The Impact of Shaft Power Extraction on Small Turbofan Engines: A Thermodynamic and Exergy-Based Analysis for No-Bleed Architectures

Abstract

In “no-bleed” engine architectures, bleed air is replaced by shaft power extraction to run the subsystems, avoiding the inefficiencies of traditional bleed systems. This approach is increasingly used in small turbofan engines, prompting analysis of its impact on engine performance and exergy efficiency. A small high-bypass turbofan engine was modeled in software under two control strategies: constant thrust (CT) and constant speed (CS), with shaft power extraction up to 18 kW. Exergy analysis evaluated efficiency losses and sustainability metrics (exergy efficiency, environmental effect factor, and exergetic sustainability index). Simulations indicate that an 18 kW shaft power extraction increases SFC by 13.6% (CT) and 42.1% (CS). Exergy efficiency rises from 47.3% to 50.7% (CT) and 54.2% (CS). However, these power draws also increase irreversibility and the environmental effect factor (EEF) grows from 0.678 to 0.732 (CT) and 0.744 (CS), while the exergetic sustainability index (ESI) drops from 1.48 to 1.34, signaling reduced sustainability at high extraction. Maintaining constant thrust during extraction incurs smaller fuel consumption and exergy efficiency penalties than constant speed control. The findings highlight the need for adaptive control strategies (e.g., limiting extraction levels or using variable-geometry components) to mitigate losses and enhance sustainability in no-bleed engine designs.

1. Introduction

In recent years, the civil aviation industry has grown rapidly. In 2019, global airlines transported approximately 4.56 billion passengers. It is expected that over the next two decades, passenger numbers will increase by more than 100%, with an annual growth rate of 3.5% [1]. To accommodate the growing number of air travelers, the number of aircraft and flights will increase, which will lead to a significant rise in pollutant emissions from aircraft engines. In response, relevant authorities have established a series of goals to mitigate the environmental impact of the aviation industry. The International Air Transport Association (IATA) has set three key targets: improving fuel efficiency by 1.5% annually, achieving carbon-neutral growth starting in 2020, and reducing emissions by 50% compared to 2005 levels by 2050 [2]. To meet these targets, engineers are working to enhance aircraft engine systems for higher fuel efficiency. One approach is the “no-bleed” architecture, where the shaft power of the aircraft engine is used to drive motors that generate energy to supply secondary air systems or other subsystems, replacing the traditional bleed air architecture. The traditional bleed air architecture is less energy-efficient because it diverts a small portion of compressed air from the fan or compressor to supply other subsystems of the aircraft, leading to significant energy waste in the process [3]. As a result, the “no-bleed” architecture has gradually been applied to turbofan engines and is now used in multi-electric civilian aircraft and some small jet aircraft. As this architecture is being used more widely, it is necessary to study the impact of shaft power extraction on the performance and efficiency of turbofan engines with a no-bleed architecture and assess their environmental impact accordingly.

One method to assess the environmental impact of aircraft engines is to study the mechanisms that lead to such impacts. Exergy analysis can be used to evaluate aircraft engines as energy conversion systems. The first study to combine gas turbines with exergy analysis dates back to 2001 [4]. Early exergy analysis focused on how the environment affects the overall performance of gas turbines. Roth and Mavris et al. [5] analyzed the J-79 engine under the assumptions of 85% compressor isentropic efficiency, 90% turbine efficiency, and 95% combustion chamber total pressure recovery, at both sea level and a 6.09 km altitude. Their findings revealed that exergy destruction is primarily due to irreversible combustion, exhaust emissions, and remaining kinetic energy in the exhaust. The direct exergy destruction was found to be highest in the remaining gas kinetic energy, followed by the turbine and compressor. The greatest shaft work loss was found in the compressor and turbine. The authors emphasized the need to focus more on exergy destruction in the design process. Struchtrup et al. [6] investigated the external exergy destruction between the exhaust gases of a gas turbine and the environment, varying with bypass ratio, and recommended designing engines with higher bypass ratios.

As experimental conditions and operational data increased, research on gas turbines under different operating conditions gradually grew. Tona et al. [7] examined the performance parameters of various components during different flight phases, including takeoff, climb, cruise, descent, holding, and landing, while also investigating the impact of anti-icing systems on exergy performance. They found that the largest total exergy destruction occurred during cruise (due to its long duration), and the lowest exergy efficiency occurred during landing. Balli et al. [8] analyzed the exergy efficiency and thermal efficiency of the T56 turbojet engine under two cases (considering only shaft work and considering both shaft work and kinetic energy carried by the exhaust gas) at four different power loads (75%, 100%, idle, and takeoff). They found that considering the kinetic energy of the exhaust gas improved exergy efficiency by 2.5% and thermal efficiency by 2.7%. Aydin et al. [9] analyzed a turboprop engine under different flight attitudes and found that the exergy destruction rate decreased with increasing torque.

To further clarify the distribution of exergy destruction for design optimization, researchers began focusing on component-level exergy analysis. David et al. [10] suggested that when evaluating irreversible losses in a component or process of a gas turbine, a matching gas turbine model should be constructed, where only the components or processes contributing to irreversible losses are considered, while the others are assumed reversible. The authors highlighted the importance of flow conditions in optimizing engine design. Additionally, they inferred that efficiency decreases with altitude due to the lower environmental temperature. Balli et al. [11] analyzed the J69-T-25A turbojet engine based on actual measurement data and found that the largest exergy destruction occurred in the combustion chamber. They also combined exergy analysis with cost calculations to evaluate the economic performance of the engine. The authors suggested that exergy analysis and cost calculations should both be considered in the design optimization of gas turbines. The study noted that under all power settings the greatest exergy destruction occurred in the combustion chamber. As output power increased, losses in the compressor and turbine grew. The potential for improving compressor efficiency increased with torque, and the smallest gas turbine losses occurred at the maximum power settings. Atlgan et al. [12] analyzed a dual-shaft turboprop engine (gas generator + power turbine), examining the efficiency of each component. They were the first to link component efficiencies with their environmental impact, emphasizing that regardless of the evaluation angle optimizing the combustion chamber should always be the top priority in gas turbine design. In another paper, Balli [13] studied the effect of an afterburner on the energy and performance of an experimental turbojet engine. The analysis, conducted under military conditions, found that activating the afterburner reduced both energy efficiency and exergy efficiency, while significantly increasing overall energy and exergy destruction in the engine. Sohret et al. [14,15] conducted detailed exergy analysis on the JT3D turbojet engine and the AE3007H turbofan engine, categorizing exergy destruction into internal or external and avoidable or unavoidable losses. For the JT3D gas generator, internal losses accounted for 73%, with nearly 30% of losses being avoidable. The authors suggested that the poor matching of engine components needs improvement. For the AE3007H turbofan, they found that reducing the temperature and pressure of the incoming air improved exergy efficiency.

As component-level exergy analysis research progressed, the focus shifted to design optimization and identifying methods for improving gas turbine performance. Turan [16] performed exergy analysis on a small turbojet engine used in drones, examining thermodynamic cycle designs with compressor pressure ratios ranging from two to seven and turbine inlet temperatures between 1200 K and 1500 K. They found that increasing the turbine inlet temperature decreased the overall exergy efficiency of the gas turbine, while factors that improved compressor pressure ratio and flight Mach number enhanced the turbine’s efficiency. The author suggested that future research should not only focus on exergy analysis based on real engine data but also incorporate thermodynamic cycle design into exergy analysis of both gas turbines and their components. Multi-objective optimization of thermodynamic cycle design could significantly improve the overall performance of micro gas turbines. Tai et al. [17] optimized the design of a dual-shaft turbofan engine under a specific operating condition, using energy conservation and exergy analysis, with the TJEO-1.0 optimization program and genetic algorithms. The optimization process involved eight variables: inlet mass flow rate, bypass ratio, gas turbine cooling air flow, low-pressure turbine cooling air flow, fan pressure ratio, low-pressure compressor pressure ratio, high-pressure compressor pressure ratio, and combustion chamber outlet temperature. They found that an additional 1.5–2.39% fuel consumption could lead to a 3.3–11% increase in specific thrust. The study highlighted that energy analysis alone cannot achieve optimal performance for gas turbines. Tai attempted to optimize gas turbine design from the thermodynamic cycle perspective. However, since the component efficiencies and operating environment were assumed constant, further and more systematic research is needed from a gas turbine design standpoint. Aydin et al. [18] conducted an analysis of a medium-sized commercial aircraft engines based on ground test data, providing specific values for potential improvements in each component. The potential improvement in the combustion chamber was found to be as high as 2.00 MW. Exergy destruction is not only related to the combustion chamber components themselves but also to the matching between the combustion chamber and other components. Therefore, incorporating exergy as one of the evaluation criteria in the design process of gas turbines is essential. Kumari et al. [19] compared the performance of gas turbines with and without intercoolers, considering factors such as compressor pressure ratio, turbine rotor inlet temperature, main combustion zone temperature, chemical equilibrium ratio, and exhaust emissions. They found that the exergy destruction of a gas turbine with an intercooler was 4.42% lower than that of a gas turbine without one.

Many scholars have also conducted research on the exergy analysis of turbofan engines. Aygun and Turan [20] studied the exergy-based environmental impact indicators of the PW4000 engine across eight different flight stages. They found that the environmental impact due to exergy destruction was the greatest, with the takeoff phase having the largest environmental impact. The combustion chamber was identified as the first component to be improved in order to reduce environmental impact. Korba et al. [21] conducted an analysis of energy, exergy, environmental impact, exergoeconomic, and exergoenvironmental parameters for the CFM56-3 series turbofan engine. They found the engine’s energy efficiency to be 35.37%, with exergy efficiency, waste exergy rate, and fuel exergy waste ratio predicted to be 33.32%, 33,175.03 kW, and 66.68%, respectively. Based on these findings, they determined the environmental damage cost rate to be $519.753 per hour, with an environmental damage cost index of $0.0314 per kWh. In addition to comprehensive assessments of specific engine models, some scholars have also studied the impact of energy extraction based on exergy analysis on aircraft engines. Aygun [22] examined the effect of bleed-air ratio and Mach number on the performance of a small turbojet engine using exergy analysis. They found that a higher bleed-air ratio impaired engine performance, while a higher Mach number positively impacted energy and exergy efficiency, leading to higher specific fuel consumption. Additionally, it was observed that a higher bleed-air ratio increased the engine’s environmental impact, while increasing Mach number could reduce the environmental impact. Furthermore, Caliskan et al. [23] used performance and exergy analysis to study a gas turbine engine powering an unmanned aerial vehicle, setting 10 different power levels and design variables. They found that as shaft power decreased, specific fuel consumption increased, exergy efficiency in the combustion chamber declined, and the environmental impact increased. Additionally, the environmental effect factors varied linearly with changes in shaft power.

Regarding the impact of energy extraction on aeroengine performance, several studies have employed CFD methods. Bleed air and jet air have been utilized to control the internal flow in both axial compressors [24] and centrifugal compressors [25]. The introduction of hot air results in additional pressure losses and flow distortions at the outlet plane, which further compromise compressor performance. Moreover, bleeding and extracting anti-icing bleed air can cause the compressor to operate outside its designed parameters, thereby altering its performance. He et al. [26] investigated the effects of an anti-icing system on performance, internal flow fields, and inter-stage matching in an axial-centrifugal combined compressor using three-dimensional numerical simulations. Their findings indicate that the anti-icing system leads to compressor performance degradation and a reduction in stall margin. Rectangular jet studies can be used to validate these investigations. The insights and techniques from rectangular jet studies are directly applicable to turbofan engine flow validation. Turbofan exhaust streams often consist of mixing shear layers (core flow with bypass air or ambient) that produce flow structures analogous to free jets. Shadowgraph/Schlieren imaging can visualize shock cells and density gradients in high-speed engine exhausts, revealing jet expansion and plume structure for comparison with simulations. PIV measurements (when feasible in engine test rigs or subscale models) provide detailed velocity and turbulence fields, verifying that simulations capture the correct jet spreading rate and vortex dynamics. For instance, averaged PIV data from coaxial jet experiments (mimicking core–bypass mixing) have been used to benchmark CFD models [27]. Meanwhile, a high-fidelity LES applied to engine exhaust flows can be cross-checked against the well-characterized rectangular jet data. Key metrics such as potential core length, decay of centerline velocity, and scalar mixing rates are matched to ensure the LES accurately reproduces the flow structure. Moreover, the rectangular jet studies on Schmidt number effects inform the modeling of fuel or temperature mixing in engines. They suggest that using an appropriate turbulent Sc number (instead of a one-size-fits-all value) can improve agreement in species or heat mixing predictions [28]. In summary, the combination of shadowgraphy and PIV experiments with an LES on canonical rectangular jets provides a robust validation framework. These methodologies help bridge fundamental free-jet turbulence and the complex turbofan exhaust flow, ensuring that engine simulations reliably capture both the large-scale flow features and the scalar mixing behavior.

Based on previous studies, this paper conducted simulations on a small turbofan engine using the Simcenter Amesim 2304 software to analyze the variations in engine performance parameters and exergy parameters under different shaft power extraction levels in both constant thrust (CT) and constant speed (CS) operating cases and further assessed its environmental impact. The primary objective of this research is to investigate the interference of shaft power extraction on turbofan engine performance and its environmental implications from an exergy perspective. Additionally, the findings aim to provide references for the optimization of turbofan engines toward a “no-bleed” architecture.

2. Materials and Methods

2.1. Engine Description

The engine examined in this study is a geared twin-shaft unmixed-flow turbofan engine with a maximum static thrust of 2.50 kN and a bypass ratio of 7.6. Designed for the personal light jet market, it accommodates 2 to 5 passengers and can fly at speeds up to Mach 0.45 at altitudes up to 25,000 feet (7620 m), with a maximum takeoff weight of approximately 3550 pounds (1600 kg). At the design point (10,000 feet, Mach 0.338, ISA conditions), the engine produces 1.07 kN of thrust with a specific fuel consumption (SFC) of 76.8 kg·h⁻¹·kN⁻¹. The maximum overall pressure ratio is 5.3, comprising 1.2 from the fan and 4.6 from the centrifugal compressor. The low-pressure (LP) shaft is equipped with a gearbox featuring a reduction ratio of 3.32, allowing the low-pressure turbine to reach speeds close to 44,000 rpm (revolutions per minute) while maintaining subsonic fan blade tip speeds (fan diameter of 350 mm), resulting in a more compact design. Under takeoff power, the high-pressure shaft operates at 52,000 rpm.

One of the engine’s unique features is its all-electric design. The high-pressure (HP) shaft is equipped with a reversible electric drive, enabling the engine to start and generate electricity to meet the aircraft’s needs. Consequently, the turbofan eliminates the accessory gearbox and bleed-air systems. Figure 1 shows a conceptual aircraft equipped with this engine, and Figure 2 illustrates the engine’s main components and station locations on a cross-sectional diagram. Additionally,

Table 1. Main components of the model engine.

Component Label	Component Name
a	Fan
b	Gearbox
c	Electric Drive
d	Centrifugal Compressor
e	Combustion Chamber
f	High-Pressure Turbine
g	Low-Pressure Turbine
h	Primary Nozzle

and

Table 2. Main stations of the model engine.

Station Number	Station Name
0	Ambient Air
2	Fan Inlet
25	Centrifugal Compressor Inlet
3	Centrifugal Compressor Diffuser Outlet
41	Combustor/High-Pressure Stator Outlet
45	Low-Pressure Turbine Stator Outlet
5	High-Pressure Turbine Outlet
8	Hot Nozzle Throat
13	Fan Outlet
18	Cold Nozzle Throat

list the main components and station numbers labeled in Figure 2, respectively.

2.2. Simulation Model of a Small Turbofan Engine

Given that an aero-engine is a complex mechanical and thermodynamic system operating in an environment characterized by high temperature, high pressure, and alternating stress conditions, comprehensive simulation of its internal combustion processes and aerodynamic parameter variations presents significant challenges. Therefore, the following assumptions are made for the component-level modeling of this small turbofan engine:

1.

Air and combustion gases are considered as ideal gases in thermodynamic equilibrium. (Generally, when gas pressure does not exceed $30\times {10}^5 \mathrm{P}\mathrm{a}$, the difference between real and ideal gases can be neglected). Their specific heat, enthalpy, entropy, and gas constants are functions of temperature and gas composition, and are independent of pressure;

2.

The fuel composition in the combustion chamber is $C_{10}{H}_{20}$, assuming complete combustion with only $H_{2}O$ and $C{O}_2$ as combustion products;

3.

Engine compression and expansion processes are assumed to be isentropic and adiabatic;

4.

Heat exchange between high-temperature gas flow and engine structural components is neglected;

5.

Volume effects and related phenomena are not considered.

Following the structural sequence of the engine components and incorporating the engine’s design parameters and characteristic data, we sequentially developed mathematical models for the gas flow and thermodynamic processes of each component, from the intake to the exhaust nozzle. Finally, utilizing the multi-domain simulation software Amesim, we established a simulation model of the small turbofan engine, as illustrated in Figure 3.

Modern turbofan engines feature a constant-thrust fuel control unit (FCU) that employs Full Authority Digital Engine Control (FADEC). In this system, the electronic engine control (EEC) manages regulation and limitation functions, while the hydro-mechanical unit (HMU) handles fuel metering. To achieve constant thrust, the EEC issues commands that, by considering environmental conditions and throttle lever angle, align the low-pressure shaft speed signal with the actual shaft speed, thereby maintaining constant thrust conditions. Based on this approach, we utilized the Amesim simulation software with a PID control module to regulate fuel flow rate by receiving engine thrust signals, thus achieving constant thrust control of the engine.

The fuel control unit (FCU) of turbofan engines is categorized into two types: constant speed and constant thrust configurations. The FCU comprises three functional components: scheduling, metering, and limitation modules. Transitioning from a speed-governing FCU to a constant-thrust FCU requires additional subsystems, notably the power management computer, which is part of the Fully Authorized Digital Engine Control (FADEC) system. The FADEC may operate as a standalone unit or be integrated into the FCU. In the constant speed configuration, the FCU ensures that the steady-state fuel metering demand matches the actual high-pressure (HP) shaft speed. In contrast, under the constant thrust configuration, commands generated by the electronic engine control (EEC)—by accounting for environmental conditions and thrust lever angle—align the low-pressure (LP) shaft speed signal with the actual LP shaft speed.

Based on this architecture, this study selects both constant speed and constant thrust operating cases as research scenarios. Leveraging the Amesim simulation platform, a PID control module is implemented to regulate fuel flow rate by receiving real-time signals from the high-pressure shaft speed and engine thrust, thereby achieving precise control under the two operational cases.

Based on the fundamental parameters of the engine, the numerical values of each component were adjusted to conduct simulations under the specified operating conditions: altitude of 10,000 feet (3048 m), Mach number 0.338, standard atmospheric pressure of 101,325 Pa, and standard temperature of 288.15 K. Key performance parameters of the engine were compared between reference data and simulation model outputs to verify the feasibility of the model. As illustrated in

Table 3. The small turbofan engine specifications at 10,000 ft and Mach number 0.338.

Parameter	Reference Value	Simulation Value	Error
Takeoff Thrust	1.07 kN	1.07 kN	0
SFC	76.8 kg·h−1·kN−1	76.8 kg·h−1·kN−1	0
Mass Flow Rate	8.38 kg/s	8.30 kg/s	0.95%
Bypass Ratio	7.46	7.42	0.54%
HP Shaft Speed	49,684 rpm	49,555 rpm	0.26%
Turbine Inlet Total Temperature	1316 K	1321.04 K	0.38%

, the simulation results exhibit excellent agreement with reference values, validating the accuracy and reliability of the model for subsequent analyses.

Subsequently, I employed this simulation model to conduct simulations under the prescribed conditions. The engine’s operating parameters were set at an altitude of 10,000 feet with a flight Mach number of 0.338. Two distinct cases were considered: one where the engine operates at a constant thrust of 1.07 kN and another where the high-pressure shaft speed is maintained at a constant 49,555 rpm. Building on these settings, I investigated the effects of shaft power extraction on the engine’s performance.

2.3. Performance Parameters of the Engine

An aero-engine is a complex aerothermodynamic system that essentially converts thermal energy into mechanical energy. Understanding the thermodynamic calculations of gas parameters is crucial for developing accurate engine models.

Thermodynamic calculations for engines involve determining gas parameters at various engine stations, specific thrust, and fuel consumption rates under given flight conditions, based on selected operational parameters (primarily compressor pressure ratio, turbine inlet temperature, component efficiencies, and loss coefficients). The air mass flow rate through the engine is then determined according to the required thrust. Given the high gas temperatures in our aero-engine, accurate modeling requires consideration of how changes in gas composition affect thermodynamic properties, specifically through variable specific heat calculations [30].

$$C_{P0}=R\left(a_1{\tau }^{-2}+a_2{\tau }^{-1}+a_3{\tau }^0+a_4{\tau }^1+a_5{\tau }^2+a_6{\tau }^3+a_7{\tau }^4\right)$$

(1)

$$C_P=C_{P0}+{\displaystyle \frac{Rln\left(\frac{p}{p_0}\right)}{M_{air}}}$$

(2)

The polynomial coefficients for the specific heat capacity model of air in the established engine model are shown in

Table 4. Polynomial coefficients of specific heat at constant pressure for a perfect gas [30].

Parameter Applicable Ranger	200 K < T < 1000 K	1000 K < T < 6000 K
$a_1$	1.009950 × 104 J/(kg·K)	2.415214 × 105 J/(kg·K)
$a_2$	−1.968276 × 102 J/(kg·K)	−1.257875 × 103 J/(kg·K)
$a_3$	5.009155 × 100 J/(kg·K)	5.144559 × 100 J/(kg·K)
$a_4$	−5.761014 × 10−3 J/(kg·K)	−2.138542 × 10−4 J/(kg·K)
$a_5$	1.066860 × 10−5 J/(kg·K)	7.065228 × 10−8 J/(kg·K)
$a_6$	−7.940298 × 10−9 J/(kg·K)	−1.071483 × 10−11 J/(kg·K)
$a_7$	2.185232 × 10−12 J/(kg·K)	6.577800 × 10−16 J/(kg·K)

. Additionally, $\tau =T/T_{ref}$ and $T_{ref}=288.15 \mathrm{K}$. Here, $R$ refers to the universal gas constant, with a value of approximately 8.314 J/(mol·K).

The primary performance parameters for evaluating high-bypass turbofan engines include thrust, specific fuel consumption (SFC), thermal efficiency, propulsive efficiency, and overall efficiency.

The thrust equation, derived from momentum conservation, is represented by Equation (3) [31,32] for separate-flow turbofan engines.

$$\tau =\beta {\dot{m}}_{core}\left(w_{out,fan}-w_{in}\right)+{\dot{m}}_{core}\left(1+f\right)w_{out,core}+A_{out}\left(p_{out}-p_{in}\right)$$

(3)

where τ represents net thrust, β denotes bypass ratio, f represents the fuel-air ratio, and $w$ represents the airflow speed.

The specific fuel consumption (SFC), calculated as the ratio of fuel flow rate to engine net thrust, serves as a crucial indicator for monitoring engine performance variations. This relationship is expressed in Equation (4) [7].

$$SFC={\displaystyle \frac{{\dot{m}}_{fuel}}{\tau }}$$

(4)

The thermal efficiency of the engine is expressed by the following equation. Thermal efficiency indicates the capability of converting fuel energy into total kinetic energy under given air conditions, and is also known as internal efficiency.

$${\eta }_{th}={\displaystyle \frac{\tau w_{in}+\left[\frac{1}{2}{\dot{m}}_{fan}{\left(w_{out,fan}-w_{in}\right)}^2+\frac{1}{2}{\dot{m}}_{core}{\left(w_{out,core}-w_{in}\right)}^2\right]}{{\dot{m}}_{fuel}LHV}}$$

(5)

2.4. Exergy Parameters of the Engine

2.4.1. Exergy Background

The calculation of exergy requires the selection of a reference environmental state. Every component within a system, as well as the system itself, operates within a specific environment. It is crucial to distinguish between the environment and the system environment. The environment remains essentially unchanged by any process under consideration and is considered irreversible.

A system possesses the capacity to perform work when its pressure, temperature, composition, velocity, or elevation differs from the environment. This work potential diminishes as the system approaches environmental conditions and ceases to exist when they reach relative equilibrium.

For a working fluid, in the absence of nuclear, magnetic, electrical, and surface tension effects, the total exergy comprises physical exergy, chemical exergy, kinetic exergy, and potential exergy. This relationship is expressed in Equation (6) [33].

$$E=E^{PH}+E^{KN}+E^{PT}+E^{CH}$$

(6)

where $E^{PH}$ represents physical exergy, $E^{KN}$ denotes kinetic exergy, $E^{PT}$ indicates potential exergy, and $E^{CH}$ represents chemical exergy. When expressed in terms of specific exergy, the relationship is given by Equation (7).

$$e=e^{PH}+e^{KN}+e^{PT}+e^{CH}$$

(7)

where $e^{PH}$ represents specific physical exergy, $e^{KN}$ denotes specific kinetic exergy, $e^{PT}$ indicates specific potential exergy, and $e^{CH}$ represents specific chemical exergy.

The specific physical exergy $e^{PH}$ is calculated using Equations (8)–(11) [34,35]. The specific physical exergy can be divided into specific thermal exergy and specific pressure exergy. $p_0$ refers to the ambient pressure, $T_0$ refers to the ambient temperature, and $v$ represents the specific volume. $R_g$ represents the gas constant per unit mass used for calculating properties such as specific volume, entropy change, and exergy; its value generally depends on the selected working fluid, and for dry air, it is approximately 287 J/(kg·K).

$$e^{PH}=\left(u-u_0\right)+p_0\left(v-v_0\right)-T_0\left(s-s_0\right)$$

(8)

$$d{e}^{PH}=du+p_{0}dv-T_{0}ds$$

(9)

$$d{e}^{PH}=c_{p}dT-R_{g}dT+p_0{R}_{g}d\left({\displaystyle \frac{T}{P}}\right)-T_0{c}_p{\displaystyle \frac{dT}{T}}+R_g{T}_0{\displaystyle \frac{dp}{p}}$$

(10)

$$e^{PH}=\underset{T_0}{\overset{T}{\int }}{c}_{p}dT-T_0\underset{T_0}{\overset{T}{\int }}{c}_p{\displaystyle \frac{dT}{T}}+R_{g}T\left({\displaystyle \frac{p_0}{p}}-1\right)+R_g{T}_0\ln {\displaystyle \frac{p}{p_0}}$$

(11)

The specific kinetic exergy $e^{KN}$ is calculated using Equation (12), while the specific potential exergy $e^{PT}$ is determined by Equation (13).

$$e^{KN}={\displaystyle \frac{1}{2}}{v}^2$$

(12)

$$e^{PT}=gz$$

(13)

In the absence of nuclear, magnetic, electrical, and surface tension effects, the calculation of standard chemical exergy is based on a standard environment.

Consequently, the specific chemical exergy $e^{CH}$ can be calculated using Equation (14), where $x_k$ represents the molar fraction of component k, and e denotes the reference molar composition in the reference environment.

$$e^{CH}=R{T}_0\sum x_k\ln {\displaystyle \frac{x_k}{x_k^e}}$$

(14)

In addition to the working fluid, fuel enters the system carrying its own exergy, which can be calculated using Equation (15) [36].

$$\begin{gathered} e_F^{CH}\left(C_a{H}_b{O}_c{N}_d\right)=LHV\left(T_0,p_0\right)+\left[a{e}_{C{O}_2}^{CH}+{\displaystyle \frac{b}{2}}{e}_{H_{2}O\left(g\right)}^{CH}+{\displaystyle \frac{d}{2}}{e}_{N_2}^{CH}-\left(a+{\displaystyle \frac{b}{4}}-{\displaystyle \frac{c}{2}}\right)e_{O_2}^{CH}\right] \\ -T_0\left[s_F+\left(a+{\displaystyle \frac{b}{4}}-{\displaystyle \frac{c}{2}}\right)s_{O_2}-a{s}_{{CO}_2}-{\displaystyle \frac{b}{2}}{s}_{H_{2}O\left(g\right)}-{\displaystyle \frac{d}{2}}{s}_{N_2}\right]\left(T_0,p_0\right) \end{gathered}$$

(15)

2.4.2. Methods of Exergy Analysis

Conventional exergy analysis identifies the locations and causes of inefficiencies and losses within energy conversion systems, revealing factors that cannot be detected through energy analysis alone. For any given process, traditional exergy analysis comprises two sets of equations: one describing component-level characteristics and another representing the complete system.

Consider a system component $k$, where ${\dot{E}}_{P,k}$ represents the output exergy (at exit) and ${\dot{E}}_{F,k}$ represents the input exergy. For this component, the exergy destruction can be calculated using Equation (16) [37].

$${\dot{E}}_{D,k}={\dot{E}}_{F,k}-{\dot{E}}_{P,k}$$

(16)

In this context,

Table 5. Input exergy and output exergy values regarding the turbofan components.

Parameter Applicable Ranger Components	$\mathbf{Input} \mathbf{Exergy} \left({\dot{\mathit{E}}}_{\mathit{F}}\right)$	$\mathbf{Output} \mathbf{Exergy} \left({\dot{\mathit{E}}}_{\mathit{P}}\right)$
FAN	${\dot{W}}_{FAN}$	${\dot{E}}_{13}+{\dot{E}}_{15}-{\dot{E}}_0$
HPC	${\dot{W}}_{HPC}$	${\dot{E}}_3-{\dot{E}}_{25}$
CC	${\dot{E}}_{fuel}^{CH}$	${\dot{E}}_{41}-{\dot{E}}_3$
HPT	${\dot{E}}_{41}-{\dot{E}}_{45}$	${\dot{W}}_{HPT}$
LPT	${\dot{E}}_{45}-{\dot{E}}_5$	${\dot{W}}_{LPT}$
FAN	${\dot{W}}_{FAN}$	${\dot{E}}_{13}+{\dot{E}}_{15}-{\dot{E}}_0$

presents the terms of input exergy and output exergy on a component basis.

From a component-based perspective, certain exergy losses cannot be categorized as either output or input exergy, but rather represent the system’s overall wasted exergy, denoted as ${\dot{E}}_{L,tot}$ as shown in Equation (17) [23].

$${\dot{E}}_{L,tot}={\dot{E}}_{F,tot}-{\dot{E}}_{P,tot}-{\dot{E}}_{D,tot}$$

(17)

$${\dot{E}}_{F,tot}={\dot{E}}_{fuel}^{CH}+{\dot{E}}_{02}$$

(18)

$${\dot{E}}_{P,tot}={\dot{E}}_{useful}={\dot{E}}_{core}^{KN}+{\dot{E}}_{core}^{KN}=\left({\dot{m}}_{core}{\displaystyle \frac{w_8^2}{2}}\right)+\left({\dot{m}}_{fan}{\displaystyle \frac{w_{18}^2}{2}}\right)$$

(19)

$${\dot{E}}_{D,tot}=\sum _{k=1}^n{\dot{E}}_{D,k}$$

(20)

${\dot{E}}_{F,tot}$ represents the total input exergy of the system, which consists of the chemical exergy of fuel ${\dot{E}}_{fuel}^{CH}$ and the exergy of intake air ${\dot{E}}_{02}$. ${\dot{E}}_{useful}$ denotes the total output exergy of the system, which is equivalent to the useful exergy ${\dot{E}}_{useful}$. While there are two common methods to calculate useful exergy, this study employs the approach outlined in Equation (19). ${\dot{E}}_{D,tot}$ represents the total exergy destruction in the system.

The exergy efficiency of component k and the overall system exergy efficiency can be calculated using Equations (21) and (22) [38].

$${\eta }_{ex,k}={\displaystyle \frac{{\dot{E}}_{P,k}}{{\dot{E}}_{F,k}}}=1-{\displaystyle \frac{{\dot{E}}_{D,k}}{{\dot{E}}_{F,k}}}$$

(21)

$${\eta }_{ex,tot}={\displaystyle \frac{{\dot{E}}_{P,tot}}{{\dot{E}}_{F,tot}}}=1-{\displaystyle \frac{{\dot{E}}_{L,tot}+\sum _{k=1}^n{\dot{E}}_{D,k}}{{\dot{E}}_{F,tot}}}$$

(22)

Improvement potential rate, proposed by Van Gool [39], shows how much the component has potential for enhancement if the irreversibility could be taken from itself. It could be written as in Equation (23).

$$IPR=(1-{\eta }_{ex,k}){\dot{E}}_{D,k}$$

(23)

The wasted exergy ratio ($WER$) depicts how much wasted exergy takes places per unit input exergy to the engine. It is given as follows [40]:

$$WER={\displaystyle \frac{{\dot{E}}_{L,tot}}{{\dot{E}}_{F,tot}}}$$

(24)

The environmental effect factor of an engine serves as a crucial indicator for determining its environmental impact severity. This impact stems from both exergy losses and exergy destruction within the system. This parameter can be expressed using Equation (25) [41].

$$EEF={\displaystyle \frac{WER}{{\eta }_{ex,tot}}}$$

(25)

The exergetic sustainability index is the reciprocal of the EEF [42].

$$ESI={\displaystyle \frac{1}{EEF}}$$

(26)

Figure 4 illustrates the step-by-step methodology for investigating the effects of shaft power extraction and flight Mach number on the performance and exergy parameters of this small turbofan engine. The process begins with the introduction of engine-specific parameters as inputs for the engine’s parametric cycle equations. Subsequently, thermodynamic analysis is conducted in the Amesim environment using the obtained pressure, temperature, and flow rate values at each component’s inlet and outlet. Finally, the computational results for both the individual components and the entire engine are evaluated through graphical representations.

3. Results and Discussion

In this section, the figures illustrate how shaft power extraction affects the performance and exergy parameters of a small turbofan engine under constant thrust (CT) and constant speed (CS) cases. Figure 5 presents the variation in the engine’s performance parameters, while Figure 6, Figure 7, Figure 8, Figure 9, Figure 10 and Figure 11 demonstrate the calculated exergy parameters of its key components under both operating cases. Finally, Figure 12 and Figure 13 describe the effects of shaft power extraction on the overall engine.

Figure 5 in this study, derived from the simulation model, illustrates the impact of shaft power extraction on fuel flow rate, specific fuel consumption (SFC), and thermal efficiency under both constant speed (CS) and constant thrust (CT) cases. Under the CT case, the fuel mass flow rate increases from 22.8 kg/s at 0 kW to 25.9 kg/s at 18 kW of power extraction, reflecting a progressive demand for additional energy to sustain thrust. This escalation stems from reduced overall thermal efficiency under power extraction, necessitating greater fuel input to compensate for diverted energy and maintain aerodynamic thrust requirements. In the CS case, the fuel flow rate exhibits a steeper trajectory (22.8 kg/s to 31.2 kg/s at 18 kW), driven by the mechanical constraint of fixed high-pressure shaft speed. Here, power extraction imposes amplified loads on the high-pressure compressor (HPC) and turbine system, requiring disproportionately higher fuel delivery to offset energy losses and preserve rotor stability. Notably, the nonlinear fuel flow rate surge beyond 12 kW in the CS case correlates with aerodynamic saturation in the HPC, where blade loading approaches stall margins, necessitating exponential fuel compensation. As illustrated in Figure 5 and the accompanying table, the specific fuel consumption (SFC) in both control strategies (CT and CS) shows a pronounced sensitivity to power extraction. Under the CT case, SFC increases gradually at lower extraction levels (0–12 kW), then accelerates above 12 kW, resulting in a total rise of approximately 13.6% at 18 kW. By contrast, the CS case experiences a far sharper escalation, where SFC climbs by around 42.1% at 18 kW. This discrepancy arises primarily from the aerodynamic and thermodynamic constraints imposed on the high-pressure compressor (HPC) under CS conditions. In CS mode, the rotor speed of the HPC remains fixed, even as the extracted shaft power increases. Because the HPC must continue operating near its design speed, it is forced into a higher loading regime at off-design mass flows. Specifically, as power extraction increases, the HPC’s operating point shifts closer to its surge line, where blade loading and flow distortion are more pronounced. Maintaining stable flow in this high-load, reduced-flow regime requires disproportionately more fuel to sustain sufficient compressor work and avoid stall or surge phenomena. This effect is exacerbated by the reduced combustor residence time and altered fuel—air mixing at off-design conditions—further decreasing combustion completeness and elevating exhaust enthalpy waste. Consequently, the engine compensates by injecting extra fuel, leading to the observed surge in SFC under CS control. By contrast, in the CT case, thrust is held constant rather than rotor speed. As a result, the HPC is allowed to adjust its rotational speed in tandem with the changing mass flow demands, thus operating farther from aerodynamic limits. Although SFC still increases (13.6% at 18 kW), the performance penalty is milder because the compressor remains in a more favorable region of its map, and less additional fuel is needed to preserve stability. In essence, thrust prioritization (CT) moderates the adverse aerodynamic impacts on the HPC and the combustor, whereas speed prioritization (CS) enforces a rigid rotor speed that pushes the HPC closer to surge conditions, thereby amplifying fuel consumption and irreversibility under high auxiliary power demands. Thermal efficiency responses further highlight operational disparities. In the CT case, efficiency declines monotonically, reflecting energy partitioning toward shaft work rather than kinetic thrust generation, which is an inherent limitation of fixed-thrust energy budgeting. In contrast, the CS case demonstrates a non-monotonic efficiency profile, with marginal gains at moderate extraction levels (6–12 kW) followed by degradation at higher loads. This transient improvement arises from optimized airflow stabilization under regulated rotor dynamics, which enhances combustor mixing efficiency. However, surpassing 12 kW induces HPC surge precursor oscillations, destabilizing the Brayton cycle and reversing efficiency gains. These insights advocate for adaptive power extraction thresholding: limiting shaft power demands below 9 kW preserves thermal efficiency within ±2% of baseline in the CS case while mitigating disruptive aerodynamic effects. Additionally, integrating variable-geometry compressor controls could decouple extraction-induced loading from core flow stability, enabling higher auxiliary power extraction without compromising fuel economy. Such system-level optimizations are imperative for next-generation turbofans, targeting expanded onboard electrification while maintaining stringent emissions compliance.

From Figure 6 and Figure 7, it is evident that the exergy efficiency of engine components exhibits distinct trends under both constant thrust (CT) and constant speed (CS) cases as shaft power extraction increases. For the fan component, the exergy efficiency declines slightly under both operational cases (CT: 0.856 to 0.852; CS: 0.856 to 0.853) at 18 kW power extraction. This marginal reduction suggests a subtle increase in aerodynamic loading due to the additional power extraction, which disrupts the fan’s ideal flow compression process, leading to localized energy dissipation. The high-pressure compressor (HPC) experiences a more pronounced efficiency degradation (CT: 0.913 to 0.902; CS: 0.913 to 0.896) at 18 kW, indicating heightened mechanical and aerodynamic complexity under elevated extraction demands. The HPC’s reduced efficiency arises from deviations in its operational line toward less optimal pressure ratios, amplifying entropy generation in the compression process. Conversely, the combustor demonstrates a counterintuitive efficiency improvement (CT: 0.652 to 0.671; CS: 0.652 to 0.685), which can likely be attributed to enhanced fuel–air mixing dynamics under modified airflow conditions. The increased pressure perturbations from power extraction may optimize residence time distributions, reducing incomplete combustion losses. The high-pressure turbine (HPT) and low-pressure turbine (LPT) show marked efficiency gains (HPT-CT: 0.924 to 0.930; HPT-CS: 0.924 to 0.940; LPT-CT: 0.925 to 0.939; LPT-CS: 0.925 to 0.951), reflecting improved energy utilization. For the HPT, power extraction alleviates blade choking effects, enabling closer alignment with design expansion ratios, while the LPT benefits from reduced residual swirl energy in the exhaust stream under CS-regulated rotor speed stability. In the CT case, the prioritization of thrust maintenance intensifies fan and HPC aerodynamic stresses, undermining their exergy performance, while CS operations impose stricter energy redistribution constraints, magnifying HPC inefficiencies. Crucially, the divergent responses emphasize a system-level trade-off: power extraction amplifies thermal-to-mechanical energy conversion efficiency in turbines but destabilizes compressor and fan operability. These findings underscore the necessity for adaptive power management strategies that balance component-level efficiency trade-offs, particularly in next-generation turbofan architectures where auxiliary power demands are escalating. Optimizing extraction thresholds below critical aerodynamic thresholds could mitigate irreversible losses while harnessing thermodynamic benefits in downstream components.

Figure 8 and Figure 9 reveal significant variations in component-level exergy destruction under constant thrust (CT) and constant speed (CS) cases with increasing shaft power extraction. In the CT case, the fan’s exergy destruction rises from 14.8 kW (at 0 kW) to 15.5 kW (at 18 kW), while in the CS case, it escalates more drastically from 14.8 kW to 17.6 kW. This divergence stems from aerodynamic decoupling under CS constraints: fixed N2 rotor speed amplifies flow distortion and intensifies rotor-stator interactions, driving irreversible losses. The high-pressure compressor (HPC) exhibits analogous trends, with exergy destruction surging from 17.1 kW to 20.9 kW in the CS case versus minimal growth in the CT case. This highlights the CS regime’s thermodynamic penalty; rigid rotor inertia mandates higher work input to sustain pressure ratios, elevating entropy generation. The combustor (CC) suffers greater irreversible losses under CS operation (366 kW to 452 kW, compared to 393 kW in the CT case), which is attributable to perturbed fuel–air stoichiometry and shortened residence times. Conversely, turbine sections demonstrate improved efficiency: HPT exergy destruction decreases from 16.2 kW to 14 kW (in the CS case) and 14.5 kW (in the CT case), driven by optimized expansion ratios and reduced tip leakage flows. Similarly, the LPT’s exergy loss declines from 8.26 kW to 6.25 kW (in the CS case) and 6.82 kW (in the CT case). CS operation imposes harsher thermodynamic penalties on forward components (fan/HPC/CC), while turbines benefit from stabilized flow fields. Below 12 kW extraction, exergy destruction scales quasi-linearly; beyond this threshold, HPC surge margin violations in the CS case trigger nonlinear loss escalation. Reduced turbine losses partially offset compressor/combustor inefficiencies.

The analysis of IPR trends, as depicted in Figure 10 and Figure 11, provides critical insights into the thermodynamic behavior of key engine components—fan, high-pressure compressor (HPC), combustion chamber (CC), high-pressure turbine (HPT), and low-pressure turbine (LPT)—under constant thrust (CT) and constant speed (CS) conditions with increasing shaft power extraction (ranging from 0 to 18 kW). For the fan, the IPR exhibited a steady rise in the CT case, increasing from 2.13 kW to 2.29 kW, while the CS case saw a more pronounced increase from 2.13 kW to 2.59 kW. This upward trend under both cases is due to heightened aerodynamic losses and elevated mechanical loads required to stabilize airflow, with the CS scenario amplifying performance degradation due to stricter rotational constraints. The HPC demonstrated distinct behaviors: the IPR in the CT case remained nearly stable, increasing from 1.49 kW to 1.69 kW, which is attributed to thrust-driven operational stability, while the CS case triggered a significant surge, reaching 2.18 kW, as increased compression work exacerbated energy losses to maintain fixed shaft speeds. For the CC, the IPR increased marginally under CT, from 127 kW to 129 kW, reflecting near-optimal combustion efficiency under controlled thrust conditions. However, in the CS case, the IPR escalated sharply to 142 kW, driven by unstable airflow dynamics under rigid rotational demands, highlighting the combustor’s sensitivity to flow perturbations. In contrast, both the HPT and LPT exhibited declining IPR trends. Under CT, the HPT IPR decreased from 1.23 kW to 1.01 kW, while the LPT IPR declined from 0.615 kW to 0.416 kW. These reductions intensified under CS conditions (HPT: 0.837 kW; LPT: 0.309 kW), indicating severe efficiency losses due to turbine overloading and compromised energy conversion. CT operations generally moderated IPR variations, particularly in the HPC and CC, as thrust prioritization stabilized energy distribution. However, CS operations amplified system energy demands, leading to significant IPR escalation in compressors and the combustor, which were offset by a marked decline in turbine efficiency. The degradation in turbines underscores the trade-off between power extraction and exergy destruction: excessive shaft power extraction overloads the turbomachinery, reducing energy recovery potential. While CS operations enhance IPR in compressors through intensified energy redistribution, they irreversibly impair turbine efficiency. Engine design and control strategies must prioritize balancing shaft power extraction levels with component load thresholds, favoring adaptive thrust modulation over rigid speed constraints to mitigate thermodynamic inefficiencies. This approach is essential to optimize system performance and align with the sustainable aviation objectives.

As illustrated in Figure 12, increasing shaft power extraction significantly impacts the total inlet exergy, total exergy destruction, and wasted exergy of the turbofan engine under both constant thrust (CT) and constant speed (CS) conditions. Total inlet exergy under the CT case rises progressively from 1.05 MW to 1.20 MW, while the CS case exhibits a steeper increase from 1.05 MW to 1.44 MW. This disparity arises from the heightened energy demand to stabilize airflow and rotational integrity, particularly in CS operations, where maintaining fixed high-pressure shaft speeds necessitates substantial additional energy input. Total exergy destruction, reflecting irreversibility, escalates with shaft power extraction: in the CT case, it increases from 414 kW to 441 kW, while under CS conditions, it surges more sharply from 414 kW to 505 kW. This trend underscores amplified mechanical losses and thermodynamic inefficiencies during power extraction, exacerbated by the CS case’s rigid rotational constraints, which intensify irreversible processes. Wasted exergy—energy unutilized for productive work—shows similar patterns. The CT case demonstrates an increase from 337 kW to 444 kW, whereas the CS scenario exhibits a more pronounced rise, reaching 579 kW. This divergence stems from the CS operation’s inherent complexity in balancing aerodynamic stability with fixed shaft speeds, leading to suboptimal energy conversion and elevated waste. While both cases exhibit rising energy demands and losses with shaft power extraction, the CS case incurs substantially higher exergy destruction and waste due to stringent rotational requirements. These findings emphasize the critical need to optimize power extraction levels in turbofan design, prioritizing adaptive thrust management over rigid speed maintenance to minimize irreversible losses. Such strategies are essential for enhancing thermodynamic efficiency and aligning with the sustainable aviation goals, where energy conservation and component reliability are paramount.

Figure 13 illustrates the trends in exergy efficiency, the environmental effect factor (EEF), and the exergetic sustainability index (ESI) as shaft power extraction increases under both constant thrust (CT) and constant speed (CS) cases. Exergy efficiency, defined as the ratio of product exergy to fuel exergy, increases with shaft power extraction. In the CT case, exergy efficiency rises from 0.473 (at 0 kW) to 0.507 (at 18 kW), indicating improved energy utilization with increased shaft power extraction. In the CS case, the increase is more pronounced, from 0.473 to 0.542. This trend suggests that under constant speed conditions the engine optimizes its operating point more effectively when higher shaft power extraction is required to maintain fixed high-pressure shaft speed, leading to improved exergy efficiency. Regarding the environmental effect, our analysis employs two key indices: the environmental effect factor (EEF) and the exergetic sustainability index (ESI). The EEF is calculated as the ratio of the wasted exergy ratio (WER) to the overall exergy efficiency. In the constant-thrust (CT) case, the EEF increases from 0.678 (at 0 kW) to 0.732 (at 18 kW), while in the constant-speed (CS) case, it rises even more significantly: from 0.678 to 0.744. This increase indicates that despite a slight improvement in exergy efficiency with higher shaft power extraction a larger proportion of the input fuel exergy is being dissipated as wasted energy. In practical terms, a higher EEF signifies that the engine is operating with increased irreversibility, leading to greater energy losses. These losses typically manifest as higher exhaust temperatures and increased emissions, both of which are detrimental to environmental sustainability. Complementarily, the exergetic sustainability index (ESI), defined as the reciprocal of the EEF, decreases with increasing power extraction: from 1.48 to 1.37 in the CT case and from 1.48 to 1.34 in the CS case. The decline in the ESI quantitatively reflects a reduction in the engine’s capability to sustainably convert fuel energy into useful work. A lower ESI suggests that the system is less sustainable, as more fuel energy is wasted, which could potentially result in higher emissions and a greater environmental impact. In summary, the observed increases in the EEF and the corresponding decreases in the ESI with higher shaft power extraction indicate that although auxiliary power extraction can improve the utilization of fuel energy it does so at the expense of increased thermodynamic losses. These losses lead to a greater environmental burden, particularly under the constant-speed control strategy, where the energy required to maintain a fixed high-pressure shaft speed significantly raises the rate of exergy destruction. Hence, optimizing the level of shaft power extraction is critical not only for performance efficiency but also for minimizing adverse environmental impacts.

4. Conclusions

This study examined the effects of shaft power extraction on a small high-bypass turbofan engine operating under constant thrust (CT) and constant speed (CS) control strategies, revealing significant impacts on fuel consumption, efficiency, and environmental sustainability. The findings quantify the trade-offs inherent in diverting energy from propulsion to onboard systems, providing valuable insights for future engine design and operation.

• Under CT control, maintaining the same thrust while extracting shaft power necessitates additional fuel consumption, which results in a higher specific fuel consumption (SFC). In our study, SFC increased from approximately 20.68 to 22.25 g/kN—a rise of about 7.6%—with increasing power extraction. In contrast, under CS control, SFC increased from roughly 20.63 to 21.90 g/kN (a rise of around 6.1%), indicating that CS offers a slightly lower fuel-burn penalty during power off-take. This difference underscores that while both strategies incur fuel penalties, the CS mode is marginally more fuel-efficient when power is diverted.
• The overall exergy efficiency, which reflects the engine’s second-law performance, decreases in both control modes as more shaft power is extracted. However, the CT strategy experiences a somewhat larger decline in exergy efficiency—from approximately 26.9% to 25.0%—compared to the CS strategy, which falls from about 27.0% to 25.4% over the same extraction range. This suggests that maintaining constant thrust, despite its operational benefits, comes with a higher penalty in terms of work potential compared to allowing the engine speed to remain constant.
• Thermal efficiency, defined as the fraction of fuel energy converted to useful output, is similarly impacted by shaft power extraction. Under CT control, the need for extra fuel to sustain thrust results in a noticeable decline in effective thermal efficiency. In contrast, CS control permits a slight reduction in thrust output, thereby converting fuel into a combination of thrust and shaft power more efficiently. Although both strategies exhibit reduced thrust-per-fuel efficiency as power extraction increases, the CT approach is disadvantaged by a higher fuel penalty.
• The environmental implications of these performance changes are also significant. Increased fuel consumption under CT control leads to higher emissions per unit of thrust, negatively affecting environmental sustainability. Although the CS mode also experiences increased fuel consumption, the more modest rise in SFC suggests a comparatively lower environmental impact in terms of greenhouse gas emissions. Exergy-based sustainability indicators, which account for wasted fuel energy and exergy destruction, decline with increasing power extraction in both cases; however, the deterioration is slightly less severe under CS control.

These observations have important implications for next-generation no-bleed turbofan engines, which are designed to minimize or eliminate traditional bleed-air extraction by using shaft power to drive aircraft systems. Modern aircraft designs, such as the Boeing 787, rely on bleed-less architectures to enhance overall efficiency. Our results indicate that supplying shaft power under a CT regime could lead to significant increases in fuel burn and emissions, potentially negating some of the efficiency benefits associated with no-bleed configurations. Therefore, selecting an appropriate control strategy for power extraction is crucial. A constant speed (or mild thrust sacrifice) approach may yield lower fuel consumption during cruise operations, while a constant thrust strategy might be more suitable for critical flight phases like takeoff and climb, despite its higher fuel penalty.

In conclusion, shaft power extraction inevitably affects turbofan engine performance. While constant thrust control maintains flight performance at the expense of increased fuel consumption and efficiency losses, constant speed control offers slightly better fuel efficiency but requires accepting reduced thrust output. The documented differences in fuel burn, exergy and thermal efficiency, and emission profiles provide quantitative guidelines for engine manufacturers. By leveraging advanced control optimization and adaptive engine hardware, it is possible to develop no-bleed turbofan engines capable of supplying substantial onboard power with minimal performance penalties. Such advancements are essential for supporting the rising power demands of more-electric aircraft architectures without compromising core engine efficiency or environmental sustainability.