Propulsion System Performance Research Articles

A Multi-Phase Brushless Direct Current Motor Design and Its Implementation in Medium-Altitude Long-Endurance Unmanned Aerial Vehicles

Nowadays, electric propulsion system implementation in vehicles is popular, and many studies and prototypes have been accomplished in this field. Aircraft are important members of the vehicle family, and Unmanned Aerial Vehicles (UAVs) are part of this family as well. Some UAVs still have conventional propulsion systems, which are less efficient and are harmful to the environment. In addition, conventional systems are vulnerable to faults in their propulsion system components. To overcome these problems, we designed a multi-phase Brushless Direct Current (BLDC) motor, to achieve fault-tolerant operation. Our designed BLDC motor was implemented in a UAV model that was created on MATLAB Simulink, based on a currently used UAV. Our design and performance analysis are shown for the BLDC motor, both standalone and as implemented in the created UAV model. The electric propulsion system performance is shown, according to the determined flight profile. We observed that the designed electric machine is capable of producing the required torque to create thrust for lifting the UAV. There are some advantages and disadvantages to using the designed electric machine in this class of UAV. This is shown in the related sections.

Multi-objective hierarchical energy management strategy for fuel cell/battery hybrid power ships

The energy management strategy and the local controller in the ship energy management system are interconnected, impacting the performance of the hybrid propulsion system. To achieve the efficient operation of the hydrogen fuel cell (FC) and battery hybrid power system, based on the modelling and analysis of the hybrid power system, a nonlinear model predictive control (NMPC) based energy management strategy is proposed, and a dynamic virtual impedance droop controller and a classical proportional-integral (PI) controller are designed as local controllers. By simulating the designed random load conditions, pulse load conditions, and actual sailing conditions using hardware-in-the-loop (HiLs) technology, six different energy management strategies and their comprehensive performance with local controllers are compared and analysed. Comparing performance in terms of energy consumption, operating pressure, control accuracy, real-time performance, and robustness, it has been proven that the energy management strategy based on NMPC, coupled with a PI controller, is superior to other strategies overall. It can balance hydrogen consumption and the stable operation of the hybrid power system. Compared to existing energy management strategies, the proposed NMPC+PI strategy can reduce hydrogen consumption by 7.00 % and 40.29 %, and FC operating pressure by 44.96 % and 49.88 %, respectively, under both designed navigation conditions and actual navigation conditions.

Wingsail performance in unsteady atmospheric surface layer winds

The performance of wind propulsion systems is evaluated in unsteady inhomogeneous winds with tools that are routinely used to predict the performance of wind turbines and which give access to the unsteady aerodynamic forces acting on the wingsail. A rigid wingsail exposed to a realistic atmospheric surface layer wind is used as a testbed. For this case, we show that standard deviations of the aerodynamic driving force are larger than 15%–20% of the mean values when the true wind velocity is larger than the ship speed. We also show that the mean aerodynamic driving forces computed by averaging the unsteady driving forces are only slightly smaller than the ones computed on the mean wind despite the strongly nonlinear dependence of the unsteady forces on the wind velocity and direction.

Multi-fidelity simulation of inlet mode transition with smooth thrust of turbine based combined cycle

A multi-fidelity simulation method of external and internal flow has been developed using commercial software to achieve a smooth thrust of the turbine-based combined-cycle (TBCC) propulsion system. This platform enables the investigation of the flow field and performance of the TBCC propulsion system at different mode transition schemes. The integrated multi-fidelity simulation includes the inlet, turbojet engine, ramjet engine, and nozzle, providing insights into the operation process of the TBCC propulsion system during the transition from turbojet mode to ramjet mode. Three mode transition schemes are proposed: critical mode transition, constant aerodynamic interface plane (AIP) Mach number mode transition, and linear mode transition. From the perspective of TBCC inlet, the performance of the critical mode transition exhibits the best performance among these mode transition schemes, while the linear mode transition performs the worst. However, from the viewpoint of the TBCC propulsion system and the hypersonic vehicle, the performance of constant AIP Mach number mode transition is the best. The non-dimensional thrust increases almost linear from 1.0 to 1.2, enabling hypersonic vehicle to accelerate steadily during the transition from turbojet mode to ramjet mode.

Autoignition of premixed hydrogen/air mixtures with uniformly dispersed carbon particles

The autoignition of a stoichiometric hydrogen/air mixture laden with uniformly distributed coal char particles is simulated with the Eulerian-Lagrangian approach under isochoric conditions. A zero-dimensional model is adopted to assess the effects of gas temperature, pressure, particle diameter, and concentration on ignition dynamics. Increasing the initial temperature reduces the ignition time and maximum heat release rate of the homogeneous reactions, while the parameters for particle reactions stabilize after reaching a critical temperature. Initial pressure exhibits a non-monotonic influence on gas phase ignition, with higher pressures promoting particle autoignition. An increase in particle diameter decreases the ignition time for the homogeneous reaction, approaching that of particle-free conditions. Meanwhile, particle ignition time first decreases and then linearly increases. Increasing particle concentration reduces the interphase disparities of ignition times, while the two-phase ignition times rapidly rise after exceeding the critical concentration. Moreover, pre-ignition temperature equilibrium (PTE) significantly impacts the ignition parameters and processes. PTE results in a minimal ignition time disparity between the gas and particles, with coal char particles markedly influencing hydrogen ignition. Failure to reach PTE leads to significant two-phase ignition time differences, with negligible impact from the solid phase on gas phase ignition. The particle effect ratio, δ, is introduced to evaluate these effects. Notably, the evolution variations in ignition time and heat release rate are determined by the existence of the PTE under corresponding initial conditions. The findings of this study are crucial for developing strategies to mitigate explosion hazards and enhance the performance of detonation propulsion systems using hybrid fuels.

Analysis of Impact of Control Strategies on Integrated Electric Propulsion System Performance During Icebreaking Process

Developing an efficient power system is an important way for icebreakers to respond to high maneuverability and strong fluctuation loads under icebreaking conditions. The performance of power systems under short-period, regularly fluctuating load-sea conditions has been intensively studied. However, the performance of the power system in the face of a long-period, stochastic multi-frequency fluctuation icebreaking process has not been fully explored, especially the parameter uncertainty and battery cycle life. In this study, an integrated electric propulsion system with an optimal control strategy is suggested for improving the power system’s dynamic performance and battery cycle life. First, an energy flow model with a diesel–electric unit as the main body and coupled energy storage system/hybrid energy storage system has been constructed. A comparative analysis of rule-based and optimization-based energy management strategies has been performed, and an optimized strategy with dynamic programming as global regulation at the upper level and model predictive control at the lower level is suggested to integrate the slow and fast dynamic powers and achieve adaptability to strong fluctuation loads. In this control strategy, the uncertainties of energy storage system/hybrid energy storage system parameters have been introduced to eliminate their impact on the system performance. Then, the icebreaking process with multi-frequency fluctuation has been simulated, and the hybrid energy storage system with battery and supercapacitor is recommended to reach multi-objective with the lowest power fluctuation of diesel–electric unit, highest efficiency, and the minimum battery degradation. Finally, the fuel oil consumption and emissions of the hybrid energy storage system have been discussed, and the optimized strategy can save fuel oil by up to 5.33% and reduce the CO2 emission by 22% during the icebreaking process, exhibiting great potential in the environmental friendliness and significant advantages in terms of low fuel oil consumption.

A comprehensive propulsion system analysis: an integrated approach utilising engine simulation and free-running model experiments

Regulations concerning the environmental impact and energy efficiency of ships are becoming increasingly stringent. To meet these demanding criteria, new technologies are actively being developed to achieve emission reductions while maintaining efficient fuel energy conversion into propulsion power. However, the propulsion system behaviour in a dynamic environment of the actual sea is highly nonlinear and complex, and a profound understanding of the mutual interactions is still lacking. This paper proposes an integrated approach for comprehensive propulsion system analysis. The key feature of this technique is the utilisation of an intelligent propeller drive controlled by a marine diesel engine simulator (MDES) to drive the free-running model of a ship, providing real-like behaviour of the engine model in real-time in response to actual measured values. The core of the MDES consists of a continuous cycle-mean value dynamic engine model supplemented with a detailed combustion cycle evaluation. The developed fast calculation algorithm of crank-angle resolved thermodynamic equations of the gas state in the engine cylinder enables the complete engine model to be integrated into the real-time environment of a physical model ship. Thus, the propulsion system's performance can be analysed under conditions that closely mimic those of the actual sea environment.

Effects of propeller cavitation on ship propulsion performance in off-design operating conditions

The propeller cavitation is closely related with its hydrodynamic performance. When the propeller works in the cavitating flow, the propeller hydrodynamic performance, in terms of thrust and torque coefficients, is reduced due to the propeller cavitation. When the high-speed and high-power ship sails in adverse sea, the varying loads on propeller will cause severer cavitation on propeller. The reduction in propulsion performance caused by cavitation will further affect the propulsion system, impacting the ship sailing performance and safety. The VP1304 propeller cavitation CFD simulation are conducted to validate the CFD method. Furthermore, the influence of propeller advance ratio and cavitation numbers on the performance of low-speed high-power series propeller in cavitating flow are studied and illustrated. This influence of cavitation has also been transferred to the propulsion system and this process are calculated by the ship propulsion system numerical model. Additionally, the sailing performance of ship propulsion system under off-design conditions, where the cavitation is more likely to occur, has been investigated in this article. Under severe heavy load conditions, it can even result in a complete loss of propulsion capability, posing significant risks. Therefore, it is necessary to further optimize control strategies for the propulsion system to mitigate the hazards caused by cavitation.

Mars 2020 Descent Stage Integrated Propulsion Subsystem: Changes and Flight Performance

On February 18, 2021, NASA’s Mars 2020 mission successfully landed the Perseverance rover in Jezero Crater, the heaviest interplanetary rover ever built, on the surface of Mars. Following up on the successful entry, descent, and landing of the Curiosity rover of the Mars Science Laboratory mission in August 2012, the Mars 2020 mission Descent Stage Propulsion System was a build-to-print sequel. The Mars 2020 Descent Stage Propulsion System had a few minor low risk changes based on the flight performance of the Mars Science Laboratory System to improve performance. The in-flight performance of the Descent Stage Propulsion System was consistent with expectations with the exception of apparent higher than expected delivered thrust from the Mars Lander Engines, which occurred on both the Mars 2020 and the Mars Science Laboratory missions. The Descent Stage Propulsion System completed its mission with significant capability margin with respect to thruster life, maximum delivered thrust, and available propellant at touchdown.

Fluid selection and parametric analysis of organic Rankine cycle applicable to the turboshaft engine with a recuperator

With ever increasing fossil fuel price and growing demands in cutting emissions, waste heat recovery (WHR) appears as a promising pathway to improve propulsion system performance, which can be potentially achieved by incorporating a recuperator. This paper explores the advantages and potentiality of further recovering exhaust heat from recuperated turboshaft engine through the concept of organic Rankine cycle (ORC) to improve fuel economy and thermal efficiency. For the intended application, working fluid selection is conducted after systematic consideration of thermophysical properties, environmental impact, health and safety issues. Furthermore, parametric analysis is carried out from the viewpoint of thermodynamics, and the genetic algorithm is also employed to obtain the maximum net power output. Targeting the implicit coupling between recuperator effectiveness and ORC performance, the potential advantages of the combined engine-ORC system are comprehensively evaluated at different operational regimes. The influence of flight condition is also discussed through sensitivity simulations for different altitudes. Results reveal that the combination of the recuperated engine with ORC cycle operated using acetone generally offers the greatest benefits, significantly reducing specific fuel consumption by 46%–59 % relative to the baseline simple-cycle engine, depending on the availability of heat source. This analytical work contributes to provide valuable insights into WHR technologies in the aviation industry.

Regenerative cooling in hybrid rocket engines based on Self-Pressurized liquid nitrous oxide

An experimental investigation of the reliability and feasibility of a regenerative cooling system in hybrid rocket engines based on saturated nitrous oxide is presented. The novelty of the work consists in the use of a cooling system based on saturated liquid nitrous oxide, wrapping the external surface of a COTS graphite nozzle. The detrimental heat fluxes developed at the throat are handled with a slight increase in assembly complexity. Ten firing tests are performed with an incremental logic of the mass flow rate from 9 to 45 g/s, which is controlled by cavitating the fluid through orifices with different diameters upstream of the cooling system. The tests have been performed at different ambient temperatures in different seasons. The multiphase state of the coolant is evaluated by measuring pressure and temperature upstream and downstream of the cavitation orifice and cooling channels. The test with the smallest mass flow rate developed the highest vapour fraction downstream of the orifice and cooling channels at 0.458 and 0.481, respectively. The cooling performance is indirectly evaluated by measuring the nozzle temperature at 3, 5, and 8.5 mm from the throat internal surface. The results show that steady temperatures are achieved inside the nozzle, with throat temperatures included between 700 and 1200 K in a chamber pressure range between 5 and 30 bar. Nozzle erosion never occurs in the entire experimental campaign, and the nozzles are totally reusable for more ignitions. The coolant heat transfer coefficient increased from 3912 to 21181 W/(m2∙K) by increasing the flow rate per channel from around 3 to 15 g/s. Compared to cryogenic oxygen, liquid nitrous oxide displays higher cooling performance. Finally, the cavitation orifice is moved downstream of the cooling system, showing worse performance of the overall propulsion system.

Simple model of turbine-based combined cycle propulsion system and smooth mode transition

Abstract Turbine-based combined cycle (TBCC) propulsion system is becoming one of the most promising propulsion systems for two-stage-to-orbit reusable launch vehicle. Mathematic model of this combined cycle engine is helpful for the basic understanding of performance analysis of this propulsion system. We developed mathematic model of TBCC propulsion system based on C++ platform in this paper. Firstly, turbojet engine was built on component level and ramjet engine was calculated through stream thrust function. Then, performance of turbine-based combined cycle propulsion system along a specific flight trajectory was investigated. According to the thrust of this combined cycle engine, mode transition point was suggested at Ma 2.5, which may achieve smooth mode transition from turbine mode to ramjet mode. Finally, mode transition based on smooth mass flow and smooth thrust criteria were studied. The thrust gap arises during smooth mass flow mode transition, particularly when the turbojet engine afterburner is powered off at the start of the mode transition, and it meets 34 % of the total thrust. Smooth thrust mode transition may be achieved by delaying the turbojet engine afterburner power off and injecting additional fuel into ramjet burner.

Modelling the nonlinear system performance of hybrid-electric propulsion systems with aerothermodynamic interdependencies

The development of commercial aircraft with hybrid-electric propulsion systems is currently a subject of extensive research in order to improve local air quality and reduce combustion emissions. Among the various types of engines being studied, the two-spool parallel hybrid-electric turbofan engine is particularly challenging due to the low-pressure compressor (LPC). The hybridisation process tends to throttle the LPC, accentuating its significance in the propulsion system. For reliable operation of such systems, accurate predictions of the LPC performance during time-sensitive manoeuvres such as a go-around are important. These manoeuvres are heavily influenced by time-dependent effects that govern the propulsion system’s performance. Often, the aerothermodynamic interplay between these effects is overlooked in propulsion models. In this study, the influence of these aerothermodynamic interdependencies on the modelling results is investigated. To investigate these aerothermodynamic interactions, a dynamic model is developed to simulate the performance of the hybrid-electric turbofan engine. In comparison, a constant mass flow model is used, which is not able to simulate these interdependencies. The results show that the aerothermodynamic interdependencies significantly affect the modelled time-resolved performance, especially for surge margin of the LPC, with this effect becoming more pronounced at higher levels of hybridisation. Therefore, the study recommends the adoption of dynamic simulation methodologies for hybrid-electric engines to guarantee high simulation precision, enhance reliability, and satisfy safety standards.

The propulsion performance of the semi-active tandem flapping foils for wave gliders: A study on vortex interactions and hydrodynamic performance

An investigation is conducted on the propulsion performance of semi-active flapping foils in tandem configuration of the wave glider, considering different vortex effects and tandem distances. The Finite Volume Method is utilized with commercial CFD software Fluent to solve the URANS equations around the flapping foil. A mesh comprising a 2D NACA0012 foil with Reynolds number Re = 42,000 is used in all simulations. The study investigates the propulsion performance of tandem flapping foil systems, focusing on the differing impacts of wave interaction on the front and rear foils. It explores how varying tandem distances and reduced frequencies influence thrust enhancement and degradation. The research reveals that while the front foil consistently benefits from thrust enhancement, the rear foil's performance is more complex, being subject to thrust enhancement or reduction due to wake vortex interactions. Detailed analyses of instantaneous thrust coefficients, pitching trajectories, and pressure contours provide insights into the hydrodynamic performance of these systems. The findings emphasize the importance of synchronization in motion between the foils for optimal propulsion and highlight the rear foil's susceptibility to changes in the wake flow, affecting its thrust generation capability. Thus, the optimal tandem distance can fully capitalize on the thrust enhancement effect of the wake interaction to improve the performance of the tandem flapping foil propulsion system.

Chemical behavior research of high-energy aerospace propellant with a mesoscale heterogeneous packing model

The NEPE propellant has a wide range of applications in the aerospace field, playing a crucial role in enhancing the performance and efficiency of propulsion systems. In this study, we have developed an elaborate physical–chemical model to simulate the transient reaction characteristics of NEPE propellants. Our approach entails a sequential algorithm to explore the microstructure of NEPE propellants, incorporating a novel semi-global kinetic reaction mechanism designed to accurately represent real-world scenarios during propellant combustion. The interplay between the condensed phase and gas phase is handled through the use of the source term method. A comprehensive examination is carried out to ensure the statistical convergence of the propellant particle distribution. Moreover, we have compared the simulated burning rate of NEPE propellant under different formulations and operating pressures (ranging from 0.5 to 2.5 MPa) with experimental cases. The predictions demonstrate excellent agreement within a 10 % margin of the experimental data, highlighting the precision with which our proposed model depicts propellant combustion. Furthermore, we have conducted simulations of the combustion of specific NEPE disk packs composed of 19.63 % 100 µm AP, 35.3 % 60 µm HMX, 8.83 % 50 µm HMX, and 36.25 % NG/BTTN binder. Our findings reveal that the variation of statistical burning rates can be described by the equation rb=3.93P0.453, Additionally, the adiabatic flame temperature of the disk packs, under various pressures, typically falls within the range of 3200–3700 K. To gain a deeper understanding of the impact of different components within the propellant on combustion, we have carried out burning tests on a series of NEPE disk packs with varying formulations, accompanied by particle-scale combustion analysis. Our observations indicate that substituting 1 % HMX particles for AP particles leads to a significant enhancement in the propellant’s burning rate, approximately 0.02 mm/s. This phenomenon confirms that HMX particles act as a potent explosive source, thereby contributing to an increased flame standoff distance. Consequently, a jet-like diffusion flame with a length scale of several microns commonly appears above the AP-binder-HMX unit.

Computational Study on Compressor-Combustor Interactions for Improved Matching of a Micro Gas Turbine

ABSTRACT Understanding complex aerodynamics/combustion interactions across major components of aeroengines, including the compressor, combustor and turbine is demanded for the improved performance of advanced propulsion systems. This study employs high-fidelity CFD simulations to investigate the coupled compressor-combustor interactions for the improved performance of a micro gas turbine. In the prototype configuration, the deficient compressor/combustor matching causes insufficient air/fuel mixing and delayed combustion inside the combustor chamber. By reducing the flow area of the compressor and redistributing the air holes on the combustor chamber, a stable united recirculation structure is formed to promote air/fuel mixing and efficient combustion, achieving a over 50% decrease in OTDF and RTDF at the combustor exit and a total 20% decrease of pressure loss in the entire engine through-flow. Compared with the single-component combustor simulation, the coupled compressor-combustor results exhibit stronger turbulence mixing, increased temperature uniformity inside the combustor chamber. Compared with the single-component compressor simulation, the compressor in the multi-component simulation shows the reduced flow angle and Mach number at the compressor outlet, leading to increased stall critical angles and delayed flow separation at the compressor diffuser and vanes. This demonstrates that the added combustor endues the compressor with an expanded operating range and a lower mass-flow rate instability boundary. This work implies that 3D multi-component CFD simulation is necessary to understand the aerodynamic and combustion interactions and improve the multi-component matching in gas turbine engines.

Implementation of direct battery driven discharge in triggerless operation of vacuum arc thrusters

The increasing demand for CubeSat missions with limited budgets and constrained timelines necessitates the development of innovative propulsion systems. This paper focuses on vacuum arc thrusters (VATs) and investigates the implementation of battery-driven discharge for triggerless firing. VATs offer a promising alternative for CubeSat propulsion, generating thrust through the pulsed ejection of plasma in a cathode arc discharge. The study explores the feasibility of direct battery-driven discharge in VATs and demonstrates stable and variable-duration pulses. Experimental testing using high C-rating lithium-ion (Li-ion) batteries showcase the advantages and operational benefits of this approach. The results highlight the potential for variable energy pulses, precise control of thrust impulse bit, and improved performance compared to capacitor-driven systems. Future research directions include optimising pulse duration for enhanced lifetime, plume analysis, and erosion rate investigations. The implementation of VATs with battery-driven discharge presents a promising solution to enhance the performance and reliability of CubeSat propulsion systems while ensuring compliance with space sustainability guidelines.

Data‐Driven Prediction of Li‐Ion Battery and PEM Fuel Cell Performance Degradations for Balanced Optimal Energy Management of Electrified Propulsion Systems

With the increasing pace of commercialization, the proton exchange membrane fuel cell (PEMFC) system‐powered fuel cell electric vehicles/vessels (FCEVs) present a highly efficient, zero tailpipe emission propulsion solution. A battery energy storage system (BESS) is normally integrated with the PEMFC system to improve its performance, energy efficiency and operational life. However, both the PEMFC system and the BESS suffer from relatively short operation life and high replacement costs. Optimal energy management strategies (EMSs) become essential to improve their working conditions, thus extending their working life based on their distinct performance degradation behaviours and achieving the minimum lifecycle costs (LCCs). Extending from the present static modelling approach, this research introduces three new methods for dynamically updating the performance and degradation models of lithium‐ion (Li‐ion) batteries and PEMFCs using real‐time operation data of a fuel cell–battery hybrid electric propulsion system. The combined methods more accurately capture the performance and capability of each specific fuel cell hybrid propulsion system’s BESS and PEMFC system. This enables precise performance tracking, degradation assessment and optimal energy management. A new integrated approach to the hybrid electric propulsion system’s component sizing design optimization and optimal energy management is introduced using these new modelling schemes, minimizing the LCC by balancing the propulsion system performance, fuel economy and the BESS and PEMFC system degradations. These modelling and optimization methods are applied to a medium‐sized vehicle and passenger ferry to produce the optimal fuel cell–battery hybrid propulsion system design and EMS to strike the best balance between fuel efficiency and the PEMFC and BESS operation life.

Life cycle assessment of ammonia/hydrogen-driven marine propulsion

Marine fuels are the main sources of pollution from shipping industry. Hydrogen and ammonia have been suggested to be alternative fuels for shipping as these two fuels do not emit carbon dioxides in the combustion process. This study employed life cycle assessment method to compare the environmental performance of propulsion systems using hydrogen and ammonia as marine fuels to fossil fuels. 2-stroke and 4-stroke engines of tankers using fossil fuels were chosen as base case scenarios. Alternative scenarios using ‘green’ and ‘blue’ hydrogen and ammonia with the support of pilot fuel were then compared to the base case scenarios. While the performance of the coming combustion concepts for hydrogen and ammonia engines are still unknown, preliminary estimations were used in this study. The results showed that hydrogen and ammonia could substantially reduce the global warming potential, compared with the fossil fuel scenarios. Hydrogen and ammonia are also expected to be highly effective in cutting down the particulate matter and the emission of black carbon.

Numerical analysis of the effects of the nozzle shape and outlet area of a waterjet propulsion system on its efficiency

The waterjet propulsion system is a marine propulsion device prevalently used on contemporary high-speed vessels. The performance of a waterjet propulsion system is considerably affected by the nozzle. In this study, the influences of the shape and the outlet area of a waterjet propulsion system on the efficiency of the propulsion system is investigated using the computational fluid dynamics method. A total of 10 different nozzle designs, including cylindrical and conical nozzles with 5 different outlet areas, are analyzed in terms of nozzle efficiency and overall efficiency, and the possible reasons and explanations behind the variations of the nozzle efficiency and the overall efficiency are proposed in this study. The simulated results indicate that the conical nozzles consistently have higher nozzle efficiency than the cylindrical nozzles, and the maximum nozzle efficiency occurs in the conical nozzle with an outlet area of 60% of the inlet duct area. The abrupt change in the flow direction at the transition between the guide vane section and the nozzle, as well as the skin friction on the nozzle wall, are predominant factors affecting the nozzle efficiency. The waterjet propulsion units equipped with conical nozzles generally have higher overall efficiency than their counterparts equipped with cylindrical nozzles, while the maximum overall efficiency occurs in both the cylindrical nozzle with an outlet area of 50% of the inlet duct area and the conical nozzle with an outlet area of 60% of the inlet duct area. The loss of mechanical energy due to viscosity and turbulence in a propulsion unit is the major source of energy loss, while the kinetic energy carried by the exit flow is also a considerable factor affecting the overall efficiencies of the propulsion units equipped with conical nozzles with relatively large outlet areas.