must not be released in the atmosphere, so it must be taken back and liquefied again by the fueling system of the airport. This aspect will probably require more complex connection between the tank and the fueling system. The low cryogenic temperature of the fuel will also have consequences on the fuel system of the aircraft.

A complex thermal management will be required to ensure that engines are suitably fed without side effects as ice accretion in the pipes and pumps. From the other side, the presence on board of very low temperature fluid that must be turned to gas during its travel to the combustion chamber offers a good opportunity for a heat sink which would be used to dissipate the heat produced by some other systems in the plane. These thermal aspects are not addressed in this paper.

As a conclusion to this section, it seems that the use of 2 as an energy vector for airplanes is a real challenge but brings some advantages which may compensate the additional volume and mass required for its use. On top of all, the airplane will not produce any CO2 when flying.

IV. Qualitative analysis of proposed architectures

In this section, the pros and cons of each proposed architecture will be discussed, and the opportunity brought by boundary layer ingestion (BLI) will be introduced in the perspective of pure thermal propulsion and hybrid partial turbo-electric propulsion. Tanks location and design have to minimize the consequences of possible hydrogen leaks, fire and engine burst.

A. Rear fuselage tank configuration

Figure 1 presents this configuration. If the fuel tank is inside the fuselage, the rear position quickly appears to be the only possibility. The front position would disable any forward access to the cabin and isolate the cockpit. The median position would split the cabin into two independent volumes which would be difficult to manage and probably not well perceived by passengers. Additionally, this position puts the tank in the possible trajectory of disk pieces in case of engine burst. The rear tank position keeps unchanged all the main operational features of a classical cabin layout and is probably the safest in comparison with any other location within the fuselage.

This type of architecture may lead to a very long fuselage, or a reduced number of seats, in comparison to a classical kerosene airplane. A long fuselage with a bipolar functional segmentation (cabin-tank) may have two consequences :

1) The load relief due to fuel consumption may bring an important forward move of the center of gravity during the flight. Fortunately, this motion will be limited due to the reduced fuel weight. A forward move of the center of gravity does not endanger the longitudinal stability but may increase trim drag.

2) A long rear fuselage may appear critical for maximum attitude on ground which may constrain the operations of the airplane in terms of take-off speed (and consequently take-off field length) and (or) approach speed (and consequently landing field length).

Both aspects would need to be addressed carefully in the design of the airplane but are not addressed in this paper.

In comparison to additional tank bodies installed outside the classical tube-and-wing arrangement, the rear fuselage tank solution offers the most efficient solution in term of wet area.

A realistic feasibility limit for such a design is given by the length of the fuselage and more especially its diameterto-length ratio. In this study, the lower diameter-to-length ratio ever built in a commercial airplane is considered as a feasibility limit for this architecture.

B. Under-wing tank pod configuration

This solution, shown in Figure 2, is probably the safest of all proposed tank positioning because it places the tanks as far as possible from the cabin. From a structural point of view, it contributes to decrease wing root bending moment because tanks are attached directly to the wing. From the point of view of operations, tank accessibility is equivalent to engine and the architecture offers the possibility to install tanks of different size which would increase the operational flexibility of the airplane.

For a twin under-wing engine mounted airplane, two tank positions are a priori possible : between the nacelle and the fuselage or on outer wing. The internal tank position would generate aerodynamic over speeds and so a lot of Nevertheless, the following points have to be checked :

1) The aerodynamic interactions between the tanks and the external wings,

2) The flexible modes and the aero-structural interactions,

3) The maximum pitch attitude during take-off and landing,

4) The ground clearances in case of banking attitude during take-off, landing or ground maneuvers,

5)

The disk burst trajectories if engines are let in a classical under-wing position.

A possible mitigation of ground clearance risks would be to install the pods in median vertical position with respect to the wing. This position may also ease the treatment of pod to wing aerodynamic interactions but with structural penalty and overall storage efficiency reduction.

An other possibility to get rid of ground clearance problems would be to attach the wing on to of the fuselage.

Consequently, the horizontal tail would be pushed on top of the vertical tail. Such a modification in the design would also bring some penalty in term of structural weight but would not modified the general conclusion about performances.

A realistic feasibility limit for pod design is given by the size of the pods themselves. In this study, an upper bound of the diameter of the pods is given by the engine diameter and an upper bound of the length of the pod is given by about 3 times the mean aerodynamic chord of the wing.

C. Piggyback tank configuration

This last solution shown in Figure 3 is the most unconventional of all proposed ones. The possibility to carry important loads piggyback has been experimented several times in the history but has never been implemented for day to day use. Here are some examples :

1) The space shuttle on top of 747,

2) Burane shuttle on top of an Antonov-225,

3) A380 wings packaged over the fuselage of an A330 (only wind tunnel tested).

The safety level of such an architecture seems to be intermediate between the rear fuselage tank and the under-wing tank pods as the tank is put outside of the body hosting the cabin. Tank accessibility is the most difficult of all proposed solutions due to the upper position. Here also, several important points must be carefully addressed :

1) The structural attachment between two long bodies may be quite tricky to design,

2) The aerodynamic interaction between the fuselage and the tank body,

3) The airplane lateral stability, 4) The disk burst trajectories if engines are let in a classical under-wing position.

For the piggyback tank layout, an upper bound for the diameter of the tank has been set to 80% of the fuselage width and a maximum length has been set to 70% of the length of the fuselage. Additionally, a dry bay is installed in the section which is exposed to engine burst.

D. Synthesis on H2 configurations

Table 5 summarizes the pros, cons and critical points of each architecture.

From this table, it seems that solution 1, rear fuselage tank, has the better profile, nevertheless, the relatively bad profile of the solution 3, piggyback tank, has to be tempered if we accept that special infrastructure devices be deployed Table 5 Summary of qualitative pros and cons of three tank positioning.

on the airport to facilitate refueling and maintenance of the airplane, this solution becomes also attractive, especially if we consider the opportunity offered by BLI which is discussed in the next section.

E. BLI opportunity

In this section, we present how BLI can be an opportunity to improve overall efficiency of wing pods (solution 2)

and piggyback tank (solution 3) architectures.

Both solutions 2 and 3 are based on external tapered bodies attached on a classical tube-and-wing architecture.

Welstead [START_REF] Welstead | Conceptual design of a single-aisle turboelectric commercial transport with fuselage boundary layer ingestion[END_REF] demonstrated that BLI technology can improve overall efficiency of an airplane, provided that additional system weights and/or drag do not jeopardize the benefit. This benefit may be important if the whole boundary layer of a bulky body can be swallowed by the propulsion system. Theoretically, this can be done on proposed architectures 2 and 3 by installing fans behind the tank bodies. These can be powered by turbo-machines or electric motors in the case of a hybrid propulsion system. Both alternatives are presented in this paper.

Installing thermal engines on wing pod tanks

This architecture is presented in Figure 4.

The main problem of this layout is the unconventional nacelle mounting which requires to deeply redesign the engine architecture or at least the engine mounts. Apart from this consideration, the main tricky points of the architecture seem to be :

1) The maximum pitch attitude during take-off and landing,

2) The ground clearances in case of banking attitude during take-off, landing or ground maneuvers, 3) The aero-structural stability,

4) The tank-wing-nacelle-fuselage aerodynamic interactions.

Possible mitigation of clearance problems would be to install the pods as upward as possible on the wing.

Installing thermal engines on piggyback

The piggyback architecture contains two tapered bodies that are candidate for BLI. Such a layout is for sure an interesting engineering challenge, but it is likely to reveal the most important benefit. The architecture is presented in Figure 5. Let's note immediately that this architecture shows very interesting features like :

1) No lateral lever arms for nacelles which will greatly reduce the required area for vertical tails (no need to balance a huge lateral moment in case of engine failure),

2) Rear nacelles will contribute to the lateral and longitudinal stability of the airplane which may counterbalance some instability introduced by the tank,

3) Longitudinal shift between the two engines rule out the problem of possible cross striking in case of engine disk burst, 4) No more possibility for an engine disk burst to hit the tank.

For this layout also, engine architecture may be challenging. Nevertheless, as nacelles are close to the fuselage, it seems to be possible to attach more or less classical engine mounts to it. The upper engine being attached on top of the rear fuselage without any link with the tank. The lower engine being attached to the rear fuselage thanks to structural beam. These possibilities are illustrated in Figure 6. Such a structure will bring its weight to the total but replaces two underwing pylons and adds some contribution to the overall yaw stability.

We identify for this architecture the following main tricky points:

1) The maximum pitch attitude during take-off and landing,

2) The structural attachment of the tank,

3) The structural attachment of the engines, 4) The lateral stability in flight.

5) The failure of the forward engine may cause the second engine to fail if it swallows debris.

The opportunity of hybridization

We consider hybridization with the objective to take benefit of boundary layer ingestion to recover part of the additional drag introduced by the hydrogen tank(s). Hybridization could allow to install electric fans with an adjusted power to take maximum benefit of BLI without having to develop disruptive engine installations.

Hybridization has a cost in terms of weight and overall efficiency. Druot et al. [START_REF] Druot | A Multidisciplinary Airplane Research Integrated Library With Applications To Partial Turboelectric Propulsion[END_REF] showed that ingesting the fuselage boundary layer with an electric fan mounted on fuselage tail cone allows to recover this cost and produces a margin benefit when only fuselage boundary layer is involved. In the case of hydrogen airplanes, we can expect a higher benefit since other bodies can be fitted with electric fans and BLI.

The hybridization of solution 1 leads to an architecture which is very closed to the one studied in ref [START_REF] Druot | A Multidisciplinary Airplane Research Integrated Library With Applications To Partial Turboelectric Propulsion[END_REF]. The benefit is expected to be a little bit higher because of the longer fuselage, and thicker boundary layer. The greater the momentum losses in the boundary layer of the fuselage, the greater the energy recovery potential. Figure 7 shows this type of architecture.

Fig. 7 Solution 1 with partial turbo-electric propulsion and fuselage BLI.

The hybridization of solution 2 makes sense only if the fuselage and both tank pods are equipped with electric tail thrusters. The resulting layout shows the same pros and cons profile as the pure thermal design but is expected to be more efficient. Figure 8 shows an overview of this architecture with a variation on pod mounting that would relax the ground clearance constraints and may ease the treatment of aerodynamic interference between the tank and the wing.

The price for this is the loss of the possibility to install simply pods of different size depending on mission requirements but the possibility to recover part of tank drag may compensate to carry a bigger fixed tank even on short routes, which also simplifies the operations.

Fig. 8 Solution 2 with partial turbo-electric propulsion and pods and fuselage BLI.

The hybridization of solution 3 may be the best chance for hybridization because it relaxes part of the difficulties of the pure thermal powered architecture with BLI whilst keeping the advantage of BLI, the cost of this being as usual, the additional mass of the power electric chain. Figure 9 gives an overview of this design.

The opportunity of fuel cell

Mechanical generators are not the only way to power body tail thrusters, fuel cells can also be used for this purpose.

The rationale is that fuel cells can also use 2 as power source, insofar as they can be fed with a fuel of the same purity as turbines. Merging fuel cells and turbomachines in the same powerplant system may have several advantages :

1) The 2 powered fuel cells are breathing air that need to be delivered with a certain pressure and flow. This air flow may be off taken from turbomachines which avoid to embark dedicated compressor.

2) The fuel cells will generate a large amount of heat that must be dissipated. Depending on fuel cell working temperature, this heat may be used for de-icing which prevent to take it from engine turbine offtakes.

3) An important flow of liquid hydrogen must be warmed before delivering it to turbo-machines (and fuel cell as well) which may use part of the heat that has to be dissipated.

The possibility of using fuel cells to power the body thrusters will be evaluated on the base of existing technological data with rough assumptions concerning the benefit of possible synergies. These assumptions are described in Section IV.E.5.

Qualitative comparison of BLI architectures

The Table 6 summarizes the pros and cons and critical points of BLI architectures.

Solution 3 with turbofans on piggyback and fuselage tails seems to be at the same time the most promising configuration in term of fuel consumption and the most challenging one to design. For this architecture, hybridization may provide an interesting compromise able to take benefit of BLI keeping the classical engine installation.

The best compromise in term of feasibility versus benefit seems to be the hybridization of solution 2 with 3 electric thrusters.

We focus now on the possible benefits of each architecture in term of fuel consumption but before that, an overview of the special models and assumptions that have been used is presented. Only models related to unconventional components are presented. Other models, related to conventional components as fuselage, wing and stabilizers are those developed by Druot et al. [START_REF] Druot | A Multidisciplinary Airplane Research Integrated Library With Applications To Partial Turboelectric Propulsion[END_REF].

V. Specific models and assumptions

In this section, we describe models that are out of the scope of classical twin turbofan tube-and-wing conceptual design. These models are related to liquid hydrogen fuel tanks, fuel cells, hybridization electric chain, and turbofan model with BLI. For all these models, a modelling approach based on top level technological parameters has been adopted to be as independent as possible from specific implementations. The basic values of these technological parameters correspond to the state of the art of the technology as it appears in different recent publications, then a forecast of these values is made for 2030 based on perceived potential evolution of each technology. The study is completed with a sensitivity analysis of the main quantities of interest versus these technological parameter values.

A. 2 tank model

This sub-section describes the tank model that have been used as well as how it has been integrated in the different airplane layouts presented above.

Tank system

We made several tests with more or less complex models trying to represent specific technical solutions for thermal insulation but none of them reveals to be satisfactory due to the great amount of uncertainty attached to any specific solution. Finally, a very simple model with only two top level parameters is adopted. The two parameters are the gravimetric and the volumetric indices respectively defined by equations ( 3) and ( 4). The main advantage of this approach is to represent a given technological level, and its possible evolution, in terms of volume and weight, without specifying the underlying technologies.

1) The gravimetric index :

= 2 2 + (3)
2) The volumetric index :

= 2 2 (4)
The gravimetric index quantifies the additional mass of tank system required to package a given mass of liquid hydrogen, for instance : a value of 0.5 for means that the tank system has the same mass of the 2 it contains, a value of 0.1 means that the mass of the tank is 9 times the mass of the 2 it contains.

The volumetric index quantifies the additional volume of tank system required to package a given volume of liquid hydrogen. A value of 0.5 for means that the tank system with its content is twice the volume of the 2 inside the tank, a value of 0.9 means that the volume of 2 is 9 times the volume of the surrounding tank system. The values of and are just enough to characterize 2 tanks at conceptual design level. A great number of publications from the last two decades are treating of the subject of 2 tanks. A few examples of these publications are given in ref [START_REF] Winnefeld | Modelling and Designing Cryogenic Hydrogen Tanks for Future Aircraft Applications[END_REF][START_REF] Boll | A holistic system approach for short range passenger aircraft with cryogenic propulsion system[END_REF][START_REF] Colozza | Hydrogen storage for aircraft applications overview[END_REF][START_REF] Gomez | Liquid hydrogen fuel tanks for commercial aviation: Structural sizing and stress analysis[END_REF][START_REF] Iulianelli | Advances in hydrogen production, storage and distribution[END_REF][START_REF] Moreno-Blanco | The fill density of automotive cryo-compressed hydrogen vessels[END_REF][START_REF] Moreno-Blanco | The storage performance of automotive cryo-compressed hydrogen vessels[END_REF][START_REF] Verstraete | Hydrogen fuel tanks for subsonic transport aircraft[END_REF]. Finally, the values shown in Table 7 are proposed as a basis and the study includes a sensitivity analysis on these parameters.

A minimum gas ullage of 2% of the available total volume for 2 is taken. This ullage is necessary so that the tank system could control the pressure inside the tank. The corresponding volume is supposed to be included in the volumetric index and does not appear explicitly in the model.

As no insulation device is able to completely prevent the heat leakage, all tanks are submitted to a more or less important boil-off effect that produces gaseous hydrogen, typically from 0.1% to 1.5% per day depending on the efficiency of the insulation and the storing volume (the smaller the ratio between the external area and the internal volume, the lower the boil-off). A part of this 2 can be kept in the tank if the tank is able to sustain the corresponding over-pressure, typically 3bars to 30bars in existing implementations. The present study being focused on airplane performances, the boil-off effect is not considered. It is assumed that the airplane is connected to the airport refueling system until a very short time before engines are started so that the boil-off can be neglected. When engines are running, even in idle, the consumption compensates the boil-off and the 2 must be heated to produce the required flow of 2 at the required temperature. The Table 8 gives a numerical application of the above model for a cylindrical tank ended with hemispherical terminations.

Table 8 Example of weights and volumes for a cylindrical tank ended with hemispherical terminations.

Tank integration

The tank located in the rear fuselage occupies the maximum available volume from the rear pressure bulkhead to an

x-wise position controlled by the total length of the tank. A minimum thickness of 20cm is taken for fuselage structure and surrounding systems. The volume shape is modelled as a cylindrical part, which may be eventually absent, and a cone trunk part. Figure 10 shows the principles of integration of this tank.

The tanks located into external pods are modelled as cylinders ended with hemispherical terminations. The tanks are nested into tapered shapes. The surrounding tank body structure has a minimum thickness of 10cm and the total unused length + of the body is equal to twice the external diameter . The tank design parameters are its external diameter and its total external length . Figure 11 shows the integration principle of pod tanks.

Fig. 11 Integration principle of pod tanks.

The mass of the surrounding structure is computed using a surface mass of 15kg/m2 wrapped around the tank external surface. This value corresponds more or less to half of the surface mass of a fuselage structure. The surrounding structure is also supposed to be 8 cm thick whatever the volume of the tank. Table 9 summarises the structural characteristics of the tank shell.

Table 9 Characteristics of external tank shell structure.

B. Power electric chain

The electric chain refers here to the electrical part of the Partial Turbo-electric architecture where a classical turbofan provides mechanical power to the input of the chain composed with the elements shown in Figure 12.

As in ref [START_REF] Druot | A Multidisciplinary Airplane Research Integrated Library With Applications To Partial Turboelectric Propulsion[END_REF], each component of the chain are modelled through two parameters only :

1) an electrical efficiency ( ) equal to the ratio of the output power over the input power, and 2) a gravimetric index ( ) equal to the ratio of the mass of the component over the maximum power it can manage in continuous mode.

The volume allocation is not applied to electrical chain components integration. The values of electrical efficiencies and gravimetric indices are mainly drawn from Siemens public data of the SP260D motor [START_REF] Anton | Hybrid-elektrische Antriebssysteme für Luftfahrzeuge und synthetischer Kraftstoff[END_REF]. Table 10 displays selected values for all six components. Considering that the state of the art technological levels are very close to maximum theoretical levels for wiring, rectifiers and inverters, no evolution of these values is considered in this study.

Nevertheless, generators and motors efficiencies still have a potential for evolution. The company H3X [START_REF]HPDM-250 Datasheet v1.1[END_REF] has recently announced a power density of about 13 kW/kg for its motors. To be conservative, a fixed value of 5 kW/kg is taken for this study for both SOA and 2030.

Table 10 Efficiencies and gravimetric indices of a typical series electric chain components.

For the cooling function, the concept of Energetic Efficiency is replaced by the Power Index which is the ratio between the required power of the cooling system over the dissipated heat power. For the wiring function, it would be more precise to consider the actual airplane architecture to evaluate its mass and the losses it generates but such an approach would require a lot of specific developments just for the sake of wiring. We then decide to model the wiring with allowances for simplicity reasons. Table 11 illustrates the above models in the context of a power chain that produces 1MW of mechanical power on its output shaft.

Table 11 Example of an electric power chain producing 1MW on its output shaft.

C. Engine models

Airplane conceptual design studies make classically use of semi-empirical engine models. Many models of that types can be found in literature [START_REF] Raymer | Aircraft design: a conceptual approach[END_REF][START_REF] Torenbeek | Synthesis of Subsonic Airplane Design: An Introduction to the Preliminary Design of Subsonic General Aviation and Transport Aircraft, with Emphasis on Layout, Aerodynamic Design[END_REF][START_REF] Roskam | Airplane Design Part I-VIII[END_REF][START_REF] Roux | Pour une approche analytique de la dynamique du[END_REF]. In this study, the model is taken from ref [START_REF] Birman | Uncertainty quantification and propagation in Conceptual Aircraft Design: from deterministic optimization to chance constrained optimization[END_REF]. These models are not based on the thermodynamic cycle of the engine but provide two relations :

• the maximum thrust as a function of engine design parameters, ambient conditions (e.g. altitude, temperature), speed and selected rating (Max Takeoff (MTO), Maxi continuous (MCN), Max climb (MCL), Max cruise (MCR), and sometimes Flight idle (FID)),

we get:

= ( , , , , ) = ( , , , , )
= 0.13

= (1 -0.13) ℎ = 0.82 (6)
where:

• is the thrust developed by the core only,

• is the hypothetical thrust developed by the fan only,

• ℎ is the mechanical power delivered by the core.

The fan power is used to drive the fan model presented below and the fuel flow is kept for latter evaluation of the SFC.

Fan model

The only geometrical parameter required to run the model is the nozzle area. This area is defined considering that the exhaust pressure is equal to the ambient pressure (adapted area). The mechanical power delivered to the fan shaft is coming from the previous approximation and we look for the air flow that goes through the fan. This air flow must satisfy, at the same time, the thermodynamic equations across the fan and the BPR which requires an iterative solving.

The fan model is based on a global vision of the involved physics. It does not intend to be very precise but to provide good orders of magnitude of both its outputs and their variations versus the inputs.

The inputs are:

• : the heat capacity of the air at constant pressure,

• : the heat capacity ratio of the air,

• : the specific gas constant of the air,

• : the fan nozzle section area,

• : the engine by-pass ratio in cruise,

• : the capability to convert mechanical energy into kinetic energy, typically 95%, The computation sequence of the iterative processes which calculates the total air flow is as follows :

= + ℎ = 1 + -1 --1 ℎ = 2 -1 -1 -1 = ℎ √ 1 + -1 2 ℎ 2 1 2 1+ 1- = = = + (7)
The set of equations ( 7) is solved iteratively to calculate . The solution is computed thanks to a non-linear equation solver (Python fsolve for instance). Then, the resulting total thrust and fuel flow are computed as follows : Table 12 Reference airplanes data for each categories.

Each category corresponds to a given set of top level requirements as shown on Table 13. The market segments corresponding to General Aviation and Commuters is not addressed in this study.

For each category, we define five hydrogen airplane variants as defined in Section IV. Each variant is evaluated versus two levels of technology maturity for hydrogen tanks (see Table 7) :

• Reference airplane

• Rear fuselage tank

• Under wing pods

• Piggy back tank

• Pods full BLI

• Piggy Back full BLI Each airplane corresponding to a couple (architecture-category) is optimized according to its own set of top level design parameters and the resulting optima are compared in terms of design seat capacity, range, maximum take-off weight (MTOW) and operating empty weight (OEW). We choose these characteristics because they give an idea of the feasibility of each architecture.

Table 13 Top Level Aircraft Requirements for each category.

A separated study is done to evaluate the interest of hybridization to take benefit of boundary layer ingestion.

All categories are optimized considering wing area and engine size but tank size is added for all hydrogen powered airplanes. The parameters are distributed as follows :

• Reference airplane : wing area, engine size

• Rear fuselage tank : wing area, engine size, tank length

• Under wing pods : wing area, engine size, tank length, tank diameter

• Piggy back tank : wing area, engine size, tank length, tank diameter

• Pods full BLI : wing area, engine size, tank length, tank diameter

• Piggy Back full BLI : wing area, engine size, tank length, tank diameter

• Piggy Back hybrid BLI : wing area, engine size, tank length, tank diameter, electric chain power

The optimization is performed using MARILib_v2.0 [START_REF] Druot | MARILib public v2.0, commit e259f023efea09ab5cf98c90bcdd1c9922ed80bb[END_REF], according to a Multidisciplinary Design Feasible (MDF) process. It is mainly composed of a system solver applied on the mass-mission adaptation problem, nested into an optimizer. MTOW is the selected criterion to be minimized. Constraints are taken from Table 13. All airplanes, including reference ones, are optimized using the same process. The overall process is described by the XDSM of Figure 13.

The feasibility of hydrogen powered architectures is evaluated according to different criteria. For rear fuselage tank, a maximum ratio of fuselage length over fuselage height is defined at 13.35 which corresponds to the A340-600. It is considered that the value of this ratio for this particular airplane is the highest manageable.

For the wing or fuselage podded architectures, it is not possible to defined so simple criteria because of the great number of degrees of freedom that could be used to relax geometrical constraints. For instance, for the wing podded airplanes, one can move the tanks upward to relax a max-pitch-on-ground clearance or work on the tapering shape of the tank. A more qualitative criteria is then used considering the "distance" in terms of size and maximum weight between the hydrogen airplane and the corresponding reference airplane optimized with the same set of requirements. For instance, a limit is set on the required power when it reaches the maximum power of the biggest available engine (about 520 kN for the GE90 115/B). This is not a sharp criteria but in the context of this study, just a global view is targeted.

Considering the characteristics of hydrogen and the performance of liquid hydrogen tanking technology, it is clear that the weight of the tanks is a critical point. As long as hydrogen is used as fuel, the weight of the tank becomes a stronger driver of performance than the weight of the fuel itself. Consequently the maximum fuel range of the airplane is a stronger driver of the design than the nominal range itself, which is significantly different from the traditional situation involving kerosene. It appears that short and medium-range airplanes show a great sensitivity of the range versus the number of passenger on board. Said differently, A limited number of passengers off can provide an important range increase. For instance, as we can see on the Payload-Range diagram of the A320-200neo-like rear tank H2 airplane (Figure 14), "only" 21 passengers (payload reduction of 2500kg) can shift the range by 1000NM. This is due, of course, to the high energy density of hydrogen.

The classical design process is modified to take account of this new behavior. As the maximum fuel range is the real driver of the design, it should be logical to run the Multidisciplinary Design Analysis (MDA) considering the max fuel range as the design range. However this also leads to a difficulty to define the nominal payload. Requiring the the tank size is automatically adjusted so that the maximum fuel range be exactly equal to 1.25 nominal range. As a consequence, the design is effectively driven by the maximum fuel mission but the nominal payload is kept in between the maximum payload and the maximum fuel mission payload, which reduces the design bias introduced by the new process. Additionally, the value 1.25 for the ratio max-fuel-range over nominal-range is quite low in comparison to what we observe on most of existing kerosene airplane. This avoids to penalize too much the hydrogen airplane which has an heavy tank to carry.

VII. Results and analysis

This study generates a great amount of numerical results. In order to present a global view of the different H2 architectures and their potential, we do not review all of them in details. This section presents the main results based on a few quantities of interest that are keys to evaluate feasibility of each architecture.

A. Result analysis per category

In this subsection results concerning categories are presented in sequence from short-range to ultra long-range airplanes. In each category, three tables are presented and discussed :

1) Presentation of hydrogen rear tank architecture in the perspective of the reference kerosene airplane.

2) Presentation of other hydrogen architectures with state of the art hydrogen tanking technology compared to the rear tank architecture.

3) Presentation of other hydrogen architectures with 2030 hydrogen tanking technology compared to the rear tank architecture .

In the first table of each category, the airplanes are supposed to be designed on the required range and capacity but when this is not possible, a reduced range and/or capacity is selected. In all cases, the main key parameter to evaluate the feasibility is the resulting MTOW. If the MTOW of the H2 airplane is higher than about 33% of the MTOW of the reference airplane, it is considered that the feasibility is questionable. The two last tables in each category are used to compare the H2 architectures in order to find the best ones. Here also, the MTOW is the key parameter. The comparison is done in the context of current technology level and in the perspective of 2030 technology as defined by the indices presented in Table 7. A global view of feasibility is proposed at the end of the section. All data can be found in the appendix.

Short-range airplanes

Table 17 presents rear tank architectures in both SOA and 2030 perspectives.

The SOA version cannot be designed on 2100NM with the required 135 passengers. The maximum possible range of 990NM is determined by the fuselage length and more precisely by the maximum fuselage length-to-height ratio of 13.3 (corresponding to the value of this ratio for A340-600). This constraint is relaxed by increasing the number of front seats from 5 to 6. Anyway, the resulting MTOW of about 140 tons is not acceptable and this version is considered as not feasible.

The 2030 version shows a quite long fuselage, as we can see on Figure 15, but nevertheless, the limit is not reached.

The resulting MTOW reveals to be 37% higher than the reference which is a bit high but still conceivable. Anyway, it is to be noticed that the maximum range of the version is half the order of magnitude of the reference one.

Table 18 presents a comparison of hydrogen architectures in SOA perspective. The comparison is done according to a 600 NM mission which is feasible for all versions. This range corresponds roughly to one third of the required range for this category. Except for the rear tank version which is limited by a fuselage length constraints, all other versions are designed with the classical five front seats of the category.

The piggyback architectures shows the lower MTOW, even lower than the rear tank one. The benefit of BLI is clear with a decrease in MTOW of about 7% at the price of a more complex and risky engine installation. The three view of the best version of the table is presented on Figure 16.

Considering the maximum range of 750 NM and the corresponding MTOW, the feasibility of this class of short-range airplanes based on the SOA liquid hydrogen technology seems questionable. Table 19 presents a comparison of hydrogen architectures in 2030 perspective.

In this case, the required range of the category can be achieved by all versions. According to the different MTOW, the piggyback versions seems to have the best potential. Especially the BLI version which is just 21% heavier than the reference version. Additionally, the BLI version provide a significant fuel benefit of about 13.3% in comparison to the rear tank version, at the price of a risky engine installation. The three view of the best version of the table is presented on Figure 17.

Medium range airplanes

Table 20 presents rear tank architectures in both SOA and 2030 perspectives.

None of the hydrogen version can be designed on 3000NM with the required 150 passengers. For each version, maximum range is limited by the maximum fuselage length-to-height ratio. The maximum range is abound 1000 NM for SOA version and about 2400 NM for the 2030 version. Considering the level of the MTOW, the SOA version seems not to be viable. The 2030 version has a MTOW which is about 12% higher than the reference one with a maximum range which is in the lower part of the category but still acceptable. The three view of this last version is presented on

Table 21 presents a comparison of hydrogen architectures in SOA perspective. The comparison is done on a 850 NM mission, but the design of the pod versions cannot be converged and the design range is therefore reduced to 600 NM for them. Considering the possible maximum range and the resulting level of MTOW, hydrogen powered medium-range airplanes seem not to be viable with the SOA tanking technology.

Table 22 presents a comparison of hydrogen architectures in 2030 perspective. The comparison is done on a 1900 NM mission which is feasible for all versions.

As for short-range category, the pod versions appear to be the least interesting. This is due to a greater wetted area and built surface than the piggyback version. It is not a good news because the pod version could probably be designed to allow the possibility to unplug empty tanks and just replace them by full ones during ground operation, which would ease refueling.

Long range airplanes

Table 23 presents rear tank architectures in both SOA and 2030 perspectives.

None of the version can match the required seat capacity and design range of the category.

The seat capacity is then arbitrarily lowered to 240 passenger to allow design convergence. Like for short and medium-range airplanes, both hydrogen versions are limited by fuselage length-to-height ratio. The number of front seats is set to 7 for both pod and piggyback versions but for different reasons. Pod versions definitely need a larger lever arm in order to reduce the size of horizontal and vertical tails, whilst piggyback versions need longer fuselage so that the tank could be shorter than the fuselage itself.

Considering the maximum range and the corresponding MTOW, the SOA version is clearly not viable.

Concerning the 2030 version, if the order of magnitude of the maximum range is compatible with the category, it appears that the resulting level of MTOW (about 50% higher than the reference one) makes it hardly viable.

It seems that the requirements of the long range category, as defined in Table 13 is not accessible to the rear tank architecture, even with 2030 assumptions for tanking performances.

Table 24 presents a comparison of hydrogen architectures in SOA perspective. It seems that the achievable maximum ranges and capacity associated to the resulting levels of MTOW put those designs out of the viability domain of the category.

Table 25 presents a comparison of hydrogen architectures in 2030 perspective. The comparison is done according to a 3000 NM mission with 240 passengers. As for previous categories, the piggyback versions exhibit the best performances. With the selected design capacity and range, the MTOW of the BLI version is far below the MTOW of the reference airplane which suggests the possibility to get closer to the requirements of the category.

Table 26 presents in the column 1 the maximum range reachable with a seat capacity and a MTOW of the same magnitude as the reference kerosene airplane. The resulting maximum range is about 4300 NM which is roughly half of the maximum range of the reference airplane. The column 2 presents the maximum reachable range if an increase of about 30% of the MTOW is accepted versus the reference kerosene airplane. In this last version, the tank diameter is increased to a diameter similar to the fuselage one. It seems clear that a maximum range of the same magnitude as the reference airplane is not achievable. Nevertheless, in both cases, resulting airplanes performances are in the lower part of the category and may be envisage-able. Three-view drawings of these versions are presented respectively on Figure 20 and on Figure 21. A particular treatment may be necessary to manage an adequate shift between the two engines.

Ultra long range airplanes

Table 27 presents rear tank architectures in both SOA and 2030 perspectives. On both cases, the capacity is arbitrarily down sized to 240 passengers and the maximum range is adjusted so that the resulting MTOW be in the same order of magnitude as the reference airplane. The SOA version is clearly out of the scope of the category and the 2030

The global conclusion is that a capacity compatible with the category seems to be achievable but the order of magnitude of the maximum range is about half of the maximum range of classical kerosene airplanes.

Table 28 presents a comparison of hydrogen architectures in SOA perspective. We note that the number of front seats is reduced to 7 in order to give enough length to the fuselage. It seems that the achievable maximum ranges and capacity associated to the resulting levels of MTOW put those designs out of the viability domain of their corresponding category.

Table 29 presents a comparison of hydrogen architectures in 2030 perspective. The comparison is done according to a 4000 NM mission with 240 passengers but the design of the pod version cannot be converged as so. The design range is then reduced to 3000NM for them.

Considering the achievable ranges in the perspective of the resulting MTOW, it appears clearly that the pod version is out of the scope of the category. The piggyback versions shows levels of MTOW significantly lower than the rear tank one, especially for BLI which is about 24% lighter. The potentiality of this version is evaluated as shown in the Table 30.

Table 30 presents in the column 1 the maximum range reachable with a seat capacity and a MTOW of the same magnitude of the reference kerosene airplane. The resulting maximum range is about 5000 NM which is roughly half of the maximum range of the reference airplane. The column 2 presents the maximum reachable range if an increase of about 30% of the MTOW is accepted versus the reference kerosene airplane. Despite a tank diameter close to the fuselage diameter, the tank is longer than the fuselage. A particular treatment would be necessary as for instance to shift the tank backward in order to have different X-wise positions for engines.

As for the long range category, here also, it appears clear that a maximum range of the same magnitude as the reference airplane is not achievable. Moreover, the obtained maximum range with a MTOW 30% higher than the reference is still out of the scope of the category. Nevertheless, it is to be noticed that the Piggyback BLI version shows a huge fuel saving of about 20.7% in comparison to the rear tank version, all other things being equal.

Three view drawings of these version are presented respectively on Figure 22 and on Figure 23.

Conclusion about thermal hydrogen architectures

The Figure 24 summarizes the feasibility of all hydrogen architectures vs categories. State of the art technology clearly not allows to build liquid hydrogen powered airplanes which could pretend to a level of performance compatible with the existing market categories between short ranges and ultra-long ranges.

The weight of the hydrogen tank is driving the design much more than the weight of the fuel itself. Consequently,

The max fuel mission is taking the lead on the airplane sizing.

If the technological maturity of hydrogen tanking can be pushed to the level identified in Table 7 then short range and medium range can be addressed with liquid hydrogen fuel.

The interest of BLI is to be noticed especially for piggyback versions that reveals to be equivalent or better than rear

VIII. Hybridization of BLI architectures

Hybridization of thermal propulsive architectures consists in introducing an electric power chain to produce part or totality of the propulsive power ref needed. The type of hybridization that have selected for this study consists in a Partial Turbo-electric electric chain as described in ref [START_REF] Druot | A Multidisciplinary Airplane Research Integrated Library With Applications To Partial Turboelectric Propulsion[END_REF]. In all cases, an amount of additional systems must be In the context of this study, hybridization can be applied to any type of architecture but the piggyback one seems to have the best potential to recover kinetic energy which otherwise would be lost in the wake. Consequently, hybridization has been studied on the piggyback architecture only.

A first sensitivity study has been done in the short-range category, assuming 2030 tanking technology has defined in Table 7. The basic architecture corresponds to the piggyback version with under wing turbofans. Electric pushers have been installed at rear position on both the fuselage and the tank as shown on Figure 9. Technical assumptions of the electric chain have been described in the Section V.B.

A sensitivity study has been done versus the power of the pushers. The airplane sizing is fixed except for the electrical power chain which total power varies from zero (reference piggyback airplane) to 7 MW ( 3.5MW per motor).

Main results are presented in Table 14 and a graph of the evolution of the block fuel of the nominal mission is presented on Figure 25.

Despite of an important increase on MTOW, the fuel consumption on the nominal mission decreases significantly by more than 5% for the maximum power tested. A saturation of the benefit can be expected around 8MW but the design could not be converged at this level of power due to the increase in MTOW with fixed wing area and total engine thrust.

However, this benefit cannot be confirmed until full re-optimization of the architecture for each level of installed power.

Table 14 Effect of BLI hybridization level on a PB short range.

Fig. 25 Fuel saving evolution versus hybridization level

To confirm the real benefit and define the optimal installed power, a full re-optimization of the architecture for several level of electrical power has been done. Main results are presented on Table 15. The optimal hybridization level seems to be around 2 MW (1 MW on each electrical BLI fan). The evolution of the fuel saving is shown on Figure 26.

The level of power of 2 MW corresponds to the point where the additional weights of the system become stronger than the benefit obtained with BLI. The resulting fuel benefit of about 2.6% is a bit disappointing if compared to the 12.5% obtained with the pure thermal BLI version. A three view of this last architecture is presented on Figure 27.

Conclusion about hybrid hydrogen architectures

The Table 16 compares the short-range rear tank version with piggyback, piggyback BLI and piggyback BLI hybrid versions. If the benefit of piggyback installation is margin versus rear tank one, the benefit of BLI reveals to be significant at a value of -13.3%. The benefit realized by the hybrid version is around -3.3%. This poor result is due to the additional weight of the electric chain. Nevertheless, such hybrid architecture allows to produce some fuel saving with a much less risky installation than the pure thermal BLI. • The weight of the hydrogen tank is predominant in the airplane sizing process in comparison to the weight of the hydrogen itself.

• As a direct consequence of the above remark, the mission which is driving the overall airplane design process is the max fuel mission instead of the nominal mission.

• State of the art hydrogen tanking technology hardly allows to build short-range airplanes in its current categorisation and does not allow to build longer range categories.

• 2030 hydrogen tanking technological level seems to allow the design of viable airplanes in the short-range category and may be in the medium range category.

• If 2030 hydrogen tanking technology level can hardly makes viable long and ultra long range airplanes, an opportunity may exists for the Middle Of the Market (MOM) which is not addressed currently by existing airplanes.

• The architectures that reveal the best potential are the rear tank version (hydrogen is nested inside the rear part of the fuselage) and the piggyback version (hydrogen tank is package in its own body fixed on top of the fuselage).

Additionally, an opportunities may exist for combined architectures (rear tank + pod tanks for instance).

• A very significant fuel saving in the magnitude of 10% may be obtained on the piggyback version if turbofans are installed at the rear end of both fuselage and hydrogen tank.

• Hybridization of the piggyback version may produce a fuel saving in the order of magnitude of 3%.

Many various assumptions had to be taken to perform this study. Moreover, specific difficulties of liquid hydrogen management have not been addressed. Consequently, further studies should be launched to refine the quantitative conclusions and precise the operational viability of liquid hydrogen as an aviation fuel. Nevertheless, an interesting research direction has been enlighten to push the economical viability of liquid hydrogen powered airplanes.

  climb to initial cruise altitude TOW = Take Off Weight of the airplane V = True air speed of the airplane Vapp = Approach speed Vz = Vertical speed of the airplane

6 )

 6 192 kg/daN/h (assuming kerosene turbofans and hydrogen turbofans have the same energy efficiency Cruise conditions : Mach 0.78 at 35000ft which gives = 231 / 7) Range=3000 NM 8) LDW=65000 kg, basic value for the kerosene powered airplane 9) g=9.81

Fig. 1

 1 Fig. 1 Airplane layout with rear fuselage tank.

Fig. 2

 2 Fig. 2 Airplane layout with under-wing tanks

Fig. 3

 3 Fig. 3 Airplane layout with piggyback tank.

Fig. 4

 4 Fig. 4 Airplane layout with integrated under wing tank-engine with BLI.

Fig. 5

 5 Fig. 5 Airplane layout with rear engine mounting and BLI.

Fig. 6

 6 Fig. 6 Engine attachment trying to re-uses classical engine side mounts.

Fig. 9

 9 Fig. 9 Solution 3 with partial turbo-electric propulsion and piggyback tank and fuselage BLI.

Fig. 10

 10 Fig. 10 Integration principle of rear fuselage tank.

Fig. 12

 12 Fig. 12 Power electric chain for the Partial Turbo-electric Series architecture.

•ℎ:

  the mechanical power delivered by the core,•: the total air flow going through the fan (an initial value is required to start the solving), • : the stagnation temperature of the flow at fan inlet, and • : the stagnation pressure of the flow at fan inlet The outputs are: • : the stagnation temperature of the flow at nozzle output, • : the static temperature of the flow at nozzle output, • : the stagnation pressure of the flow at nozzle output, • ℎ : the mach number of the flow at nozzle output, • : the corrected air flow per square meter at fan nozzle output, • : the air flow going through the fan nozzle, and • : the air flow going through the core.

Fig. 13 XDSM

 13 Fig. 13 XDSM graph of the Overall Optimization process.

Fig. 14

 14 Fig. 14 Payload-Range diagram, A320-200neo-like, rear tank H2, 2030 techno level.

Fig. 15

 15 Fig. 15 Short-range, rear tank, 2030 techno level.

Fig. 16

 16 Fig. 16 Short-range, 750NM, piggyback tank BLI, SOA techno level.

Fig. 17

 17 Fig. 17 Short-range, piggyback tank BLI, 2030 techno level.

Fig. 18

 18 Fig. 18 Medium range, rear tank BLI, 2030 techno level.

Fig. 19

 19 Fig. 19 Medium range, piggyback tank BLI, 2030 techno level.

Fig. 22

 22 Fig. 22 Long range, piggyback tank, 2030, MTOW ref.

Fig. 24

 24 Fig. 24 Feasibility matrices

Fig. 26

 26 Fig. 26 Fuel saving evolution versus hybridization level with re-sizing

Table 3 Comparison of the storage efficiency of different volume shapes for LH2 density of 71 kg

 3

.m

-3

Table 6 Summary of qualitative pros and cons of five architectures with BLI.

 6

Table 7 State of the art and 2030 forecast of

 7

2 storage indices.

Table 15 Effect of BLI hybridization level on optimized PB short range

 15

		1.0 MW 1.5 MW 2.0 MW 2.5 MW 3.0 MW
	MTOW (kg)	81815	82760	83790	84885	86032
	OEW (kg)	61906	62870	63906	64996	66130
	Tank mass (kg)	18698	18639	18623	18640	18684
	Power chain mass (kg)	1180	1770	2360	2950	3540
	Emotor mass (kg)	367	550	733	917	1100
	Nominal block fuel (kg) 4521	4507	4503	4507	4518

Table 16 Comparison between Rear tank, PB, PB BLI and PB BLI Hybrid IX. Conclusion In

 16 this study, six different architectures of liquid hydrogen powered airplanes have been analysed (rear tank, pod tank, pod tank BLI, piggyback tank, piggyback tank BLI and piggyback tang BLI hybridized) according to four different categories (short range, medium range, long range and ultra long range) in the perspective of two level of maturity for hydrogen tanking technology (state of the art and 2030 forecast). Several interesting conclusion can be expressed :

		Rear tank Piggyback Piggyback BLI PB BLI Hybrid
	MTOW (kg)	85797	80479	75862	83790
	OEW (kg)	65720	60449	56568	63906
	Tank mass (kg)	16459	19087	16710	18623
	Nominal block fuel (kg) 4658	4616	4037	4503

Table 18 Short-Range Hydrogen architecture comparison SOA

 18 Rear Tank Pod Tank Pod Tank BLI Piggyback Piggyback BLI

	Nominal seat count (int) 135	135	135	135	135
	Front seats count (int)	6	5	5	5	5
	Design range (NM)	2100	600	600	600	600
	Max fuel range (NM)	2625	750	750	750	750
	Fuselage length (m)	52.36	37.25	37.25	37.25	37.25
	Fuselage width (m)	3.86	3.35	3.35	3.35	3.35
	Tank length (m)	15.69	13.12	12.64	16.89	15.45
	Tank diameter (m)	3.46	2.50	2.50	3.00	3.00
	MTOW (kg)	85797	106644	103334	86439	80215
	OEW (kg)	65720	89327	86173	69684	63804
	Nominal block fuel (kg) 4658	1766	1679	1453	1262

Table 19 Short-Range Hydrogen architecture comparison 2030 XI. Medium range airplanes

 19

		Reference Rear Tank SOA Rear Tank 2030
	Nominal seat count (int) 150	150	150
	Front seats count (int)	6	6	6
	Design range (NM)	3000	850	1900
	Max fuel range (NM)	4223	1062	2375
	Fuselage length (m)	39.32	53.85	54.08
	MTOW (kg)	76595	125704	85923
	OEW (kg)	41882	105578	64396
	Body aspect ratio (adim) 9.7	13.3	13.4

Table 20 Medium Range Rear tank architecture versus Reference

 20

	Nominal seat count (int) 150	150	150	150	150
	Front seats count (int)	6	6	6	6	6
	Design range (NM)	850	600	600	850	850
	Max fuel range (NM)	1062	750	750	1062	1062
	Fuselage length (m)	53.85	37.99	37.99	38.13	38.13
	Fuselage width (m)	3.86	3.86	3.86	3.86	3.86
	Tank length (m)	15.72	14.85	14.24	26.26	23.21
	Tank diameter (m)	3.46	2.50	2.50	3.00	3.00
	MTOW (kg)	125704	120727	116575	129837	116939
	OEW (kg)	105578	101279	97321	109357	97175
	Nominal block fuel (kg) 2804	2088	1979	3023	2568

Table 21 Medium Range Hydrogen architecture comparison SOA

 21

		Rear Tank Pod Tank Pod Tank BLI Piggyback Piggyback BLI
	Nominal seat count (int) 150	150	150	150	150
	Front seats count (int)	6	6	6	6	6
	Design range (NM)	1900	1900	1900	1900	1900
	Max fuel range (NM)	2375	2375	2375	2375	2375
	Fuselage length (m)	54.08	38.71	38.71	38.71	38.71
	Fuselage width (m)	3.86	3.86	3.86	3.86	3.86
	Tank length (m)	15.36	14.64	14.06	25.29	22.82
	Tank diameter (m)	3.46	3.00	3.00	3.00	3.00
	MTOW (kg)	85923	94287	91596	86014	80699
	OEW (kg)	64396	71838	69518	64164	59638
	Nominal block fuel (kg) 4497	5206	4917	4742	4129

Table 22 Medium Range Hydrogen architecture comparison 2030 XII. Long range airplanes

 22

		Reference Rear Tank SOA Rear Tank 2030
	Nominal seat count (int) 320	240	240
	Front seats count (int)	9	8	10
	Design range (NM)	6000	1300	4600
	Max fuel range (NM)	8385	1625	5750
	Fuselage length (m)	62.70	74.64	89.48
	MTOW (kg)	252763	352673	376477
	OEW (kg)	128723	313212	308593
	Body aspect ratio (adim) 10.1	13.2	13.3

Table 23 Long Range Rear tank versus Reference

 23

		MTOW ref MTOW ref x 1.3
	Nominal seat count (int) 320	320
	Front seats count (int)	7	7
	Design range (NM)	3500	4200
	Max fuel range (NM)	4375	5250
	Fuselage length (m)	63.32	64.15
	Fuselage width (m)	4.87	4.87
	Tank length (m)	47.26	55.34
	Tank diameter (m)	4.00	4.50
	MTOW (kg)	254684	332506
	OEW (kg)	198251	264376
	Nominal block fuel (kg) 19275	29713

Table 26 Long Range (ultimate) Piggyback tank BLI 2030 XIII. Ultra long range airplanes

 26 Reference Rear Tank SOA Rear Tank 2030 Max range RT 2030 Max capa RT 2030

	Nominal seat count (int) 310	240	240	240	300
	Front seats count (int)	9	10	10	10	10
	Design range (NM)	7300	1100	4000	4600	4000
	Max fuel range (NM)	10583	1375	5000	5750	5000
	Fuselage length (m)	63.06	64.36	78.60	89.15	89.22
	MTOW (kg)	290612	297668	289749	374235	353275
	OEW (kg)	143837	261275	234802	306756	285934
	Body aspect ratio (adim) 10.2	9.6	11.7	13.3	13.3

Table 27 Ultra Long Range Rear tank versus Reference

 27

Acknowledgments

An Acknowledgments section, if used, immediately precedes the References. Sponsorship and financial support acknowledgments should be included here. The preferred spelling of the word "acknowledgment" in American English is without the "e" after the "g." Avoid expressions such as "One of us (S.B.A.) would like to thank. . . " Instead, write "F. A. Author thanks. . . " Sponsor and financial support acknowledgments are also to be listed in the "acknowledgments" section.

• the specific Fuel Consumption (SFC) or fuel flow ( ) as a function of engine design parameters, ambient conditions (e.g. altitude, temperature), speed and thrust.

Engine design parameters are most often :

• The Sea Level Static Thrust (SLST)

• The By Pass Ratio (BPR)

We express the maximum thrust and fuel flow semi empirical model as follows:

In this study we use the semi-empirical model derived by Druot [START_REF] Druot | A Multidisciplinary Airplane Research Integrated Library With Applications To Partial Turboelectric Propulsion[END_REF]. Such relations proved to deliver consistent figures for high level conceptual design purpose as long as engines are working in free air stream. But in the context of boundary layer ingestion (BLI) the engine model must be able to capture the effect of a variation of the mean air speed at inlet position. The mean air speed at inlet position can be computed as proposed in ref [START_REF] Druot | A Multidisciplinary Airplane Research Integrated Library With Applications To Partial Turboelectric Propulsion[END_REF].

From a global point of view, an engine is composed of a core which deliver mechanical power to a fan. The core being responsible of part of the thrust. The model of the fan is based on thermodynamic principles and takes into account varying inlet speed. The mechanical fan shaft power, delivered by the core, is deduced from the semi empirical model of turbofan. The following section explains this in details.

Fan shaft power model

The modelling approach is based on two observations :

• For modern turbofans with BPR higher or equal to 5, the core-thrust-over-fan-thrust ratio is in the range 10% to 16% in a wide range of thrust and flying conditions. This has been measured on existing engine models. A constant value of 13% is then selected. A sensitivity study reveals that this value is not critical regarding the modeled BLI effect which means that a variation of several percents of the core-thrust-over-fan-thrust ratio does not have significant impact on computed efficiency improvement.

• The power efficiency of a modern fan (fan thrust x airspeed / shaft power) in cruise is close to 82%.

From these observations, the following model has been derived. The objective here is to compute effective thrust and fuel flow corresponding to given altitude, speed and rating. The semi-empirical model of turbofan is used to get a link between these input data and the corresponding fuel flow, fan shaft power and core thrust.

The initial semi-empiric engine model is used to deliver consistent values of fuel flow, fan shaft power and core thrust and can be considered as a very rough model of core. The fan model delivers the fan thrust according to the shaft power and the inlet air speed. Finally, the total thrust and the SFC are assembled with outputs from both models as shown in the set of equations 8.

In the case of BLI, the inlet air speed is reduced due to the effect of the boundary layer and this is the only effect that is moving the working point of the fan, resulting in a higher thrust for a similar input shaft power. Even if very simple, this modelling approach delivers good approximation of BLI effect as long as the whole boundary layer of a fuselage-like body is involved. The reader can refer to ref [START_REF] Druot | A Multidisciplinary Airplane Research Integrated Library With Applications To Partial Turboelectric Propulsion[END_REF] for an other illustration of these principles.

VI. Study process

For each selected airplane architecture, four operational and market categories have been selected together with one reference airplane for each of them:

• Short range (A220-100),

• Medium range (A320-200neo),

• Long range (A330-800),

• Ultra long range (A350-900).

Some important parameters of each category reference airplane are shown in Table 12. version cannot achieve more than half the maximum range of the reference airplane. Nevertheless, neither the maximum fuselage length-to-height ratio nor the MTOW limit at 1.3MTOW reference are reached for those two version.

The two last column of Table 27 illustrate the maximum range that can be achieved by keeping the capacity to 240 passengers and the maximum capacity that can be achieved. Both versions are limited by fuselage length-to-height ratio and the MTOW of the max range version is also close to the limit.

Appendix X. Short-range airplanes