Modeling and Simulation of a Distributed-Electric Propulsion System with PROOSIS ^†

Abstract

This paper presents a concise modeling and simulation study of a turboelectric distributed propulsion (TeDP) system for a hybrid wing body (HWB) aircraft. A whole-system 0D model has been implemented in PROOSIS that includes the thermodynamic model of the turboshaft and fan array, as well as an electrical subsystem model addressing generators, motors, and cryogenic cooling for high-temperature superconducting (HTS) machines. Boundary layer ingestion (BLI) was explicitly modeled in the inlet–fan interaction. Parametric studies explored control strategies that minimized fuel consumption across the flight envelope. The design and off-design analyses demonstrated that coupling BLI with distributed fans can deliver significant aerodynamic benefits, while the integrated mission simulation highlighted the system-level implications of electrical conversion and control and quantified potential fuel savings.

1. Motivation

During the 2030–2050 time frame, the environmental impact caused by civil aviation—CO₂ and NOx emissions, as well as noise levels—must be substantially reduced to meet the requirements set by authorities [1]. Consequently, new conceptual designs emerge, which involve revolutionary changes in structure and propulsive systems [2,3].

The blended wing body (BWB) N3-X prototype introduced by NASA in 2009 [4,5] represents a clear example of revolutionary aircraft configurations. This aircraft employs two wingtip-mounted turboshaft engines driving electric generators that power an array of fans embedded in the aft fuselage. Preliminary cycle analyses of this turboelectric distributed propulsion (TeDP) system demonstrated potential fuel burn reductions exceeding 60% relative to contemporary aircraft.

TeDP systems seek to improve propulsive efficiency by exploiting the advantages that multiple distributed fans actually offer. The benefits are twofold: by having many fans, large bypass ratios can be achieved and, at the same time, by positioning these carefully within the fuselage wake, boundary layer ingestion (BLI) reduces overall drag and enhances propulsive efficiency. Nevertheless, BLI also introduces challenges in fan stability and inlet distortion, which require advanced aerodynamic and control strategies [6,7].

On the other hand, a noticeable drawback of TeDP concepts is their inherent reliance on high-temperature superconducting (HTS) electrical machines to achieve the required power density without excessive mass. Several studies have dealt with the design and integration of such HTS motors for future greener aviation [8,9], as well as in other sectors [10]. While significant progress has been made in the detailed design of stator and rotor topologies in fully superconducting synchronous motors [11], these machines, still, must operate at cryogenic temperatures, necessitating dedicated refrigeration systems such as cryocoolers. Several alternatives have been studied along the years in this regard, with different fuels used as heat sinks, to enable HTS distributed propulsion concepts in future aviation [12]. In summary, although superconducting technology offers significant reductions in resistive losses, the cryogenic subsystem introduces complexity, parasitic power draw, and reliability concerns.

While numerous conceptual studies have dealt with particular aspects of TeDP systems, to assess their potential—for instance, Refs. [13,14] discussed the electric grid and electrical power system design, Refs. [15,16] analyzed the aerodynamic effects of distributed propulsion, Refs. [17,18] presented several propulsive system architectures pre-design and integration aspects, and [19] compared key performance parameters for different degrees of power hybridization—relatively few have combined a detailed thermodynamic engine model with a realistic electrical subsystem and system-level control logic. The work presented in this paper addresses this gap by developing a multi-fidelity PROOSIS model that integrates all key elements—thermodynamic cycle, BLI, cooling requirements, electrical power conversion, and control—into a unified simulation framework. This enables quantitative evaluation of efficiency gains, design of optimal control strategies, and mission-level analyses to estimate fuel savings for a representative BWB configuration.

2. Methodology

The operation of this aircraft’s propulsive system is represented in Figure 1. Two turboshaft engines ingest the free stream during flight and generate mechanical power on a shaft that, in turn, drives an electrical generator (eGen in Figure 1). Through this generator, the mechanical energy extracted from the power turbine (PT) is converted into electrical energy. The power management and distribution (PMAD) system comprises all conversion devices and electrical buses: firstly, the alternate current (AC) produced by the generator is transformed, by means of a power converter, into direct current (DC) for distribution; finally, a series of inverters reconvert this high-voltage DC into AC, and this electrical power is supplied to electric motors (eMot in Figure 1) that drive the fans. Thus, most of the thrust is produced by the fans distributed along the upper rear surface of the fuselage, with only a residual contribution coming from the turboshafts that generate the mechanical power.

The present work examines this propulsion system configuration—with special emphasis on the thermodynamic cycle involved—through different analyses based on steady-state (design and off-design) calculations. To do so, a model has been developed within the simulation software PROOSIS that includes the turboshaft engine, the electrical system and the array of fans.

Model Description

The model’s architecture (see Figure 2) represents half of the propulsion plant of the proposed TeDP concept: one of the turboshaft engines, its corresponding electrical generator and power conversion and distribution devices, and one half of the fans array. Thus, it couples the thermodynamic and electrical subsystems, introducing gearbox/mechanical-electrical conversion efficiencies, and accounting for cooling parasitics. The turboshaft engine consists of a gas generator—i.e., low pressure compressor (LPC) and high pressure compressor (HPC), and high pressure turbine (HPT) and low pressure turbine (LPT)—plus a separate PT that extracts shaft power to drive a synchronous independently excited electric generator [20,21]. The AC provided by the generator is converted and transported by means of a DC high-voltage bus. An array of permanent magnet electric motors is mechanically coupled to an array of fans with variable nozzle outlet area. Finally, cryocooler models estimate the refrigeration power and mass [22], and the cooling power is subtracted from net available electrical power. At the inlet stage, the BLI effects are taken from CFD-derived curves of both the pressure and the Mach number ratios ($P_{t10}/P_{t0}$ and $M_{10}/M_0$, respectively) versus the effective capture height [6]. These ratios reduce inlet total pressure and effective inlet velocity, changing the fan operating point, thrust and specific fuel consumption (SFC).

The system has four degrees of freedom, which can be tweaked to study and design efficient control strategies for the whole propulsion plant. Namely,

• Engine operating regime (power output), controlled via the turbine fuel flow.
• Fans’ rotational speed, controlled by means of the electric motors’ operating frequency.
• Bypass ratio, modified via the variable outlet area of the fans’ nozzles.
• Converter/bus allocations, which are determined by the excitation voltage of the electric generator.

3. Results

3.1. Design Point Results

The design point corresponds to cruise flight at an altitude of 35,000 ft and Mach 0.84, chosen as representative of the N3-X hybrid wing body (HWB) configuration [4]. The objective was to size the TeDP system such that the combined fan array delivered the required net thrust at this condition. The design process iteratively converged on an array of 15 fans with a pressure ratio (PR) of 1.3. This fan design leads to a high propulsive efficiency and ensures adequate stall margin while meeting the critical geometrical constraints (fan spacing and available span distance).

Figure 3 demonstrates that the inclusion of BLI produces a propulsive efficiency gain of around 9%. The analysis shows that this benefit arises mainly from the redistribution of low-momentum air into the fan inlet. Even with varying the design fan PR, the BLI-corrected inlet maintained 6–8% propulsive efficiency advantage over the clean-inlet reference case across a wide Mach number range (0.7–0.85).

The model was validated against data found in [4,6]. At the aerodynamic design point (ADP) flight condition, turbomachinery polytropic efficiencies, required overall thrust, fan and compressors and nozzle pressure ratios, HPC outlet total temperature ($T_{3t}$), turbine inlet total temperature ($T_{4t}$), power required for cryocooler operation, and geometric constraints (such as available structural span and minimum fan spacing), all were specified. Using these inputs, the remaining cycle variables predicted by the model—including mass flow rates (and therefore bypass ratio), number and diameter of the fans, propulsive efficiency, and SFC—show deviations below 5% with respect to the original data. These results confirm the consistency of the PROOSIS implementation for preliminary TeDP cycle studies.

3.2. Off-Design and Parametric Studies

After defining the design point, an off-design analysis was carried out aiming at finding an efficient control strategy for the whole propulsion plant. In particular, minimizing the SFC for each operating condition was chosen as the main target of the control law. In any TeDP vehicle, as the PMAD system transforms the generator’s electrical power into a variable frequency current output, the fan array and the turboshaft’s PT rotational speeds can be decoupled. This “new” system’s degree of freedom, as compared with the traditional turbofan engine, in essence, decouples the turbine’s running line from the fans’ operating lines. Hence, the performance of the aircraft under varying fan and turbine running lines was analyzed, with the focus on minimizing the SFC while maintaining the required thrust levels.

In a nutshell, for each operating point along the aircraft’s mission, the overall bypass ratio can be controlled by the variable outlet area of the fans’ nozzles, while the fans’ PR can be controlled via the electric motors’ rotational speed (i.e., their working frequency). Hence, for a given power output supplied by the electric generator, there is total freedom to choose the operating point within the fan map (fan corrected mass flow and fan PR). Similarly, in the turbine, for a given fuel flow (i.e., turbine inlet temperature), the variable generator’s frequency allows to choose the most efficient rotational speed to carry out the power extraction.

This off-design study—in which thrust levels are ensured by choosing the appropriate values of turbine fuel flow and electric motors’ rotational speed—aims, therefore, at finding the combination of the remaining control variables—namely, fans’ corrected mass flow and turbine’s rotational speed—that yields minimum SFC. Fan corrected mass flow is parametrized by means of the BETA coordinate along a constant-speed line (in the fan map), while turbine rotational speed is parametrized by means of its value relative to design, NcRdes. Figure 4 shows the variation in the engine’s SFC as a function of the turbine’s corrected speed under multiple flight conditions, for a range of BETA values.

The system’s SFC is minimized when fan thrust is maximized relative to that of the turbojet. Fan thrust consists of a momentum term—dependent on mass flow and jet velocity—and a pressure term defined by the pressures of the secondary flow after and before the fan stage ($P_{18}$ and $P_{10}$, respectively): as BETA increases, the mass-flow term decreases because the jet velocity rises while mass flow drops, reducing their product. In take-off, the pressure term is negligible due to the fan nozzle being fully open, but in other flight conditions it becomes increasingly negative as BETA decreases. Since higher BETA increases the fan PR and thus $P_{18}$, the pressure term grows while $P_{10}$ stays nearly constant. Therefore, maximum fan thrust at take-off requires the lowest possible BETA, whereas in other regimes an intermediate value—around 0.3—provides the best compromise. Additionally, the turbine’s rotational speed that minimizes the fuel consumption corresponds to the points of maximum working efficiency. In view of the previous results, an “optimal” combination of BETA and NcRdes can be found for each flight condition.

In addition to the ADP validation discussed at the end of Section 3.1, results from the PROOSIS model were validated against data found in [4,6] for three additional off-design operating conditions: cruise, take-off, and RTO. For each case, flight conditions and overall required thrust were used as model inputs, and the resulting bypass ratio, specific fuel consumption, overall pressure ratio, and main cycle temperatures ($T_{3t}$ and $T_{4t}$), as yielded by the PROOSIS model, all were found to agree with the reference values from [4,6] within a 10% margin. It should be noted that, similarly to the present study, the reference analyses in [4,6] assume as well that fan and turbine operating lines can be adjusted to achieve minimum SFC at each operating point.

3.3. Integrated Mission Simulation

After validating the design and off-design performance, the complete TeDP system model was run to simulate a representative flight mission. The goal being to evaluate its overall performance, control behavior, and potential fuel savings compared to a conventional turbofan-powered reference aircraft. The system can be controlled acting on the parameters described at the end of Section Model Description. Throughout the flight envelope, a control law for the propulsive system is designed, such that the SFC is minimized and the required thrust is met, while keeping the electrical system stable. One of the most relevant findings extracted from this study is that the electric motors’ frequency has a direct impact on being able to achieve minimal SFC at each flight condition (see Figure 5).

Assuming that the system follows the designed control law for minimal SFC, a simulation of the aircraft performance along the whole flight profile can be executed to get an estimation of the fuel savings in comparison with a reference aircraft, namely a B777-200 LR, whose data is taken from [23]. The simulation computed is a 14,000 km range mission and is divided into a 20 min take-off segment, a 15 h cruise, and a 20 min descent phase. This, together with the operational empty weight (OEW) of the aircraft, as well as the payload (PL), allows getting the necessary fuel weight (FW), and hence the necessary maximum take-off weight (MTOW), to complete the mission. The results, which are represented in

Table 1. Flight simulation results.

	OEW (kg)	PL (kg)	FW (kg)	MTOW (kg)	Savings
B777-200 LR [23]	154,584	53,500	126,915	348,676	-
N3X-PROOSIS	121,472	53,500	43,226	222,590	66%

, show a fuel saving of approximately 66%.

4. Conclusions

The results obtained from the PROOSIS-based modeling and simulation of the TeDP system provide quantitative insight into the potential and limitations of this emerging propulsion architecture. At the aerodynamic level, the inclusion of BLI improved propulsive efficiency by approximately 9% at cruise, in line with previous studies such as NASA’s N3-X. This gain results primarily from the re-energization of the fuselage wake and the associated reduction in aircraft drag.

From a thermodynamic perspective, the distributed turboelectric architecture allowed the decoupling between turbine and fan rotating speeds, enabling both to operate near their respective efficiency peaks. The design point, characterized by a fan PR of about 1.3 and a corrected turbine speed ratio (NcRdes) close to 0.97, minimized SFC while maintaining adequate performance margins. These findings confirm that integrated power management between the gas turbines and the electric fans is essential to fully exploit TeDP advantages.

The inclusion of HTS machines as generators and motors proved to be a key enabling technology for the TeDP concept. The electrical subsystem exhibited an overall conversion efficiency of approximately 94% during cruise, which is consistent with theoretical expectations for HTS-based systems operating at cryogenic temperatures (20–50 K). Nevertheless, the cryogenic cooling system introduced a measurable parasitic load, consuming roughly 3–4% of the generated electrical power.

Finally, the mission-level control laws implemented in PROOSIS demonstrated that coordinated management of turbine fuel flow, fan rotational speed, and electrical power distribution can maintain stable and efficient operation throughout a complete flight profile.