Engine Design Study for Free Double Piston Integrated Composite Cycle Engine

Abstract

The Composite Cycle Engine (CCE) enhances the conventional Joule/Brayton cycle by replacing the high-pressure compressor with a high-quality piston-based gas generator that enables extremely high compression, combustion, and expansion of the working fluid before entering the classic Joule burner. This piston-based topping cycle unlocks much more efficient fuel utilization. This paper studies a CCE concept featuring a system of free double piston (FDP) units for a potential long-range (LR) application in 2045, benchmarked against an advanced turbofan engine representative of the same time frame. In-house-developed simulation tools for the piston system and the overall power plant, as well as aircraft non-linear trade factor analysis, are used for different levels of conceptual assessment. First, the cooling demand inside the FDP system is determined. An engine cycle parametric study is then performed for the design point top-of-climb (ToC). Off-design performance is further studied, demonstrating a 9.3% improvement in thrust-specific fuel consumption (TSFC) in cruise relative to the baseline engine. After incorporating the engine weight and nacelle geometry effects, the engine reaches a total mission fuel burn reduction of around 14.7% compared to the baseline engine. The concept evaluation shows the fuel burn potential of the CCE in the future LR aviation sector and lays the foundation for further climate impact analysis.

1. Introduction

In past decades, the conventional turbofan has improved its overall performance through advanced gas turbine technology to reach higher thermal efficiency and reduced fuel burn. This trend dictates that the engine operates at a higher burner outlet temperature ($T_4$) and overall pressure ratio (OPR). With turbocomponent efficiencies at or even well above 90% and combustion temperatures approaching close-to-stoichiometric levels, significant further efficiency gains from classic Joule/Brayton cycle machines become extremely hard to obtain. To reach the net-zero carbon emissions target by 2050, novel propulsion concepts have been researched in recent years. The ULTIMATE (Ultra-Low Emission Technology Innovations for Mid-Century Aircraft Turbine Engines) project explored several revolutionary heat engine concepts for aircraft propulsion systems [1], where the Composite Cycle Engine (CCE) has emerged as the most promising candidate. The CCE is an innovative propulsion option that fundamentally changes the thermodynamic cycle of the engine by adding a piston system to the gas turbine architecture. A potential of double-digit fuel burn reduction compared to the geared turbofan (GTF) technology in 2035 was shown [2,3]. The currently running MINIMAL project investigates different CCE concepts with different configurations and fuel variants [4]. This paper presents the initial conceptual design and mission burn assessment of the long-range (LR) CCE with a free double piston (FDP) system benchmarked against an advanced GTF in 2045.

1.1. Composite Cycle Engine

The Composite Cycle Engine (CCE) modifies the thermodynamic cycle of a gas turbine engine by adding an intermittent closed-volume cycle on top of the Joule/Brayton cycle. The additional combustion takes place inside a piston unit, placed between a low- or intermediate-pressure compressor and a Joule burner. The piston enables a hectopressure rise during the compression process, after which high-pressure, high-temperature combustion and expansion occur [5]. Kaiser et al. [6] implemented a crankshaft-based CCE, showing a notable fuel burn improvement over a 2035 GTF. However, the significant weight penalty and mechanical complexity of the piston system, as well as higher NO_x emissions, were highlighted. Eilts et al. [7] and Nickl et al. [8] investigated different CCE architectures and obtained a similar conclusion about the benefits and concerns of the CCE. Despite the promising increase in thermal efficiency, the piston system contributes to a higher propulsion system mass, and the high-temperature combustion inside the piston engine inevitably leads to high NO_x production. Hence, a compact piston system design and feasible NO_x mitigation technologies are crucial for the success of the CCE concept.

1.2. Free Double Piston Unit

To mitigate the weight penalty issue associated with CCEs, the free double piston (FDP) system is proposed as a compact self-sustained gas generator. In an FDP, a free piston oscillates between two opposed combustion chambers at the end of the cylinder bore. The compression and expansion processes occur without a crankshaft or gearbox. Since the FDP does not require lubrication oil for bearings of the mechanical parts, the piston system can operate under an elevated permissible material temperature [9]. This relaxed material constraint enables the possibility of compressed air cooling inside the FDP system. Another benefit of the FDP design is an improvement in power transmission efficiency. First, the absence of the connecting rod removes the transmission losses in the bearings. Second, eliminating lateral forces from crankshaft movement leads to reduced vibration inside the system [9]. The simplicity in the mechanical parts, however, leads to complexity in controlling the free piston oscillation movement. Challenges to avoid piston bore collision and misfiring require advanced piston cylinder trajectory control, as described in [10,11]. The implementation of control strategies in FDP operation is challenging and would require further modeling and experiments. This paper examines the overall thermodynamic performance of the FDP system. Precise control of the free piston movement remains a challenge for such an application, but it is not addressed within the scope of this study. For a more detailed FDP system description, the reader is referred to Ref. [12].

In previous studies [5,6], crankshaft-based CCEs were primarily researched, and only a short-range FDP-based CCE was developed by Kaiser [13]. In this study, an FDP-based CCE with sustainable aviation fuel (SAF) is investigated for a potential LR application in 2045. The FDP system and the surrounding engine components are modeled inside Bauhaus Luftfahrt’s in-house-developed propulsion system performance synthesis framework. Three main sizing-relevant operating points and initial part-power operation studies are performed to investigate CCE operating characteristics. A design mission fuel burn evaluation is performed in aircraft-level assessment platforms, where a non-linear trade factor analysis is applied to capture the cascading effects of aircraft sizing. The main cycle parameters of the CCE and fuel burn analysis over the designed mission are compared with a 2045 GTF. Overall, this work represents an initial assessment from engine cycle design to aircraft-level performance of the FDP-CCE for future LR aircraft. While the present study concentrates on the engine design aspects and fuel burn optimization, non-CO₂ effects, especially NO_x emissions, are highly important in order to identify CCE designs for minimum climate impact. For the CCE NO_x assessment methodology, the reader is referred to Ref. [14].

2. Design Methodology

2.1. Propulsion System Modeling

The propulsion system is implemented in Bauhaus Luftfahrt’s modular in-house MATLAB^®-based computational framework, Aircraft Propulsion System Synthesis (APSS). In the current work, APSS was executed with MATLAB ^® version R2024b. The tool has been used in a number of previous studies for conventional and non-conventional propulsion systems [15,16], including CCEs [5,6], and is similar in its modeling detail to the commercially available gas turbine design tool GasTurb^® v12 [17]. Fluid properties are computed using temperature-dependent NASA polynomials [18], and pressure dependency is accounted for in the fluid property calculation. The working fluid is characterized by the ideal gas equation, and a correction factor accounting for real gas effects is applied, as proposed in Ref. [13].

The investigated CCE that was implemented in APSS is schematically presented in Figure 1. The numbering corresponds to the standard thermodynamic station designation [19]. Ambient air (0) is ingested in the intake (1), reaches the fan inlet (2), and is subsequently split into the bypass stream (13) and the core stream (21). The core stream enters the intermediate-pressure compressor (IPC, 21) before entering the FDP system (3), where it is compressed further and partially combusted. The detailed FDP system architecture and modeling are described in more detail in Section 2.2. A portion of the compressed gas from the FDP system is used for high-pressure turbine (HPT) cooling, as indicated by the blue arrow. The flow rate is determined following the turbine cooling model introduced in Ref. [20]. Once routed through the FDP, the working fluid is combusted with fuel in the gas turbine (or Joule) combustion chamber (GT-CC, 35) and subsequently expanded in the high-pressure turbine (HPT, 4) and the low-pressure turbine (LPT, 45). The HPT is mechanically connected to the high-pressure spool of the IPC, whereas the LPT drives the fan via a gearbox on the low-pressure spool. The bypass flow is routed around the core flow through the bypass nozzle (18), whereas the turbine exhaust core flow exits through the core nozzle (8). The connecting ducts between components, e.g., between the compressor and the FDP, and potentially required manifolds and buffering volumes are not shown in Figure 1 for simplicity.

Figure 1. Schematic of the investigated Composite Cycle Engine (CCE) with station indexing and component block diagrams.

At the cycle design point, the compression processes occurring in the fan and the IPC, where the pressure ratio ($\Pi$) is prescribed, are modeled via individual polytropic efficiencies ${\eta }_{pol}$. In the Joule combustion chamber, pressure losses are prescribed, and the fuel-to-air ratio is adjusted to meet the turbine inlet temperature. In the turbine, the power required by the compression section and potential power offtakes are imposed, which fixates the turbine pressure ratio. For the turbine components, isentropic efficiencies are prescribed. The off-design behavior of the turbocomponents is modeled using suitable component maps chosen from the GasTurb ^® Map Collection 3 [21].

The mass estimation of the engine is done in a post-processing step using component-based empirical relations outlined in Ref. [13]. In the cited work, the total engine mass predicted by the methodology was validated against a PW1100G engine (IAE International Aero Engines, East Hartford, CT, USA), and a relative deviation of 0.6% was obtained. The mass breakdown includes all components depicted in Figure 1; additionally, masses of shafts, disks, ducts, and casings are taken into account. Auxiliary systems, such as electrical or lubrication, are estimated by a factor of 15% of the engine mass, and the mass of additional accessories increases linearly with the ToC thrust requirement [22]. For the gearbox mass estimation, the TO thrust for the LR engine is taken into account, and the heuristic from Ref. [23] is used. To obtain the total power plant system (PPS) mass, nacelle, thrust reverser, cowling, and nozzle masses are added to the bare engine mass using empirical relations [13]. The mass estimation of the FDP system is briefly summarized in Section 2.2.2.

2.2. Piston System Modeling and Integration

2.2.1. Internal Flow Path Description

In the present work, a simplified FDP system is modeled that closely resembles the original design revealed by Klingels [12]. The working fluid entering the device passes first through the piston compressor (PC) via its inlet valves, where it is compressed owing to the combustion taking place in the mechanically connected piston engine (PE). Subsequently, the pressure-driven exhaust valves open and the flow exits the PC and is routed through a duct into the PE via its inlet valves for closed-volume combustion. After the combustion process, the exhaust valves open and the flow is ejected into another duct directed towards the gas turbine combustion chamber (GT-CC). Figure 2a shows an overview of the aforementioned components and the internal routing of the main flow. To reduce the propagation of unsteady flow fluctuations through the engine, buffer volumes are added upstream and downstream of the system (not explicitly shown in Figure 2). Furthermore, as indicated in Figure 2b, in addition to the main flow, a fraction of the compressed exhaust gas from the PC is routed as a secondary flow through a set of internal ducts and cooling channels, deliberately located close to the PE to alleviate the occurring heat loads during combustion. This secondary flow does not pass through the PE and is instead mixed with the PE exhaust gas further downstream. There are a few additional secondary flows within the system, including a lubrication flow in the cavity between the piston and the cylinder liner (air-riding characteristic of the piston). Due to their expected low flow rates compared to the previously introduced flows, these have not been modeled explicitly in the present study in a first approximation. The reader may refer to the patent for further details [12].

Figure 2. (a) Main and (b) secondary flow routing through the FDP system (blue—PC intake, low temperature; orange—compressed air, medium temperature; red—PE exhaust, high temperature). Figure adapted from Klingels [12].

2.2.2. Piston Engine Modeling

The piston engine is modeled in the in-house piston engine performance simulation tool using a single-zone cylinder modeling approach. It resolves the thermodynamic state within the cylinder over time/crankshaft angle ($\varphi$) without resolving the spatial flow field in the cylinder. The calculation provides crank-angle-resolved relevant thermodynamic properties, such as temperature ($T\left(\varphi \right)$), pressure ($p\left(\varphi \right)$), and integrated cycle data (heat loss Q and power output P). Mass and energy conservation are solved in a control volume, as illustrated in Figure 3, where m stands for mass and H, Q, and W represent total enthalpy, heat, and work, respectively. The subscripts of $in$ and $ex$ denote intake and exhaust flows. Since the single-zone model does not account for the spatial distribution and flow of fuel and air, the combustion dynamics, such as mixing and flame-wall interaction, of the piston engine are simplified by this modeling approach. Nevertheless, the single-zone model approximates global parameters, including heat release rate and mass flows, which are most important for a whole-engine assessment.

Figure 3. Mass flow and energy balance of the piston engine single-zone model within the indicated control volume.

To cope with the location-dependent heat release and heat transfer within the cylinder, semi-empirical models are used in zero-dimensional models. For simplicity, the combustion process in the PE of the FDP is assumed to be equivalent to conventional crankshaft-based piston combustion. Even without a detailed resolution of the specifics of the free piston motional characteristics, the zero-dimensional performance model validated for crankshaft-based engines is a reasonable starting point for the simulation of the FDP system. Initial evaluations indicate that the free piston motion characteristic closely resembles a sinusoidal profile, with increased deceleration before and acceleration after the top dead center. Nevertheless, preliminary analysis shows that describing the piston motion with a sinusoidal wave function introduces only minor deviations.

The heat release rate is prescribed by the empirical Wiebe function with two Wiebe parameters $w_a$ and $w_m$ [24], given by the following equation:

$${\displaystyle \frac{\mathrm{d}{Q}_{fuel}}{\mathrm{d}\varphi }}={\displaystyle \frac{Q_{fuel,tot}}{\Delta {\varphi }_{CD}}}{w}_a(w_m+1){\left({\displaystyle \frac{\varphi -{\varphi }_{SOC}}{\Delta {\varphi }_{CD}}}\right)}^{w_m}exp\left[-w_a{\left({\displaystyle \frac{\varphi -{\varphi }_{SOC}}{\Delta {\varphi }_{CD}}}\right)}^{w_m+1}\right],$$

(1)

where $Q_{fuel}$ denotes the heat release, $\varphi$ the crankshaft angle, $\Delta {\varphi }_{CD}$ the combustion duration, and ${\varphi }_{SOC}$ the start of combustion. The total amount of released energy ($Q_{fuel,tot}$) is calculated as the product of the total fuel mass ($m_{fuel}$) in the cylinder and the fuel lower heating value (LHV) as follows:

$$Q_{fuel,tot}=m_{fuel}·\mathrm{LHV}.$$

(2)

For lean combustion systems, the Wiebe parameter $w_a$ is set to 6.908, which represents a combustion efficiency of 99.9%. If rich combustion is considered, $w_a$ is adapted to account for a reduced combustion efficiency.

The heat transfer from the hot gases in the cylinder to the surrounding piston walls is modeled using Newton’s law of cooling according to

$$\dot{Q}=a_{heat}·\alpha A\left(T_g-T_W\right),$$

(3)

where $\dot{Q}$ is the wall heat transfer rate, $a_{heat}$ is a calibration factor, $\alpha$ is the wall heat transfer coefficient, A is the total wall surface area, $T_g$ is the bulk gas temperature and $T_W$ is the wall temperature averaged over the heat transfer surface. To calculate the amount of heat transferred, a semi-empirical model to obtain the heat transfer coefficient ($\alpha$) introduced by Hohenberg [25] is used. The Hohenberg correlation reads as follows

$$\alpha =130·V^{-0.06}{p}^{0.8}{T}^{-0.4}{\left(v_m+1.4\right)}^{0.8},$$

(4)

with the cylinder volume (V), pressure (p), and temperature (T) at the current crankshaft angle position, as well as the cylinder mean velocity ($v_m$). It should be noted that the values in Equation (4) are in SI units except for the pressure, which has to be inserted in bars. The calibration factor ($a_{heat}$) is adjusted to reproduce the results in NASA-CR-188232 [26]. A more detailed description of the methods used in the in-house piston engine performance simulation tool is available in Ref. [13].

The piston compressor is modeled using the same single-zone thermodynamic conservation laws as used for the piston engine, including wall heat transfer, but without the heat release term due to combustion. The annular geometry of the piston compressor, in contrast to the circular piston engine, is taken into account.

To evaluate the performance of the CCE, the mass estimation of the piston system is crucial. The FDP cylinder mass estimation is based on Ref. [13]. A bottom-up mass modeling approach is applied, where the cylinder head, casing, and piston are taken into account. The piston is assumed to be a hollow cylinder. The wall thickness of the considered components is fixed at 10 mm. The wall thickness assumption requires validation in future studies to ensure it can withstand the imposed structural and heat loads. The high peak pressures and the elevated liner temperature in the piston engine cycle pose high requirements on material-specific properties. When compared to the cylinder block of a classic crankshaft-based piston engine, the structural load cases for an FDP-based engine are much relieved [27,28]. The FDP wall thickness is estimated at the upper range of typical values for crankshaft-based engines [29] to ensure sufficient resistance for both mechanical loads and thermal stresses. In the absence of a detailed component mass model for the FDP auxiliary systems, the additive weight was mapped as a factor relative to the bare FDP unit. The plumbing and other supporting structures around the FDP unit are conservatively estimated to be in the same order as the device itself, i.e., adding 100% of the bare FDP weight.

2.2.3. Integration in Engine Performance Environment

The FDP system is represented by a series of different interconnected components in APSS, as outlined in Figure 4. Besides the main flow of the working fluid, the schematic depicts the occurring heat fluxes, fuel flows, and secondary flows within the FDP. In line with the patent, the main flow passes through a buffer volume, the piston compressor (31), an interconnecting PC-to-PE duct, then the piston engine (33), and finally through a mixing duct before exiting the FDP system and being routed into the GT-CC for residual combustion. The split between main and secondary flow within the FDP is realized in the PC-to-PE duct; the secondary flow exiting the PC-to-PE duct does not pass through the PE but is directly routed through the cooling duct and the mixing duct (35), where it mixes with the main flow exiting the PE. To adequately represent the heat fluxes outlined in the patent, the PC-to-PE duct and cooling duct take up the heat rejected by the PC and the PE, respectively. A fraction of the PE heat flux is also rejected into the surrounding bypass flow.

Figure 4. FDP system block diagram, as implemented in the in-house performance tool APSS.

The key piston compressor and piston engine parameters are integrated in the CCE calculation as described previously. Owing to the comparatively high computational effort for the piston simulation, the relevant piston parameters are incorporated into APSS via surrogate modeling techniques. Therefore, feed-forward neural network-based surrogate models are created based on the work from Ref. [20] for the piston engine and the piston compressor. Design parameters that best describe their performance are selected to define the parametric space covered by the surrogate model. In accordance with the number of inputs, 30,000 and 3000 simulation points, distributed over the design space via Latin hypercube sampling [30], are calculated for the regression and validation data, respectively. The regression dataset has been validated against the validation data group. Since the parametric space of the surrogate model extends to abnormal engine operation, including long combustion durations and early or late valve opening and closing timings, the mean relative error of the critical outputs, including intake air flow, exhaust fuel air ratio, exhaust temperature, power, and heat, is in the range of 2%. However, the errors do not directly propagate to the performance outputs of the CCE modeling due to the interaction between all output parameters. The uncertainty of the surrogate model on engine level is evaluated in Section 4.

2.3. Performance Synthesis and Key Input Parameters

To compute a full engine in APSS, several inputs need to be set. Standard operating conditions are represented by a flight Mach number, altitude, $\Delta T$ according to the International Standard Atmosphere (ISA), and a thrust requirement. In addition, the fan diameter, OPR, turbine entry temperature, component tip speeds, and power offtakes are specified. Connecting ducts between components are accounted for by pressure losses of the order of 1%. To specify the FDP system, the number of pistons, the piston mean velocity, valve timings, liner temperature, the PE air–fuel equivalence ratio ($\lambda$), and the pressure ratio for the PE are prescribed to meaningfully reflect advanced technology with an entry-into-service (EIS) of 2045. Moreover, the percentage of heat that remains within the FDP system compared to the heat that is transferred into the bypass duct (see Figure 4) is defined.

Using the above assumptions, an iterative scheme for both design and off-design calculations is established. The top-of-climb (ToC) condition is chosen as the design point, and the design and target variables are summarized in Table 1. For the FDP, an iterative scheme was established as a function of the most relevant design parameters. The FDP inner diameter is sized such that the mass flow rates match between the PC inlet and the IPC outlet, whereas the FDP outer diameter is iterated such that the PE and PC power requirements coincide. To account for the FDP internal cooling flow that passes through the cooling duct without being injected into the PE (see Figure 4), the PC pressure ratio is iterated to meet a target cooling duct outlet temperature. The piston engine compression ratio, which relates the cylinder volume at bottom dead center to the top dead center, is iterated to achieve the piston engine’s maximum pressure. As mentioned in Section 2.2.2, the PC and PE are mechanically connected. This is not precisely represented in the model but approximated by the simulated piston motions.

Table 1. Iterative scheme implemented in APSS at design point (ToC).

Design Parameter	Target Parameter
Engine Level
Intake-reduced flow rate $w_{2,corr}$	Fan tip diameter $D_{2,tip}$
IPC pressure ratio ${\Pi }_{21}$	Overall pressure ratio (OPR)
Fan inner pressure ratio ${\Pi }_{2,i}$	Fan-specific work split $\Delta h_i/\Delta h_o$
Fan outer pressure ratio ${\Pi }_{2,o}$	Streamtube net thrust $F_{N,st}$
Fan tip speed $u_{2,tip}$	Fan tip speed predicted as function of $p_{13}/p_2$
Bypass ratio (BPR)	Ideal nozzle exit velocity ratio $v_{18}/v_8$
IPC inlet hub-to-tip ratio $D_{21,hub}/D_{21,tip}$	IPC inlet hub diameter $D_{21,hub}$
Gearbox shaft gear ratio	LPT tip speed $u_{45,tip}$
FDP Level
FDP inner diameter $D_{FDP,i}$	Mass flow convergence in the FDP
FDP outer diameter $D_{FDP,o}$	Power convergence in the FDP
Piston compressor pressure ratio	Outlet temperature of cooling duct (see Figure 4)
Piston engine compression ratio	Piston engine maximum pressure

In off-design, all geometrical parameters are fixed and only the operating conditions are adapted; turbocomponent efficiencies are read from the selected and suitably scaled component maps. The burner outlet temperature $T_4$ and the relative spool speeds of the low-pressure and high-pressure shafts are varied to meet the off-design thrust requirements. Within the FDP, the PE air-to-fuel equivalence ratio ($\lambda$) and the piston velocity are iterated to meet the mass flow and power convergence; the PE compression ratio is adjusted with respect to the PE maximum pressure. The piston compressor pressure ratio is treated as a free design parameter, introducing an additional degree of freedom in off-design operation.

2.4. Baseline Aircraft Design Methodology

To facilitate appropriate aircraft-integrated evaluation and benchmarking of CCE concepts against similarly advanced but conventional GTF engines, a set of aircraft designs generated to cover a wide market range is employed. These aircraft, referred to as the baseline aircraft, represent the short- (SR), medium- (MR), and long-range (LR) market segments. They are derived as evolutionary variants of the Airbus A220-300 (Airbus Canada, Mirabel, QC, Canada), A321XLR (Airbus Operations, Hamburg, Germany), and A350-900 (Airbus Operations, Toulouse, France) reference aircraft and are powered by the MINIMAL baseline engines, i.e., advanced ultra-high-bypass-ratio GTF power plants. The baseline aircraft specifications include technological enhancements within the tube-and-wing framework without relying on disruptive technologies, apart from the introduction of liquid hydrogen (LH₂) on the SR platform. These configurations are illustrated in Figure 5, and, along with their corresponding reference aircraft, they are designed with the Bauhaus Luftfahrt Aircraft Design Environment (BLADE) [31,32], which primarily employs semi-empirical methods for aircraft sizing, focusing on mass estimation, aerodynamics, and overall aircraft performance [33,34,35].

Figure 5. Baseline aircraft configuration illustrations (scaled relative to each other).

Most of the top-level aircraft requirements (TLAR) aim to match the performance of the reference aircraft operated today, while certain requirements are modified to anticipate the evolution of air traffic until the entry-into-service (EIS) year and reduce their climate impact. A collection of all TLARs employed for the aircraft design process is shown in Table 2.

Table 2. Baseline aircraft TLARs.

Requirement	Units	SR	MR	LR
Technology freeze year (TRL6)	-		2035
Design range	nmi	2000	4200	8000
Design PAX (single-class)	-	150	200	330
Design payload	t	14.7	18.9	31.3
Maximum payload	t	18.7	22.9	54.0
Cruise Mach number	-	0.7	0.78	0.85
Cruise altitude	-	FL350 *	FL350	FL370
Maximum operating altitude	-	FL410		FL430
One-engine-inoperative ceiling (drift-down)	-		≥FL170
Diversion range	nmi		200
Holding duration	min		30
Contingency fuel ** (%)	%		5
Take-off field length (MTOM, SL, ISA+15)	m	≤2140	≤2940	≤2980
Landing field length (MLM, SL, ISA)	m	≤1510	≤1620	≤1970
Time to climb	min		≤25
Top-of-climb specific excess power	fpm		≥300
Airport compatibility wing span limits	-	ICAO Code C (≤36 m)	ICAO Code C (≤36 m)	ICAO Code E (≤65 m)
Approach speed	KCAS	≤140 (Approach Category C)

* Maintain efficient low-altitude operation down to FL200. ** Percentage of trip fuel.

More specifically, based on the available literature and various research projects [36,37], a one-engine-inoperative (OEI) ceiling of FL170 is imposed for all aircraft so that a 100 feet per minute (fpm) climb rate can be maintained at ISA conditions, and the climb time to cruising altitude is limited up to 25 min. A top-of-climb-specific excess power lower limit of 300 fpm is enforced for all missions to ensure sufficient performance reserves to respond to air traffic restrictions and collision avoidance maneuvers [38]. Regarding airport compatibility, the same International Civil Aviation Organization (ICAO) requirements as the reference aircraft are used to specifically restrict wingspan. Moreover, the take-off field length (TOFL) and approach speed requirements are defined based on the reference aircraft performance such that, in combination with the ICAO limitations, the same airports as the reference aircraft are accessible by their baseline counterparts.

To determine suitable technology options, results provided by various research projects and studies [36,39,40,41,42] are adopted, and their potential performance enhancement is quantified in the form of “improvement factors”, which scale the results of the models employed within the aircraft design loop. These factors are shown in Table 3.

Table 3. Aircraft technology improvement factors.

	SR	MR	LR
Fuselage advanced composites	0.95	0.90	0.95
Wing advanced composites
Empennage advanced composites
Landing gear advanced materials
Operator item advanced materials
Air conditioning	1.70
De-icing	1.50
Electrical (distribution/generation)	1.73	1.73	2.40
Hydraulics (distribution/generation)	0.00
Fly-by-light controls	0.76

In particular, a structural weight reduction may be achieved through the extensive utilization of carbon fiber-reinforced polymers. A weight reduction of 10% is assumed for the MR and 5% for the SR and LR aircraft considering the assumptions found in Refs. [36,39,40], input from project partners, and aligning these assumptions with the Horizon Europe project HOPE [41]. Similarly, additional weight reductions are achieved through advancements in cabin furnishings and operator items, resulting in a 10% improvement for the MR and 5% for the SR and LR aircraft. As for the aircraft’s baseline subsystems, an all-electric architecture is assumed, similar to Ref. [36]. Electrifying all subsystems replaces hydraulically and pneumatically powered systems, such as the environmental control system and the actuation systems for the flight controls and the landing gear. The effects of this are also quantified in Table 3.

For all aircraft cases investigated, a high aspect ratio wing is used, with an aspect ratio of 12, similar to Ref. [36]. In the cases where the resulting wing span exceeds the ICAO box limitations, a wing folding mechanism similar to the Boeing 777X (Boeing Commercial Airplanes, Everett, WA, USA) is implemented. Several improvements are also assumed for the designed GTF engines, and, since the reference and the baseline aircraft operate with different fuel types (kerosene vs. SAF/LH₂) and at different Mach numbers, the overall engine efficiency [20] is identified as an appropriate metric for comparisons. This efficiency is calculated based on the aircraft cruising speed and thrust-specific power consumption (TSPC, as defined in Equation (5) [43]), so 10%, 7%, and 9% improvements are found for the SR, MR, and LR baseline engines, respectively [4,44]. The definition of TSPC is written as

$$\mathrm{TSPC}={\displaystyle \frac{P_{supply}}{F_0}};\mathrm{TSPC}=\mathrm{TSFC}·\mathrm{FHV}$$

(5)

where $P_{supply}$ denotes the power supply from all energy sources, including electrical power and chemical energy sources; $F_0$ stands for the generated net thrust. For conventional heat engine cycles, TSPC is related to TSFC with the fuel heating value (FHV).

As the SR baseline aircraft is operated with LH₂, analytical methods and models are employed to determine several properties regarding its fuel system and tanks. Their assumptions are primarily based on Ref. [45] and include both structural and thermodynamic considerations, as introduced in Ref. [46], which are applicable to both components. As the focus of the current document lies in the LR platform employing a SAF-fueled FDP architecture, the LH₂ aspects of this study are not further discussed.

To perform the aircraft design process within BLADE, the reference aircraft are first modeled so that the methods and the models of BLADE are meaningfully calibrated. Most of their data is taken from the published Aircraft Characteristics Airport and Maintenance Planning documents [47], as well as drawings published for airport planning operations [48]. Several design rules are then applied to perform the baseline aircraft sizing. The wing area and position are defined by a specified wing loading and static margin derived from the reference aircraft, which may be adapted in case the approach speed constraint is violated. Similarly, the horizontal and vertical stabilizers are scaled based on the reference aircraft stability volume coefficients, and their position is fixed relative to the fuselage tail’s end so that, in the case of the SR aircraft, as the fuselage length increases to accommodate the hydrogen tanks, the empennage is positioned accordingly. The main and nose gear lengths are adapted to satisfy a set of safety angles and clearances based on the reference aircraft. The baseline engine models are provided by Chalmers University of Technology and are integrated into BLADE as surrogate models based on the process defined in [20]. The surrogate models follow the same design methodology as described in Section 2.2.3 and consist of design and off-design input parameters that define the parametric space of the engine operation. A regression dataset with 20,000 points is validated against the validation dataset with 2000 points. The neural network achieves less than 1% of mean relative error across all outputs. During the aircraft design loop, the aforementioned design rules are applied, and the engine design thrust is dynamically adapted based on a specified subset of the TLARs, from which the most constraining one is selected at each iteration. This process is repeated to generate new designs and perform parameter studies, which are particularly important for the generation of non-linear trade factors that may be used in independent engine design studies.

2.5. Non-Linear Trade Factor Analysis

As the MINIMAL project aims to evaluate radical engine concepts while introducing aircraft-level sensitivities in the engine-specific design studies, a set of non-linear trade factors is generated and a process for utilizing them is presented in the current document. This process is based on the method introduced in Ref. [39]. As stated in [39], linearized trade factors may over-predict fuel burn improvements by 2–3% when evaluating large TSFC changes. The approach allows for thrust requirement adaptation and is sensitive to imposed changes in engine mass and size.

Therefore, variations in engine mass (total power plant system mass, excluding pylons), TSFC (streamtube control volume), and nacelle size (length and diameter) are analyzed, for which a new aircraft design of each class is generated. These variations are performed by applying scale factors to the outputs of the models within BLADE, and, therefore, considering the TSFC variations, all values along each mission are scaled equally.

Via utilizing these non-linear trade factors, an iterative approach may be employed to support an engine design study as follows. First, the design thrust of the baseline case is selected. Based on this requirement, a new engine concept is designed such that, in the case of a CCE architecture, an improvement in TSFC along with a heavier mass is achieved. The relative change in these two variables is used to determine a new design thrust. Furthermore, changes in the nacelle diameter and length are used to determine an additional increment on the calculated design thrust, which will then result in a new design thrust requirement that is used in the next iteration. This process is repeated until the convergence criteria are met. These new engine characteristics are finally employed to determine the energy demand improvements over the reference or baseline aircraft. Instead of only utilizing the design point, the TSFC and thrust demand at three operational points of interest (take-off rotation, top-of-climb, and mid-cruise) may be used. For this approach, an equivalent TSFC (TSFC_eqv) must be obtained by calculating a weighted mean of the TSFC values at these points. The TSFC_eqv is written as

$${TSFC}_{eqv}=f_{CR}·{TSFC}_{CR}+f_{ToC}·{TSFC}_{ToC}+ f_{TO}·{TSFC}_{TO},$$

(6)

where $f_{segment}$ stands for the fractional fuel burn associated with each point, corresponding to either the design or typical mission of the aircraft. The non-linear trade factors are shared as an attachment to this document in the form of tabulated data such that automated processes may be set up by interested parties.

3. Results

This section covers the whole-engine performance (design and off-design) and concept evaluation results of the LR-FDP-CCE. In the design point study at ToC, a sensitivity study on the FDP internal cooling is first performed, followed by an OPR and $T_4$ analysis. In the off-design assessment, the part-power curve is evaluated at the CR condition, keeping the Mach number, altitude, and $\Delta T$ ISA constant while varying thrust. The final results at both CR and TO are presented. On the aircraft level, the result of the baseline aircraft methodology is presented alongside the CCE result.

3.1. Design Study

3.1.1. FDP Cooling System

The LR-FDP-CCE model is constructed upon the technology assumption of an advanced GTF in 2045, utilizing sustainable aviation fuel (SAF). The implementation of an FDP cooling mechanism is critical for subsequent engine sizing studies since the cooling behavior influences engine performance. To understand the internal cooling effect of the FDP, as illustrated in Figure 4, a sensitivity study on the outlet temperature of the internal cooling bleed is performed. Cycle parameters at the chosen design point, ToC, and characteristic values of the piston system are shown in Table 4. The parameters are employed for all design point studies unless stated otherwise. The piston parameters are assessed for an EIS2035 short-range FDP-CCE, taken from Ref. [13]. The analysis assumes that no substantial advancements in piston technology will occur from 2035 to 2045. A liner temperature of 1000 K is permitted given that oil lubrication is considered unnecessary in the FDP system. A higher temperature is omitted to respect the thermal constraints in the material. The mechanical transmission efficiency is higher than a standard crankshaft-based variant owing to the absence of a crankshaft and bearings. The current engine study assumes 10 FDP system units, corresponding to 20 piston engine cylinders. To determine the optimal number of FDP units, the architectural design of the CCE and the associated failure modes will need to be further evaluated.

Table 4. Parameters for SAF-based LR-CCE at ToC.

Parameter	CCE Cycle
Altitude [m]	10,668
Mach [-]	0.84
Thrust [kN]	82.3
$\Delta T$ ISA [K]	10
Fan diameter [m]	3.56
Parameter	Piston System
Piston engine peak pressure [bar]	150 [13]
Mean piston velocity [m/s]	24 [13]
Liner temperature [K]	1000 [13]
Mechanical transmission efficiency [%]	99.5 [13]

Due to the partial fuel burn in the piston system, the burner exit temperature and the OPR are significantly lower in a CCE than in a typical comparable GTF. In a CCE cycle, the OPR is defined as the piston compressor outlet pressure over the intake pressure. The preliminary $T_4$ and OPR values, chosen as an initial step for assessment, are taken from Ref. [2]. A similar value range is also presented in Ref. [3]. Dedicated studies on the cycle design at ToC are performed in Section 3.1.2. To roughly estimate the cooling effectiveness of the internal cooling bleed, as mentioned in Section 2.2.3, the current thermal solution assumes that 50% of the wall heat loss through piston combustion is absorbed by the cooling duct, and the other half is rejected into the bypass (see Figure 4). However, the temperature increase in the bypass flow due to this heat rejection is neglected for now. As a result, the TSFC is slightly underestimated.

Since the FDP system is a self-sustained gas generator, the pressure ratio across the piston compressor is an indicator of the generated power from the piston engine. In the FDP internal cooling study, the amount of required cooling mass flow impacts the available power output of the piston engine. Hence, the compression work done by the piston compressor is affected, and the piston compressor pressure ratio is determined as a key output parameter. The cooling mass flow also takes away working fluid for the combustion process and impacts fuel efficiency and cycle-specific work output. Hence, TSFC and BPR are important parameters when considering best and balanced trade-offs in finding a feasible thermal solution.

As shown in Figure 6, when the cooling temperature constraint is increased to the upper limit of the 1000 K liner temperature, defined in Table 4, the percentage of internal cooling mass flow relative to the core flow drops to around 7%, as shown in Figure 6a. Illustrated in Figure 6b, the pressure ratio across the piston compressor increases with a higher cooling duct outlet temperature since a higher percentage of working fluid contributes to the power generation in the FDP system. When the piston compressor pressure ratio changes under different cooling constraints, the number of IPC stages is adapted based on the stage loading and efficiency optimization. A step change in the curves occurs at around 985 K, where the number of IPC stages reduces from 7 to 6. The variation in IPC stage count is indicated with a dashed line in Figure 6. The increase in specific work output of the FDP system leads to a decrease in TSFC and an increase in BPR, as shown in Figure 6c and Figure 6d, respectively. To choose an exit temperature of the cooling duct for future engine studies, the lower boundary is determined by the piston compressor exit flow, around 800 K, and the upper boundary is defined by the 1000 K liner temperature. Through observation of the piston system temperature levels, and TO and CR point consideration, an exit temperature of 900 K is chosen for the internal cooling air as a trade-off between engine efficiency and the temperature limit of the component material.

Figure 6. Output parameters of the SAF-LR-CCE under different cooling duct outlet temperatures: (a) Percentage of internal cooling bleed/core flow. (b) Piston compressor pressure ratio. (c) TSFC. (d) BPR. The dashed line indicates the change in IPC stage count.

3.1.2. Cycle Definition

From the study shown in Figure 6, an exit temperature constraint of 900 K is implemented in the cooling duct inside the FDP system. A two-dimensional study on $T_4$ and OPR is presented in Figure 7. A cooling air model is implemented to account for variations in HPT cooling as the thermal loading of the turbine component changes, whereas the LPT is treated uncooled in the cycle study. The TSFC dependencies on $T_4$ and OPR are shown in Figure 7a. In contrast to a conventional GTF, the whole-engine performance improves when the burner exit temperature decreases. This characteristic of the CCE results from an increased fuel burn in the FDP system given that closed-volume combustion is more efficient than the nearly isobaric combustion in the Joule burner. The blue line in Figure 7 marks the highest permissible inlet temperature for the Joule burner ($T_{35}$) of 1150 K, which is assumed due to the material temperature limit and considered as an operational constraint of $T_{35}$ not exceeding 1200 K at TO. This basic constraint is adopted from previous studies of crankshaft-based CCE concepts [3]. Furthermore, at a higher OPR, the temperature levels in the FDP system increase, causing growth in the internal cooling bleed, as shown in Figure 7b. The impact of the FDP internal cooling is also reflected in BPR, shown in Figure 7c. At a given fan diameter and thrust requirement, BPR changes together with the cycle-specific work capacity. As shown in Figure 7c, BPR increases toward high $T_4$ and low OPR due to a less demanding cooling requirement in the FDP. Although the CCE has a lower TSFC at low $T_4$ and high OPR, the BPR decreases due to the increasing demand for the FDP internal cooling. Figure 7 shows the piston system weight resulting from the hollow cylinder mass method described in Section 2.2.2, which decreases toward high $T_4$ and high OPR, directly resulting from the shrinking size of the FDP devices as turbo-precompression is increased with OPR and cycle-specific work output is enhanced with $T_4$. Hence, trade-offs between TSFC and piston mass are inevitable when selecting the $T_4$ value at the engine sizing point. The $T_4$ value is chosen mainly based on TSFC optimization. The aircraft-level evaluation (Section 3.4) will show that the TSFC gain outweighs the weight penalty. Based on the prescribed $T_{35}$ limit, a design point (marked with the yellow square point) at $T_4$ = 1400 K and OPR = 32.4 is chosen for TSFC optimization. $T_4$ is chosen to allow for sufficient operational flexibility both during the part-power operation in CR as well as maximum thrust demands during TO. This temperature margin is considered to avoid entering invalid cycles (higher $T_{35}$ than $T_4$) in CR.

Figure 7. $T_4$ and OPR study for SAF-LR-CCE: (a) TSFC. (b) FDP internal cooling bleed. (c) BPR. (d) FDP mass.

A comparison of an advanced GTF in 2045 and the established CCE is shown in Table 5. The CCE operates at a significantly lower $T_4$ and OPR due to the added combustion in the FDP, as previously mentioned. The TSFC improves by 9.8%, with a 20.4% increase in BPR compared to the GTF. The HPT relative cooling bleed is notably reduced due to the lower operating temperatures in the CCE.

Table 5. SAF-LR-CCE performance at ToC compared to an advanced GTF.

Parameter	GTF	FDP-CCE
$T_4$ [K]	1828	1400
OPR [-]	69.8	32.4
TSFC [g/kN/s]	14.16	12.77
BPR [-]	14.2	17.1
Relative HPT cooling air [%]	20	8.4

3.2. Off-Design Analysis

After determining the geometry of the turbo components and the piston system in the design studies, the CCE is evaluated at the off-design points. In the part-load study, the part-power thrust is reduced to a relative thrust ($F{N}_{rel}$) of 50% at the ToC point. The relative thrust values focus on the typical range for CR. Idle operation may be considered in future research. The assessment is performed at FL350, Mach number 0.85, and $\Delta T$ ISA at 0 for all operating points. In the current study, the piston compressor pressure ratio is kept constant, the same as the value at ToC, for all part-load operating points. For a more detailed off-design operation study, the change in compression work distribution between the IPC and the piston compressor under low-power operation should be examined.

The GTF and the CCE part-power curves are compared in Figure 8, where the CR points for both engines are marked in circles. The CCE exhibits a relatively flat bucket curve, with TSFC values consistently lower than those of the GTF (Figure 8a). The phenomenon may be explained by the second combustion in the cycle, where more fuel burn takes place in the piston engine. As shown in Figure 8b, the fraction of fuel burn in the FDP increases from 76% to around 84% when the thrust is reduced to half of the value at ToC. As $F{N}_{rel}$ decreases further beyond the CR point, the FDP fuel burn over total fuel burn increases more rapidly. This trend is governed by a sharper change in the PE air-to-fuel equivalence ratio, associated with an increasing piston engine efficiency at low $F{N}_{rel}$. Based on the trends discovered in Figure 8, at low $F{N}_{rel}$, fuel consumption in the relatively inefficient Joule burner is reduced, while the piston system continues to deliver a sufficient power level for operation. Hence, the shape of the CCE bucket curve is less sensitive to the thrust changes and demonstrates a minimum at lower $F{N}_{rel}$. The characteristic of an enlarged improvement in TSFC toward a lower $F{N}_{rel}$ may be particularly beneficial for climate assessment when the engine operates at a lower power mode to avoid contrail generation, for instance. Further analysis on changing the flight altitude is essential to determine a realistic contrail avoidance benefit over GTFs, but the current CCE part-power performance shows promising results. The assumption of a constant pressure ratio across part load operation may result in complexity in off-design engine control. To provide enough power output and meet the peak pressure while operating at lower temperature and pressure levels, the compression ratio changes in part power. Such practical challenges are further detailed in Section 4.

Figure 8. (a) Comparison of part-power performance of the CCE and the GTF. (b) FDP fuel burn percentage in part-power mode.

The overall performance of the selected three operating points is shown in Table 6. The highest temperature level occurs at TO, where $T_{35}$ reaches 1181 K and $T_4$ reaches 1535 K. The $T_{35}$ limit of 1150 K set at ToC allows a slightly raised temperature at TO without risking an inlet temperature for the Joule burner higher than 1200 K in TO. The TSFC in CR improves by 9.3%, and BPR increases by 18.1% relative to the 2045 GTF, consistent with the range observed in the ToC comparison in Table 5. The piston engine peak pressure is set at 250 bar [49] at TO, defining the highest permissible mechanical loads on the piston system. Compared to the other operating points, the piston compressor pressure ratio is reduced at TO due to the restriction of $T_{35}$. Since a high fraction of fuel burn in FDP at TO does not yield significant fuel burn benefits, as shown in Section 3.4, a trade-off is made to meet material temperature constraints. A higher FDP cooling demand is expected at TO due to the higher temperature levels. The ratio of the FDP fuel burn versus total fuel burn is the lowest at TO and highest at CR. The highest fraction at CR is beneficial for fuel burn assessment since a higher fuel consumption in the FDP system leads to a larger TSFC improvement. The present work assumes active valve control in the FDP cooling system, allowing for varying FDP internal cooling mass flow in off-design mode. For a passive cooling flow system design with a fixed amount of cooling mass flow in all operating points, a multi-point design is necessary to account for the most constraining heat load operation.

Table 6. SAF-LR-CCE performance at different operating points.

Parameter	ToC	TO	CR
Altitude [m]	10,668	0	10,668
Mach [-]	0.84	0.24	0.85
Thrust [kN]	82	317	65
$\Delta T$ ISA [K]	10	0	0
$T_{35}$ [K]	1150	1181	1057
$T_4$ [K]	1400	1535	1216
OPR [-]	32.4	25.3	27.1
TSFC [g/kN/s]	12.77	7.83	12.15
BPR [-]	17.09	18.88	18.54
Piston engine peak pressure [bar]	150	250	125
Piston compressor pressure ratio [-]	3.58	3.05	3.58
FDP internal cooling bleed/core flow [%]	11	15	13
Piston engine compression ratio [-]	7.98	5.91	7.71
FDP fuel burn/total fuel burn [%]	70	61	77

3.3. Baseline Aircraft Results

Based on the aircraft design process outlined in Section 2.4, the main baseline aircraft results are shown in Table 7. In this case, the block energy consumption per passenger (PAX) and nautical mile is selected as an appropriate metric for comparison as the reference and baseline aircraft utilize different fuel types and may operate over different ranges.

Table 7. Integrated baseline aircraft results.

	Units	SR	MR	LR
Maximum take-off mass	t	63.4	91.1	250.4
Operating empty mass	t	45.2	48.9	132.6
Wing reference area	m2	126.8	113.8	394.3
Design thrust, top-of-climb, ISA+ 10	kN	21.0	29.3	73.8
Take-off thrust, sea-level, M0.2, ISA+15	kN	77.1	104.7	250.9
Thrust-specific power consumption, mid-cruise, ISA+10	W/N	534.8	608.1	611.8
Lift-to-drag ratio, mid-cruise, ISA+10	-	18.8	18.8	22.2
Design mission block energy per PAX and NM	MJ/PAX/NM	1.12	1.06	1.29
Design mission relative improvement to year 2020	%	−12.5	−16.4	−20.4
Take-off field length, MTOM, sea-level, ISA+15	m	2140	2940	2980
Approach speed, MLM, sea-level, ISA	KCAS	129	137	140

The smallest energy consumption reduction is found for the SR aircraft at −12.5% as it utilizes LH₂ as its energy carrier, leading to higher structural masses and a longer fuselage. In particular, a front-and-aft tank configuration is employed, and their gravimetric indexes are found to be 49.3% and 48.9%, respectively. The fuel system mass for this configuration is found to be 767 kg. As for the MR and LR aircraft, 16.4% and 20.4% improvements in the energy consumption are determined, respectively. The LR aircraft, which operates over longer ranges, is more sensitive to the technology improvements applied and thus experiences the largest enhancement. As is evident from the results, the engine sizing is driven by the imposed TOFL limitation, which matches the TLARs outlined in Table 2.

3.4. Concept Evaluation

In this section, the nonlinear trade factor analysis described in Section 2.5 is applied to evaluate the design mission fuel burn of the CCE. The impacts of streamtube-based TSFC (TSFC_st), engine weight, and nacelle geometry are incorporated to resize the SAF-LR-CCE aircraft. The mass breakdown of the GTF and the CCE comparison are shown in Table 8. The turbocomponents in the CCE are around 4% lighter, primarily due to the absence of the HPC. A higher cycle-specific work capacity also results in a smaller turbine sizing for the CCE. At this stage of the mass breakdown analysis, the fan diameter is kept the same for the GTF and the CCE. After applying the non-linear trade factor analysis, the sizing thrust requirement is subjected to change for the CCE. Due to the compactness of the FDP device, changes in fan cowling size are neglected in the first instance. The core cowling size in the CCE will need to be considered with a more precise piston space estimation. Currently, no increase from the piston system has been added yet. Despite the preliminary weight assumption of the nacelle, a total of 18.2% weight increase in the CCE is relatively small compared to the crankshaft-based results in Ref. [6]. This is mainly due to the compact mechanical design of the FDP, where no bearings and crankshafts are needed. It is also important to emphasize that the current cylinder wall thickness for the FDP system is assumed to be 10 mm. At a liner temperature of 1000 K, the material is subjected to high thermal stress. By combining these characteristics, the technology assessment of the piston engine yields a rather optimistic outlook. Therefore, a more detailed thermal solution could lead to an increase in the FDP system mass estimation.

Table 8. Weight comparison between the GTF and the CCE.

Weights [kg]	GTF	FDP-CCE	Relative Difference [%]
Turbo engine	6032	5788	−4.04
Nacelle	3909	3909	0
FDP system	0	2055	-
Total	9940	11,752	18.2

To calculate the design mission fuel burn of the SAF-LR-FDP-CCE, the equivalent TSFC (TSFC_eqv) is calculated based on the method in Section 2.5, and the weighting factors are obtained from Table A1. Based on the previous engine study and mass estimation results, the SAF-LR-FDP-CCE possesses a lower TSFC_st but a higher engine weight compared to the 2045 GTF. In each iteration, the novel engine is resized with a fixed specific thrust, while the nacelle geometry is adapted to meet the new thrust demand at ToC.

The LR-CCE result, with the aircraft sizing cascade effects from the non-linear trade factor analysis, is summarized in Table 9. Under the new sizing thrust, the TSFC_eqv improves by around 11%, and the engine weight results in a minor increase of 10.7%. Due to an improved energy efficiency, the nacelle diameter is slightly reduced as the sizing thrust reduces. For the design mission fuel burn, the LR-CCE yields a 14.7% fuel reduction.

Table 9. SAF-LR-CCE fuel burn assessment.

Parameter	GTF	FDP-CCE
ToC TSFCst [g/kN/s]	13.96	12.81
CR TSFCst [g/kN/s]	13.90	12.37
TO TSFCst [g/kN/s]	7.94	7.55
Nacelle diameter [m]	4.06	4.01
Engine weight [kg]	9940	11,004
Relative fuel burn [%]	ref	−14.7

The non-linear trade factor analysis results are visualized in Figure 9 and Figure 10, where the extrapolated points are highlighted in red. The LR-CCE performance at ToC (marked with the yellow square), regarding the new thrust demand and the corresponding TSFC_st, is illustrated in Figure 9. The final design leads to a reduction in thrust demand at ToC of around 6.3%. The mission fuel burn visualization with respect to the CR TSFC_st is shown in Figure 10, where the LR-CCE is marked with the yellow circle. To estimate the impact of uncertainty in the piston mass estimation, a sensitivity study on the assumption of the piston system auxiliary mass is performed, while the relative equivalent TSFC remains the same as in Table 9. The results are presented in Table 10, demonstrating that the double-digit fuel burn improvement only diminishes when the auxiliary mass is assumed to be four times as heavy as the FDP system itself. In comparison to the baseline GTF, engine weight would increase by approximately 50% in this case. Hence, despite the uncertainty involved in auxiliary system mass estimation, significant fuel burn perspectives remain. At the current stage, only the fuel burn optimization has been taken into account. Hence, the fuel burn improvement indicates the upper boundary of the CCE conceptual design. When incorporating climate optimization, the fuel burn improvement is likely to be reduced.

Figure 9. ToC thrust visualization for the CCE against the LR baseline aircraft regarding engine mass and ToC TSFC_st.

Figure 10. Block energy assessment for the CCE against the LR baseline aircraft regarding engine mass and CR TSFC_st.

Table 10. Sensitivity analysis of piston system auxiliary weight impact on fuel burn.

Piston Auxiliary Weight Assumption [%]	Rel. Engine Weight [%]	Rel. Fuel Burn [%]
50	13.1	−15.5
100	18.2	−14.7
200	28.6	−13.1
400	49.2	−9.5

4. Discussion

Engine design and concept evaluation are conducted for an FDP-based CCE in a future long-range scenario. The FDP system exhibits several benefits over an advanced GTF baseline. The $T_4$ and OPR study shows that CCE turbomachinery operates at much lower temperature and pressure levels, reducing the cooling demand in turbine components. These findings are consistent with crankshaft-based variants of the CCE concept [5,6]. At ToC and CR operating points, the TSFC of the CCE improves by 9.8% and 9.3% over the 2045 GTF, respectively. Unlike the crankshaft-based CCE, the FDP-CCE does not require oil lubrication for bearings. Therefore, the cylinder liner temperature can reach up to 1000 K. A compressed air cooling mechanism is implemented, illustrating that only 13% of the core flow is required for CR and 15% for TO. These results confirm that the presented cooling method is feasible and reduces the FDP system’s mechanical complexity. Future research on detailed thermal solutions inside the FDP is required and is currently in progress to estimate the amount of heat dissipated into the bypass and its impact on fuel efficiency. With the compact mechanical design, the FDP-CCE has a lower weight penalty from the piston system compared to Refs. [3,6].

In the part-power curve study, due to the additional combustion in the piston engine, the TSFC minimum of the CCE bucket curve occurs at a lower thrust level compared to the GTF minimum TSFC point. The observation aligns with the part-load characteristic discovered in [5] as the piston system maintains a high power output in part-load operation. In contrast to [6], where the TSFC gain remains approximately constant at low relative thrust levels, the present results show an increasing TSFC benefit relative to the 2045 GTF as the relative thrust decreases to half of the ToC thrust. This new finding attests to promising CCE performance in lower part power and provides an initial indication of enhanced operational flexibility, including for climate-optimized flight techniques. A key challenge in CCE part-load operation is accomplishing precise off-design control of the FDP. While maintaining a constant pressure ratio across the part-power mode is desirable, it presents significant challenges for piston motion and control in practice. Future work may include assessing control laws for off-design operation, with a focus on the coupled dynamics of piston compression ratio, piston motion, and combustion.

The aircraft level evaluation with the non-linear trade factor analysis leads to an improvement of 11% equivalent streamtube-based TSFC and a reduction of 14.7% fuel burn on the long-range design mission relative to the GTF, while the engine weight only increases by around 10.7%, significantly lower than the relative engine weight increase in the crankshaft-based CCE [6,13]. The comparatively modest PPS mass increase is a direct result of the compact FDP system design. Furthermore, the aircraft sizing cascade effects captured by the non-linear trade factor analysis lead to a lower sizing thrust requirement for the CCE due to its superior energy efficiency. It is important to note that uncertainty in the piston system surrogate model may result in a certain degree of performance deviation. In an effort to quantify this uncertainty, the impact of neural network errors on key performance parameters was assessed. The deviation in TSFC for the chosen engine design was less than 1%, which translates to around 1% of the fuel burn deviation in the aircraft assessment. Overall, the CCE achieves a robust double-digit fuel burn reduction within the system’s error ranges.

While the FDP-CCE concept shows promising aspects in thermodynamic performance and structural simplicity, climate impact needs to be assessed in the future, such as NO_x emissions or other non-CO₂ effects. Previous studies show that adding an intercooler can be advantageous for NO_x reduction [6]. Hence, future studies may research the intercooled FDP-based CCE architecture and focus on vitiated air methods (i.e., through water/steam injection and/or exhaust gas recirculation) since incorporating non-CO₂ climate effects is essential to realistically estimate the fuel burn advantages and climate impact. The research from Ref. [14] presents a NO_x assessment on the piston engine level, including water injection and exhaust gas recirculation studies. The initial NO_x assessment is also studied at the CCE level. Future work on a more detailed climate assessment of the CCE design, including various architectural exploration and NO_x mitigation strategies, will be conducted to further understand the NO_x effects.

5. Conclusions

An FDP-CCE engine design study has been performed in the current work using an in-house propulsion system synthesis tool, and the results were compared to a baseline 2045 GTF. At ToC and CR operating points, the TSFC of the CCE improved by 9.8% and 9.3%, respectively, in comparison with the GTF. The compressed air cooling mechanism required 15% of the core flow at the TO condition while respecting the material temperature constraints at all the operating points. A part-power study demonstrated that the CCE reaches a TSFC minimum at a lower thrust level and possesses a more gradual bucket curve than the GTF. On the aircraft level, the CCE concept achieves a 14.7% relative fuel burn reduction for the design mission, with an increase of 10.7% in propulsion system weight. While non-CO₂ climate effects have not yet been taken into account, the CCE concept demonstrates high fuel efficiency and significant fuel burn potential for the LR application.

Appendix A.1

To determine TSFC_eqv in Equation (6), the masses of the fuel consumed over three relevant segments—namely take-off, climb and cruise—are summed, and a fraction of this sum is estimated for each segment, referred to as the fuel fraction. These fractions are shown in Table A1, considering all three aircraft platforms (SR, MR and LR).

Table A1. Design mission segment fuel fractions.

Segment	SR	MR	LR
Take-off	0.014	0.007	0.005
Climb	0.155	0.077	0.049
Cruise	0.831	0.916	0.946

Table A1. Design mission segment fuel fractions.

Segment	SR	MR	LR
Take-off	0.014	0.007	0.005
Climb	0.155	0.077	0.049
Cruise	0.831	0.916	0.946

The data for the non-linear trade factors are shown in the tables below for LR, MR, and SR, respectively. Only the most relevant columns are included. Other relevant data can be found in the supplementary Excel file. It is important to note that the SR aircraft is fueled by LH₂. The MR and LR aircraft use SAF as fuel. The relative thrust is abbreviated as rel. thrust in the tables below.

Table A2. TSFC and engine mass non-linear trade factors for the design mission of the LR baseline configuration.

Fuel Flow Factor [-]	Engine Weight Factor [-]	${\mathit{TSFC}}_{\mathit{eqv}}$ [g/kN/s]	Engine Mass [kg]	TO Thrust [N]	ToC Thrust [N]	CR Thrust [N]	Mission Block Energy /PAX/NM [MJ/NM]	Mission Relative Block Energy [-]
0.7	0.9	9.756	6884	200,838	51,562	38,143	0.747	0.578
0.7	1	9.752	7776	203,608	52,288	38,647	0.757	0.586
0.7	1.33	9.739	10,951	213,838	54,940	40,455	0.791	0.612
0.7	1.66	9.724	14,541	225,408	58,008	42,522	0.83	0.643
0.7	2	9.705	18,786	239,185	61,705	45,001	0.877	0.679
0.8	0.9	11.14	7403	213,642	54,889	40,043	0.897	0.694
0.8	1	11.135	8375	216,988	55,760	40,634	0.91	0.704
0.8	1.33	11.117	11,867	229,011	58,963	42,782	0.957	0.74
0.8	1.66	11.095	15,865	242,636	62,660	45,282	1.011	0.782
0.8	2	11.068	20,662	259,135	67,090	48,349	1.077	0.833
0.9	0.9	12.518	8011	228,533	58,836	42,315	1.068	0.827
0.9	1	12.511	9082	232,372	59,891	43,026	1.086	0.84
0.9	1.33	12.485	12,957	246,650	63,727	45,637	1.149	0.889
0.9	1.66	12.452	17,492	263,514	68,246	48,803	1.226	0.949
0.9	2	12.418	22,604	282,128	73,301	52,286	1.308	1.012
1	0.9	13.887	8742	246,020	63,559	45,126	1.268	0.981
1	1	13.877	9940	250,820	64,868	46,024	1.292	1
1	1.33	13.836	14,338	268,678	69,592	49,396	1.383	1.07
1	1.66	13.8	19,179	287,012	74,605	52,846	1.47	1.137
1	2	13.757	24,735	308,124	80,358	56,845	1.57	1.215
1.05	0.9	14.561	9202	256,985	66,490	47,024	1.388	1.074
1.05	1	14.551	10,459	261,895	67,808	47,920	1.413	1.094
1.05	1.33	14.512	15,020	280,003	72,701	51,334	1.504	1.164
1.05	1.66	14.47	20,092	299,918	78,108	55,106	1.603	1.241
1.05	2	14.423	25,860	322,249	84,201	59,354	1.712	1.325

Table A2. TSFC and engine mass non-linear trade factors for the design mission of the LR baseline configuration.

Fuel Flow Factor [-]	Engine Weight Factor [-]	${\mathit{TSFC}}_{\mathit{eqv}}$ [g/kN/s]	Engine Mass [kg]	TO Thrust [N]	ToC Thrust [N]	CR Thrust [N]	Mission Block Energy /PAX/NM [MJ/NM]	Mission Relative Block Energy [-]
0.7	0.9	9.756	6884	200,838	51,562	38,143	0.747	0.578
0.7	1	9.752	7776	203,608	52,288	38,647	0.757	0.586
0.7	1.33	9.739	10,951	213,838	54,940	40,455	0.791	0.612
0.7	1.66	9.724	14,541	225,408	58,008	42,522	0.83	0.643
0.7	2	9.705	18,786	239,185	61,705	45,001	0.877	0.679
0.8	0.9	11.14	7403	213,642	54,889	40,043	0.897	0.694
0.8	1	11.135	8375	216,988	55,760	40,634	0.91	0.704
0.8	1.33	11.117	11,867	229,011	58,963	42,782	0.957	0.74
0.8	1.66	11.095	15,865	242,636	62,660	45,282	1.011	0.782
0.8	2	11.068	20,662	259,135	67,090	48,349	1.077	0.833
0.9	0.9	12.518	8011	228,533	58,836	42,315	1.068	0.827
0.9	1	12.511	9082	232,372	59,891	43,026	1.086	0.84
0.9	1.33	12.485	12,957	246,650	63,727	45,637	1.149	0.889
0.9	1.66	12.452	17,492	263,514	68,246	48,803	1.226	0.949
0.9	2	12.418	22,604	282,128	73,301	52,286	1.308	1.012
1	0.9	13.887	8742	246,020	63,559	45,126	1.268	0.981
1	1	13.877	9940	250,820	64,868	46,024	1.292	1
1	1.33	13.836	14,338	268,678	69,592	49,396	1.383	1.07
1	1.66	13.8	19,179	287,012	74,605	52,846	1.47	1.137
1	2	13.757	24,735	308,124	80,358	56,845	1.57	1.215
1.05	0.9	14.561	9202	256,985	66,490	47,024	1.388	1.074
1.05	1	14.551	10,459	261,895	67,808	47,920	1.413	1.094
1.05	1.33	14.512	15,020	280,003	72,701	51,334	1.504	1.164
1.05	1.66	14.47	20,092	299,918	78,108	55,106	1.603	1.241
1.05	2	14.423	25,860	322,249	84,201	59,354	1.712	1.325

Table A3. Nacelle geometry non-linear trade factors for the design mission of the LR baseline configuration.

Nacelle Diameter Factor [-]	Nacelle Length Factor [-]	Nacelle Diameter [m]	Nacelle Length [m]	Rel. TO Thrust [-]	Rel. CR Thrust [-]	Rel. ToC Thrust [-]
1	1	4.06	6.5075	0.99999	1	0.99999
1.1	1	4.4918	6.5452	1.0116	1.0167	1.0118
1	1.1	4.0703	7.1766	1.0051	1.009	1.0052
1.1	1.1	4.5057	7.2221	1.0179	1.0271	1.0183

Table A3. Nacelle geometry non-linear trade factors for the design mission of the LR baseline configuration.

Nacelle Diameter Factor [-]	Nacelle Length Factor [-]	Nacelle Diameter [m]	Nacelle Length [m]	Rel. TO Thrust [-]	Rel. CR Thrust [-]	Rel. ToC Thrust [-]
1	1	4.06	6.5075	0.99999	1	0.99999
1.1	1	4.4918	6.5452	1.0116	1.0167	1.0118
1	1.1	4.0703	7.1766	1.0051	1.009	1.0052
1.1	1.1	4.5057	7.2221	1.0179	1.0271	1.0183

Table A4. TSFC and engine mass non-linear trade factors for the design mission of the MR baseline configuration.

Fuel Flow Factor [-]	Engine Weight Factor [-]	${\mathit{TSFC}}_{\mathit{eqv}}$ [g/kN/s]	Engine Mass [kg]	TO Thrust [N]	ToC Thrust [N]	CR Thrust [N]	Mission Block Energy /PAX/NM [MJ/NM]	Mission Relative Block Energy [-]
0.7	0.9	9.684	2848	93,166	24,056	19,321	0.68	0.642
0.7	1	9.679	3200	94,149	24,312	19,557	0.688	0.649
0.7	1.33	9.663	4430	97,515	25,222	20,381	0.716	0.675
0.7	1.66	9.646	5819	102,055	26,439	21,336	0.748	0.706
0.7	2	9.63	7441	107,603	27,944	22,472	0.786	0.742
0.8	0.9	11.061	2942	95,970	24,792	19,693	0.794	0.75
0.8	1	11.055	3310	96,982	25,076	19,945	0.804	0.759
0.8	1.33	11.035	4623	101,282	26,236	20,864	0.839	0.792
0.8	1.66	11.015	6110	106,550	27,663	21,927	0.881	0.831
0.8	2	10.996	7810	112,867	29,381	23,149	0.929	0.877
0.9	0.9	12.436	3051	99,067	25,634	20,103	0.915	0.864
0.9	1	12.429	3445	100,490	26,021	20,389	0.927	0.875
0.9	1.33	12.406	4847	105,647	27,410	21,412	0.972	0.918
0.9	1.66	12.384	6414	111,530	29,023	22,565	1.022	0.965
0.9	2	12.361	8202	118,675	30,973	23,892	1.079	1.019
1	0.9	13.81	3190	103,057	26,710	20,593	1.044	0.986
1	1	13.802	3606	104,635	27,141	20,904	1.059	1
1	1.33	13.777	5090	110,293	28,693	22,020	1.114	1.052
1	1.66	13.751	6742	117,118	30,554	23,274	1.172	1.107
1	2	13.726	8617	125,046	32,724	24,700	1.238	1.169
1.05	0.9	14.497	3264	105,172	27,284	20,873	1.112	1.05
1.05	1	14.488	3691	106,828	27,737	21,198	1.129	1.065
1.05	1.33	14.461	5221	113,006	29,430	22,356	1.187	1.121
1.05	1.66	14.434	6915	120,122	31,379	23,653	1.25	1.18
1.05	2	14.407	8834	128,442	33,659	25,128	1.321	1.247

Table A4. TSFC and engine mass non-linear trade factors for the design mission of the MR baseline configuration.

Fuel Flow Factor [-]	Engine Weight Factor [-]	${\mathit{TSFC}}_{\mathit{eqv}}$ [g/kN/s]	Engine Mass [kg]	TO Thrust [N]	ToC Thrust [N]	CR Thrust [N]	Mission Block Energy /PAX/NM [MJ/NM]	Mission Relative Block Energy [-]
0.7	0.9	9.684	2848	93,166	24,056	19,321	0.68	0.642
0.7	1	9.679	3200	94,149	24,312	19,557	0.688	0.649
0.7	1.33	9.663	4430	97,515	25,222	20,381	0.716	0.675
0.7	1.66	9.646	5819	102,055	26,439	21,336	0.748	0.706
0.7	2	9.63	7441	107,603	27,944	22,472	0.786	0.742
0.8	0.9	11.061	2942	95,970	24,792	19,693	0.794	0.75
0.8	1	11.055	3310	96,982	25,076	19,945	0.804	0.759
0.8	1.33	11.035	4623	101,282	26,236	20,864	0.839	0.792
0.8	1.66	11.015	6110	106,550	27,663	21,927	0.881	0.831
0.8	2	10.996	7810	112,867	29,381	23,149	0.929	0.877
0.9	0.9	12.436	3051	99,067	25,634	20,103	0.915	0.864
0.9	1	12.429	3445	100,490	26,021	20,389	0.927	0.875
0.9	1.33	12.406	4847	105,647	27,410	21,412	0.972	0.918
0.9	1.66	12.384	6414	111,530	29,023	22,565	1.022	0.965
0.9	2	12.361	8202	118,675	30,973	23,892	1.079	1.019
1	0.9	13.81	3190	103,057	26,710	20,593	1.044	0.986
1	1	13.802	3606	104,635	27,141	20,904	1.059	1
1	1.33	13.777	5090	110,293	28,693	22,020	1.114	1.052
1	1.66	13.751	6742	117,118	30,554	23,274	1.172	1.107
1	2	13.726	8617	125,046	32,724	24,700	1.238	1.169
1.05	0.9	14.497	3264	105,172	27,284	20,873	1.112	1.05
1.05	1	14.488	3691	106,828	27,737	21,198	1.129	1.065
1.05	1.33	14.461	5221	113,006	29,430	22,356	1.187	1.121
1.05	1.66	14.434	6915	120,122	31,379	23,653	1.25	1.18
1.05	2	14.407	8834	128,442	33,659	25,128	1.321	1.247

Table A5. Nacelle geometry non-linear trade factors for the design mission of the MR baseline configuration.

Nacelle Diameter Factor [-]	Nacelle Length Factor [-]	Nacelle Diameter [m]	Nacelle Length [m]	Rel. TO Thrust [-]	Rel. CR Thrust [-]	Rel. ToC Thrust [-]
1	1	2.6893	4.2283	1	1	1
1.1	1	2.9679	4.2422	1.0066	1.0118	1.0068
1	1.1	2.6952	4.6614	1.0045	1.0091	1.0046
1.1	1.1	2.976	4.679	1.0121	1.0219	1.0124

Table A5. Nacelle geometry non-linear trade factors for the design mission of the MR baseline configuration.

Nacelle Diameter Factor [-]	Nacelle Length Factor [-]	Nacelle Diameter [m]	Nacelle Length [m]	Rel. TO Thrust [-]	Rel. CR Thrust [-]	Rel. ToC Thrust [-]
1	1	2.6893	4.2283	1	1	1
1.1	1	2.9679	4.2422	1.0066	1.0118	1.0068
1	1.1	2.6952	4.6614	1.0045	1.0091	1.0046
1.1	1.1	2.976	4.679	1.0121	1.0219	1.0124

Table A6. TSFC and engine mass non-linear trade factors for the design mission of the SR baseline configuration.

Fuel Flow Factor [-]	Engine Weight Factor [-]	${\mathit{TSFC}}_{\mathit{eqv}}$ [g/kN/s]	Engine Mass [kg]	TO Thrust [N]	ToC Thrust [N]	CR Thrust [N]	Mission Block Energy /PAX/NM [MJ/NM]	Mission Relative Block Energy [-]
0.7	0.9	3.118	2182	67,403	16,779	14,228	0.695	0.619
0.7	1	3.118	2454	68,242	16,989	14,404	0.704	0.627
0.7	1.33	3.116	3401	71,139	17,736	15,020	0.733	0.653
0.7	1.66	3.113	4434	74,282	18,548	15,692	0.766	0.682
0.7	2	3.108	5603	77,853	19,469	16,456	0.802	0.715
0.8	0.9	3.562	2264	69,978	17,434	14,720	0.822	0.732
0.8	1	3.561	2548	70,857	17,664	14,908	0.832	0.741
0.8	1.33	3.558	3538	73,965	18,467	15,566	0.868	0.773
0.8	1.66	3.553	4621	77,365	19,346	16,287	0.908	0.809
0.8	2	3.548	5853	81,231	20,340	17,110	0.953	0.849
0.9	0.9	4.004	2353	72,731	18,146	15,248	0.957	0.852
0.9	1	4.003	2650	73,726	18,398	15,453	0.97	0.864
0.9	1.33	3.998	3692	77,145	19,290	16,183	1.015	0.904
0.9	1.66	3.992	4842	80,965	20,273	16,990	1.065	0.948
0.9	2	3.985	6158	85,304	21,390	17,915	1.121	0.999
1	0.9	4.444	2462	76,056	19,001	15,890	1.108	0.986
1	1	4.442	2774	77,126	19,276	16,113	1.123	1
1	1.33	4.435	3873	80,843	20,243	16,901	1.177	1.048
1	1.66	4.428	5090	84,994	21,302	17,773	1.236	1.101
1	2	4.422	6490	89,765	22,513	18,782	1.306	1.163
1.05	0.9	4.663	2519	77,781	19,451	16,227	1.187	1.057
1.05	1	4.661	2840	78,887	19,740	16,459	1.204	1.072
1.05	1.33	4.654	3969	82,806	20,740	17,277	1.263	1.124
1.05	1.66	4.647	5224	87,096	21,851	18,189	1.328	1.183
1.05	2	4.642	6720	92,789	23,274	19,382	1.415	1.26

Table A6. TSFC and engine mass non-linear trade factors for the design mission of the SR baseline configuration.

Fuel Flow Factor [-]	Engine Weight Factor [-]	${\mathit{TSFC}}_{\mathit{eqv}}$ [g/kN/s]	Engine Mass [kg]	TO Thrust [N]	ToC Thrust [N]	CR Thrust [N]	Mission Block Energy /PAX/NM [MJ/NM]	Mission Relative Block Energy [-]
0.7	0.9	3.118	2182	67,403	16,779	14,228	0.695	0.619
0.7	1	3.118	2454	68,242	16,989	14,404	0.704	0.627
0.7	1.33	3.116	3401	71,139	17,736	15,020	0.733	0.653
0.7	1.66	3.113	4434	74,282	18,548	15,692	0.766	0.682
0.7	2	3.108	5603	77,853	19,469	16,456	0.802	0.715
0.8	0.9	3.562	2264	69,978	17,434	14,720	0.822	0.732
0.8	1	3.561	2548	70,857	17,664	14,908	0.832	0.741
0.8	1.33	3.558	3538	73,965	18,467	15,566	0.868	0.773
0.8	1.66	3.553	4621	77,365	19,346	16,287	0.908	0.809
0.8	2	3.548	5853	81,231	20,340	17,110	0.953	0.849
0.9	0.9	4.004	2353	72,731	18,146	15,248	0.957	0.852
0.9	1	4.003	2650	73,726	18,398	15,453	0.97	0.864
0.9	1.33	3.998	3692	77,145	19,290	16,183	1.015	0.904
0.9	1.66	3.992	4842	80,965	20,273	16,990	1.065	0.948
0.9	2	3.985	6158	85,304	21,390	17,915	1.121	0.999
1	0.9	4.444	2462	76,056	19,001	15,890	1.108	0.986
1	1	4.442	2774	77,126	19,276	16,113	1.123	1
1	1.33	4.435	3873	80,843	20,243	16,901	1.177	1.048
1	1.66	4.428	5090	84,994	21,302	17,773	1.236	1.101
1	2	4.422	6490	89,765	22,513	18,782	1.306	1.163
1.05	0.9	4.663	2519	77,781	19,451	16,227	1.187	1.057
1.05	1	4.661	2840	78,887	19,740	16,459	1.204	1.072
1.05	1.33	4.654	3969	82,806	20,740	17,277	1.263	1.124
1.05	1.66	4.647	5224	87,096	21,851	18,189	1.328	1.183
1.05	2	4.642	6720	92,789	23,274	19,382	1.415	1.26

Table A7. Nacelle geometry non-linear trade factors for the design mission of the SR baseline configuration.

Nacelle Diameter Factor [-]	Nacelle Length Factor [-]	Nacelle Diameter [m]	Nacelle Length [m]	Rel. TO Thrust [-]	Rel. CR Thrust [-]	Rel. ToC Thrust [-]
1	1	2.4447	3.8779	1	1	1
1.1	1	2.698	3.8907	1.0061	1.0126	1.0066
1	1.1	2.4511	4.277	1.0047	1.0089	1.0053
1.1	1.1	2.7054	4.2916	1.0116	1.0221	1.0122

Table A7. Nacelle geometry non-linear trade factors for the design mission of the SR baseline configuration.

Nacelle Diameter Factor [-]	Nacelle Length Factor [-]	Nacelle Diameter [m]	Nacelle Length [m]	Rel. TO Thrust [-]	Rel. CR Thrust [-]	Rel. ToC Thrust [-]
1	1	2.4447	3.8779	1	1	1
1.1	1	2.698	3.8907	1.0061	1.0126	1.0066
1	1.1	2.4511	4.277	1.0047	1.0089	1.0053
1.1	1.1	2.7054	4.2916	1.0116	1.0221	1.0122