Small aircraft fuel system model analysis

University of Minho School of Engineering Leonardo Beckhauser Mazzitelli Small Aircraft Fuel System Model Analysis october 2023 University of Minho School of Engineering Leonardo Beckhauser Mazzitelli Small Aircraft Fuel System Model Analysis Master’s Dissertation Master’s degree in Mechanical Engineering Area of Specialization in Mechatronic Systems Dissertation supervised by Professor Doctor José Mendes Machado Professor Doctor José Carlos Teixeira october 2023 Copyright and Terms of Use for Third Party Work This dissertation reports on academic work that can be used by third parties as long as the internationally accepted standards and good practices are respected concerning copyright and related rights. This work can thereafter be used under the terms established in the license below. Readers needing authorization conditions not provided for in the indicated licensing should contact the author through the RepositóriUM of the University of Minho. License granted to users of this work: CC BY https://creativecommons.org/licenses/by/4.0/ i Acknowledgements Here, I want to thank all the people involved who somehow contributed to my success in developing this master’s thesis. Firstly to CEiiA, with whom I collaborated by developing this work, which gave me the opportunity to develop my thesis in the field of aeronautics, which has always been my wish. To Paulo Watanabe, my supervisor at the company, who contributed to my knowledge about airplane fuel systems. To Professor José Mendes Machado, my supervisor at the University of Minho, who supported me in the field of system modeling and gave me good guidelines. To Professor José Carlos Fernandes Teixeira, my Co-supervisor at the University of Minho, who invested time and effort in supporting me in the field of fluid mechanics as well as pushing me to keep working hard. To Pedro Vale, my colleague and friend, who always kept me motivated throughout this process. To my family, who was my source of love, energy, and determination, always there for me, offering wise advice. ii Statement of Integrity I hereby declare having conducted this academic work with integrity. I confirm that I have not used plagiarism or any form of undue use of information or falsification of results along the process leading to its elaboration. I further declare that I have fully acknowledged the Code of Ethical Conduct of the University of Minho. University of Minho, Braga, october 2023 Leonardo Beckhauser Mazzitelli iii Abstract An aircraft’s fuel system can be understood as a set of components that act together to store, manage, and deliver fuel to the engines. In this context, the model of such a system tries to represent its behavior through mathematical equations that describe pumps, valves, and tanks and their dynamic interaction, thereby creating a means for performing comprehensive studies. With the model, systems engineers can evaluate the aircraft fuel system architecture and performance from conceptual to more detailed design phases. This master’s thesis focuses on developing a generic twin-engine aircraft fuel system model using MATLAB/Simulink software, which later is used to perform simulations on the system’s behavior under various scenarios and extract valuable insights about its fluid mechanical behavior. Aircraft fuel system modeling requires knowledge about the system’s characteristics, functions, and components. In this work, the system is treated as a fluid-mechanical circuit. Hence, the theoretical introduction presented here connects fundamental concepts of aircraft fuel systems with fluid-mechanical systems modeling, which were the two core areas of this thesis. In addition, brief considerations are given on CS-23, which is the set of regulations to which the aircraft category discussed here is subject. Much of this work was dedicated to building, simulating the model, and choosing the most suitable software. Throughout the thesis, discussions about modeling include the development stages, modeling techniques, and the choice of MATLAB/Simulink over other tools. With the built model, various simulations were performed, demonstrating its capabilities and limitations and providing a reference for aircraft fuel system design. Some results verified the high influence of the nozzle area and pipe lengths on the scavenge jet pump’s flow ratio and the dihedral angle´s influence on minimizing unusable fuel quantities. In addition, studies were performed on the refueling case, where the pressure surge phenomenon and flow imbalance are analyzed, and finally, the crossfeed valve impact during an engine failure scenario is studied. Keywords Aircraft fuel system, System modeling, MATLAB/Simulink iv Resumo Um sistema de combustível de uma aeronave pode ser entendido como um grupo de componentes que atuam em conjunto para armazenar, gerir e fornecer combustível aos motores. Nesse contexto, o modelo de tal sistema tenta representar seu comportamento por equações matemáticas que descrevem bombas, válvulas, tanques, e sua interação dinâmica, assim criando meios para realizar estudos abrangentes. Com o modelo, engenheiros de sistemas podem avaliar a arquitetura e desempenho do sistema desde fases conceptuais até as mais detalhadas de um projeto. Essa tese de mestrado foca no desenvolvimento de um modelo genérico de um sistema de combustível de uma aeronave bimotora utilizando o software MATLAB/Simulink, que mais tarde é usado para simular o sistema em diversos cenários e extrair noções valiosas sobre o seu comportamento fluido-mecânico. A modelação de um sistema de combustível de uma aeronave requer o conhecimento de suas características, funções e componentes. Neste trabalho, o sistema é tratado como um circuito fluido-mecânico, pelo que a introdução teórica deste trabalho conecta conceitos fundamentais do sistema de combustível de aeronaves com a modelação de sistemas fluido-mecânicos, que foram as duas áreas centrais desta tese. Adicionalmente, são apresentadas breves considerações sobre a CS-23, que é o conjunto de regulações as quais a categoria de aeronave aqui discutida está sujeita. Grande parte deste trabalho dedicou-se à construção, simulação do modelo e à escolha do software adequado. Ao longo da tese é discutido o desenvolvimento do modelo, técnicas de modelação e a escolha do MATLAB/Simulink em detrimento de outras ferramentas. Com o modelo, várias simulações foram feitas, demonstrando suas capacidades e limitações e fornecendo uma referência para projetos de sistema de combustível. Alguns resultados verificam a grande influência da área do bico e comprimento das tubagens no rácio de caudais produzido pela bomba injetora e o impacto significativo que o diedro positivo tem na diminuição do combustível inutilizável.Adicionalmente são feitos estudos sobre o reabastecimento, incluindo análises de picos de pressão, desequilíbrio de caudais e por final estuda-se o impacto da válvula de cruzamento num cenário de falha dum motor. Palavras-chave Sistema de cobustível de aeronave, Modelação de sistemas, MATLAB/Simulink v Contents 1 Introduction 1 1.1 Motivation ...................................... 1 1.2 Basic notes about airplanes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 1.3 Historicalbackground................................. 4 1.4 Thesisobjectives ................................... 5 1.5 ReadingGuide .................................... 5 2 Aircraft Fuel System Fundamentals 7 2.1 FuelSystemFunctions ................................ 8 2.1.1 FuelStorage................................. 8 2.1.2 Refueling and Defueling . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 2.1.3 EngineandAPUfeed............................. 12 2.1.4 FuelTransfer................................. 14 2.1.5 FuelJettison................................. 15 2.1.6 OtherFunctions ............................... 16 2.2 Fuelproperties .................................... 16 2.2.1 Vaporpressure................................ 17 2.2.2 FlashandFirePoint ............................. 18 2.2.3 FreezePoint................................. 18 2.2.4 Density ................................... 18 2.2.5 SpecificEnergy................................ 18 2.2.6 JET-AFuel.................................. 19 2.3 CS-23 ........................................ 19 2.4 Chaptersummary................................... 20 3 Aircraft Fuel System Modeling 21 vi List of Symbols Greek Symbols Symbol Description Unit ΓWing dihedral angle º ∆PPressure differential Pa ∆PLPressure loss due to friction Pa ηEfficiency − ρFluid density kg m−3 ωShaft angular velocity rad s−1 Roman Symbols Symbol Description Unit ACross-sectional area m2 CHydraulic capacitance m3Pa−1 CoOrifice coefficient - CDDrag Coefficient - CLLift Coefficient - Cte Constant - DDiameter m xiii DDrag force N HHeight, head or a vertical distance m IHydraulic Inertance Pa s2m−3 LLevel or length m LLift force N MFlow ratio - NPressure ratio - PPressure Pa P0Atmospheric pressure Pa PhHydrostatic pressure Pa QVolumetric flow rate m3s−1 RHydraulic resistance Pa s m−3 SSurface Area m2 TThrust force N UFluid velocity m s−1 VVolume m3 WWeight N ZDistance from a reference in the vertical axis - bHeight, head or a vertical distance m bWingspan m cChord Line length m ePipe elevation m gGravitational acceleration m s−2 xiv mMass kg pPressure Pa r1Nozzle-to-throat ratio - r2Diffuser inlet-to-outlet ratio - tTime s ˙mMass flow rate kg s−1 ~x Airplane longitudinal axis - ~y Airplane lateral axis - ~z Airplane vertical axis - xv Chapter 1 Introduction Due to aircraft systems’ increasing complexity and reliability, it has become almost mandatory for any project to have computational tools to test the systems in a low-cost setup and ensure financial success. In this context, computational tools are software capable of modeling and simulating 1, 2, or 3D models of engineering physical systems such as fluid, electrical, and hydraulic networks. The aircraft fuel system is much more complex and essential than the general public would at first realize, especially in the case of large transport twin-engine aircraft [1]. Even for smaller airplanes, modeling such a system can be precious since simulations provide a low-cost way of testing different configurations and scenarios. Some common problems that models and simulations highly support include system requirements validation, fluid network design, and analysis, including pump location optimization, verification of refuel times, and sizing of the worst-case vent system (in case of emergency descent). 1.1 Motivation Aircraft fuel systems are a critical part of an aircraft since they are responsible for storing, managing, and providing the fuel flow at the correct rate and pressure to ensure proper engine operation. Besides its vital role, modern aircraft fuel systems may include advanced features for the system’s thermal and health management, unusable fuel control, fuel gauging, and others. One big motivation for the modeling and analysis of such a system comes first from the complexity of the aircraft systems and the costs avoided by ensuring most of the errors are corrected in an early phase of the aircraft design. A significant motivation for developing a fuel system dynamic model is the ability to simulate test cases within minutes or seconds instead of making a real case test of an aircraft mission, which could take hours [2]. Additionally, the simulations are an easy way of testing different system configurations and scenarios. Various configurations can be achieved by varying the number and location of tanks and pumps, the wing dihedral angle, and the valve pressure drop coefficient. These variations in the system are not only studied to improve the perfor1 mance of the system itself but also to bring advantages in other areas, such as aircraft mass and balance, avionics, and structural strength. Some examples of simulation scenarios can be the ground refueling process, engine feed function, and the occurrence of an engine failure or valve malfunction. These scenarios can be switched in every simulation setup, and the necessary boundary conditions and parametrization are set automatically. Another reason for using models that can accurately represent a physical system is that the results extracted from the simulations can be used as support for design decision-making and certification processes. Moreover, the system model gives the user the ability to monitor the system’s behavior in detail, having access to individual components if needed, which otherwise, in an actual physical inspection, would not be as straightforward. 1.2 Basic notes about airplanes Since this work deals with airplane’s specific terms and fundamental concepts, it is essential to introduce some basic concepts about airplanes, which later will help interpret the fuel system characteristics and functions. To begin, a reference frame must be specified, and this is the airplane’s body axis system, which is a reference frame attached to the body of the airplane (Figure 1). Figure 1: Airplane body axis system. The airplane’s principle relies on Newton’s second law of motion: The engine accelerates the air backward, accelerating the airplane forward as a reaction called the thrust force. The acceleration gives the airplane the necessary speed to generate lift, which is the upward force that makes the airplane fly. The primary forces acting on the airplane’s body can be shown in the schematic from figure 2. The vectors L,W,T, and Dare the lift, weight, thrust, and drag forces, respectively. The drag is the force caused by friction due to the air resistance to the airplane motion. The lift and drag forces can be calculated through equations 1 and 2: 2 Aerodynamic Center Center of gravity Figure 2: Main forces applied to the airplane body during flight. Take-off Climb Cruise Descent Approach Landing Altitude (m) Direction of travelOrigin Destination 10,000 3,000 TOC TOD Initial climb Figure 3: Flight Phases vs altitude graph. L=1 2CLρU2S(1) D=1 2CDρU2S(2) Both lift and drag forces increase proportionally to the square of the airplane’s velocity U2, so the price to pay for generating a lot of lift is to deal with the significant dissipating drag component. The most critical phase for the airplane’s engines is the take-off, when the aircraft accelerates until it reaches the required speed for the lift force to overcome its weight. The typical flight phases are shown in Figure 3, which indicates that commercial airplanes reach altitudes up to 11,500 meters, where the outside pressure is about 0.2 atm [3]. This brings a lot of operational constraints, mainly because of fuel volatility, which is a critical fuel characteristic to be discussed in chapter two. 3 For the airplane to take off and climb, it needs a lot of acceleration, so these two phases of flight are the most fuel-demanding, while cruise, descent, approach, and landing consume less fuel. This will be important for modeling and simulating the fuel system behavior over time and defining the maximum flow rate output for pumps. 1.3 Historical background The evolution of aircraft fuel systems has been a significant aspect of aviation history, spanning over a century from the Wright Flyer to modern aircraft. At the beginning of the 20th century, the first airplanes, like the Wright Flyer and 14-Bis, used a simple fuel system that relied on gravity to deliver fuel to the engine [4]. Over time, airplane engines became more advanced and reliable, and fuel systems evolved to keep up. During World War II, fuel systems became even more sophisticated, with features like multiple fuel and self-sealing tanks to keep planes safe from enemy fire. As jet engines were introduced in the 1950s, fuel systems became even more complex to accommodate their needs. Today, airplanes are continually evolving to become more fuel-efficient, with materials, aerodynamics, and engine technology advancements. In recent years, the aviation industry has been working on developing alternative fuels to reduce its carbon footprint and become more sustainable. Airplane engines can be powered by various energy sources, which include fossil fuels, electrical batteries, or hydrogen. Recently, the popularity of electrical batteries and hydrogen has dramatically increased since many aviation-related companies are prioritizing sustainability. However, despite the increasing popularity of electrical batteries, their implementation is hindered by their low specific energy. On the other hand, hydrogen has a very high specific energy, but its storage is limited as it needs to be stored at extremely high pressures. Fossil fuels are still favored as an energy source for thrust generation since they have advantages over the newest technologies, and therefore, aircraft fuel systems still have room for development. Although this thesis focuses on fuel, it is essential to stress that electrical batteries and hydrogen are promising alternatives to fossil fuels, and their exploration is necessary to accelerate sustainability achievements. Today’s aircraft fuel systems include modern features such as automatic control of the center of gravity through fuel management, accurate fuel properties sensing, fuel leak detection and prevention, thermal management, fire suppression systems, and in-flight refueling (air refueling). The next generation of fuel system designs is expected to improve sustainability to some degree. Therefore, research on fuel system technologies must be encouraged to shorten the way to a greener world. 4 1.4 Thesis objectives This master’s thesis was developed alongside the Portuguese aerospace company CEiiA (Center of Engineering and Product Development), which established some goals for the conceptual phase of the aircraft design, one of them being the development of a fuel system model. The fuel system model aims to represent the behavior of a generic fuel system of a small aircraft under CS-23 regulations and simulate the system to analyze flow rate, pressure, and tank level variation under different conditions and flight scenarios. To reach this objective, intermediate goals were defined and accomplished, such as: • Having a deep understanding of typical aircraft fuel system characteristics and main components; • Understanding the physics behind the components and their interaction within the system; • Conduct a literature review to find common system modeling practices and the best-suited computational tool; • Studying physical system modeling, understanding software solver methods and capabilities; • developing a flexible and adaptable fuel system model with system parametrization. The end goal of this thesis was to perform simulations with the model created t the model’s capabilities and provide relevant insights into fuel system modeling literature. 1.5 Reading Guide The structure of this master’s thesis is divided into six chapters, which are briefly explained here for organization purposes. Chapter 1 introduces the airplane fuel system, highlights the reasons for aircraft fuel system modeling, and later introduces the reader to some important facts about airplanes. Chapter 2 covers the fundamental knowledge of aircraft fuel systems with a brief discussion about the aviation regulatory authorities and fuel properties. Chapter 3 is also part of the literature review, where concepts about dynamic system modeling are discussed and how this modeling theory can be applied in fluid-mechanical circuits, such as the fuel system, and at the end shows the mathematical modeling of some of the essential components of the fuel system. Chapter 4 starts with the software selection process and later the model development process, when the choices for the final model architecture are made. Chapter 5 presents case studies that reveal 5 the model’s capabilities, simulation results and analysis, and also the model’s limitations. Chapter 6 is the final chapter, where conclusions are presented and future work is discussed. 6 Chapter 2 Aircraft Fuel System Fundamentals In the early days of aviation, the aircraft’s fuel system was basically a fuel tank connected to an engine, which consumed this fuel to generate the necessary thrust for the aircraft to be pushed forward. By accelerating forward, the airplane gains speed, and at some point, the lift force generated from its wing will overcome its weight, thus lifting the aircraft. Over the years, with more passenger demand, engineers developed larger, safer aircraft requiring more reliable fuel storage systems and management. Today’s generic aircraft fuel system comprises fuel tanks, valves, filters, pipes, pumps, and other accessories. These components are interconnected and distributed along the aircraft structure and provide the critical functions of a fuel system. Two main functions are fuel storage and engine feed (both already present in the Wright Flyer aircraft), while fuel transfer, jettison, measurement, and indication are other functions that developed later. The fuel tank is typically located within the wing, as shown in figure 4. Figure 4: Typical fuel system arrangement [1]. 7 Figure 11: Feed system block diagram schematic, neglecting the fuel temperature effect on the pump’s requirements [1]. failure, the feed tanks from this wing would be unused, creating a mass difference between the right and left wings, thus shifting the center of gravity laterally. For this purpose, the crossfeed valve is a crucial component included in most fuel system designs. This valve works as a shutoff valve that connects the feed lines from both sides of the airplane. When set to open, the crossfeed valve enables the feed tanks from both wings to feed a single engine, avoiding a lateral imbalance scenario. 2.1.4 Fuel Transfer In applications where multiple tanks are needed, the fuel transfer system is required. The fuel transfer can happen by the aid of gravity or by transfer pumps. The first case, often called gravity transfer, occurs only in the direction of the wing root, with the aid of the flapper valves, which are uni-directional valves. Between each tank, there is a flapper valve, often called a baffle check valve, which is the device that enables the transfer of fuel inboards when the head difference between two tanks is greater than the cracking pressure of the valve. The other method uses transfer pumps, typically jet pumps, which will be covered later. The transfer function allows the airplane to address operational issues, such as: • Airplane’s center of gravity (CG) shift in-flight; • Wing bending moment alleviation; • Maximum and minimum tank fuel quantities. 14 The position of the center of gravity (CG) is a critical operational consideration for large aircraft due to the significant variation in its position between full and empty fuel tank conditions. The CG must stay within a given range, the so-called static margin, and the fuel transfer system can be helpful by transferring fuel from the outboard tanks to the inboard tanks. The transfer system also manages the wing load alleviation. The airplane’s wing is subjected to a strong bending moment around the ~x axis caused by the lift force. To counteract this, the fuel can be kept in the outboard section of the wing for an extended period, thus reducing the bending moment and, hence, the magnitude of the structural stress cycles. The level of fuel can also be monitored and controlled by the fuel transfer system. This is useful, mainly because the pumps and valves are located at certain heights within the tank, and if the fuel level is too high, there could be a risk of fuel entering the vent lines, while if the fuel level is too low, the boost pumps can experience fuel starvation. As mentioned before, the scavenge jet pump can be used for transfer purposes. One common application of jet pumps in the transfer system is auxiliary tank scavenging. The scavenge jet pump is responsible for extracting unusable quantities of fuel from the corners of the auxiliary tanks and discharging it into the feed tank or collector cell. The motive source for the scavenge pump can come from the engine fuel metering unit (which bypasses the excess fuel delivered to the engine), an engine-driven fuel pump, or even a centrifugal boost pump. 2.1.5 Fuel Jettison The need for fuel jettison is explained by the difference between the Maximum Take Off Weight (MTOW) and Maximum Landing Weight (MLW) of an airplane. The larger the aircraft, the more significant the difference between MTOW and MLW, and the more critical the fuel jettison function becomes. Considering the case of an emergency a few minutes after take-off, the fuel consumed onboard so far is negligible, meaning that the aircraft’s weight is much higher than what it is allowed for landing. To execute an emergency landing, part of the fuel onboard must be dumped, which is done by the fuel jettison system, illustrated by figure 12. The challenge associated with the fuel jettison is providing the pumps and lines with the necessary capacity to dump fuel as quickly as possible since the emergency landing procedure usually happens in a very short time interval. The jettison system faces its worst-case scenario when larger airliners need to execute an emergency landing with almost full fuel tanks. The time it will take to dump all the necessary fuel can take from 30 to 45 minutes. This is, of course, a long time to wait in an emergency scenario, so in most cases, the captain might decide to land the aircraft even with the weight above the MLW, and the risk of landing gear 15 Figure 12: Fuel jettison schematic [1]. collapse or permanent structural deformation must be recognized, as well as potential sub-consequences. 2.1.6 Other Functions As this work primarily concerns fluid mechanics, less attention will be given to the sensing and control aspects. Therefore, fuel quantity gauging, fuel management, and control are briefly discussed. Fuel quantity gauging involves measuring fuel content and delivering mass quantity data. It faces challenges like variable fuel properties, attitude shifts due to maneuvers, and tank structural distortions. This function provides continuous and precise fuel quantity information, essential for flight planning, safety, and maintaining proper weight and balance. It employs sensors and algorithms to adapt to changing conditions and communicates this information to both the flight deck and the refueling station. On the other hand, fuel management encompasses the coordination, control, and monitoring of all fuel system operations. Its complexity varies, from simple systems in small aircraft to intricate, automated setups in large, long-range transports. Fuel management handles tasks like automatic refueling, managing engine-out situations, and cross-feed operations. In larger aircraft, it automates fuel distribution to optimize balance and consumption. It interfaces with various aircraft systems, minimizing crew workload and enhancing operational safety and fuel efficiency across all aircraft types. 2.2 Fuel properties When studying aircraft fuel systems, it is crucial to discuss the physical properties of fuels, as they play a pivotal role in understanding their behavior and safety considerations. Fuel specifications were first established in the 1940s to regulate properties such as composition, volatility, energy, stability, lubricity, 16 and corrosion. Its production comes from crude oil, and after the distillation process, various types of hydrocarbons can be extracted, including kerosene, which is from what most aviation fuel is derived. In this section, some fuel properties that are mentioned throughout the thesis are outlined, and they are fuel vapor pressure, flash point, fire point, and freeze point. 2.2.1 Vapor pressure One major issue in aircraft fuel systems is managing fuel vapor pressure. This property is the pressure at which the fuel begins to vaporize at a given temperature. If the fuel vaporizes within the tank, it can lead to various hazardous situations, including the engine’s inability to receive fuel, as the pumps cannot pump vaporized fuel. The main challenge associated with fuel vapor pressure is preventing the fuel from vaporization when the aircraft reaches high altitudes, where the air pressure is reduced. The temperature is also a critical factor for the fuel vapor pressure. As it increases, the vapor pressure tends to decrease, as shown in figure 13. The graph shows that the JP-4 type fuel is more volatile than the Jet-A type, meaning that for the same temperature, it will resist less vaporization, and this is another reason for implementing closed vent systems in military applications. Figure 13: Vapor pressure versus Temperature [1]. 17 2.2.2 Flash and Fire Point The flash point is the lowest temperature at which the fuel will form sufficient vapor capable of igniting. The Fire point, on the other hand, is the lowest temperature at which the fuel vapors created can sustain a fire even without the ignition source. Within an aircraft fuel system, the temperature of the fuel should remain below these points, ensuring there will be no risk of fuel vapor ignition. 2.2.3 Freeze Point When the airplanes reach high altitudes, the temperature can drop to about -50ºC, and this can be below the freezing point of some of the hydrocarbons contained in the fuel, which is a mixture of them. Although the fuel might not be completely frozen, wax crystals are formed due to some hydrocarbon freezing, which may lead to pump inlet blockage. For this purpose, engine manufacturers may require a minimum inlet pressure for their pumps so these scenarios are avoided. 2.2.4 Density The fuel density is the amount of mass contained in a given amount of volume. Typically, aviation fuel quantities are informed to the pilot in terms of mass because the mass is what is actually converted to energy, not the volume. The volume of the tanks is always the same, but the mass of fuel it can carry depends on the fuel density. One important factor about the density is it affects the pressure created by the fluid in terms of liquid height, referred to as the hydrostatic pressure, which will be discussed later. 2.2.5 Specific Energy The specific energy is probably one of the most critical factors behind choosing fossil fuels over electrical batteries to power the aircraft’s engines. The specific energy is the amount of energy contained in a given amount of mass. For the sake of comparison, aviation fuel (Jet A) has 43.2 [MJ/kg] of specific energy, while a modern electric battery may have around 1.62 [MJ/kg], which is about 4% of the jet fuel’s specific energy [7]. It is worth noting that gas turbine engines typically waste 2-3 thirds of fuel energy as heat, indicating that there is still room for improvement if it is to remain the primary energy source. 18 2.2.6 JET-A Fuel Jet fuel, also known as aviation turbine fuel (ATF) or avtur, is specifically formulated for use in gas turbine engine-powered aircraft. It is colored transparent to light yellow. The most widely used types of jet fuel for commercial aviation are Jet A and Jet A-1, which are manufactured according to an internationally recognized standard. The model presented in this thesis has been simulated using the Jet-A fuel properties, which appear in the table 1 [8]: Table 1: Jet-A and Jet-A1 properties. Jet A-1 Jet A Flash point 38 °C Autoignition temperature 210 °C [9] Freezing point −47 °C −40 °C Density at 15 °C 0.804 kg/L 0.820 kg/L Specific energy 43.15 MJ/kg 43.02 MJ/kg As seen, the most significant difference between Jet-A and Jet-A1 is in the freezing point, with the Jet-A1 being more suitable for long-haul international flights, especially when flying over polar regions. 2.3 CS-23 The CS-23 (Certification Specification 23) is a regulatory set of standards established by EASA for small civil aircraft with a maximum takeoff weight (MTOW) of 5,700 kg or less. To ensure the safety and reliability of aircraft fuel systems, compliance with CS-23 is crucial as it sets rigorous requirements and testing procedures to prevent fuel-related accidents, such as leaks, fires, or engine failures. These rules safeguard passengers, crew, and aircraft by guaranteeing the integrity of fuel systems, making it an essential aspect of aviation safety and certification [10]. One general requirement for the fuel systems under CS-23 regulations is that ”Each fuel system must be constructed and arranged to ensure fuel flow at a rate and pressure established for proper engine and auxiliary power unit functioning under each likely operating condition, including any maneuver for which certification is requested and during which the engine or auxiliary power unit is permitted to be in operation” . The fuel flow is a consequence of the engine demand, which will be specified by the engine’s manufacturer. The fuel flow pressure at the engine fuel system inlet must be at least 5 psi (34.5 kPa) 19 above the fuel vapor pressure to minimize fuel vaporization, even in high altitudes. Another relevant requirement states that ”Each fuel system for a twin-engine airplane must be arranged so that, in at least one system configuration, the failure of any one component will not result in the loss of power of more than one engine or require immediate action by the pilot to prevent the loss of power of more than one engine” . This imposes that the left and right sides of the fuel system should operate independently. Regarding the fuel system components, one key requirement is that the fuel tank must have an expansion space of not less than 2% of its total capacity; this must be considered when setting boundary conditions in the model. Another important requirement when building a fuel system model is that there must be at least one pump for each turbine engine, plus an emergency pump in case of failure. The valves are also subjected to regulations, where one of them says that ”There must be a means to allow appropriate flight crew members to rapidly shut off, in flight, the fuel to each engine individually” . This means the model should include controlled shutoff valve components for the engines. 2.4 Chapter summary As seen in this chapter, the aircraft fuel system is critical for the aircraft’s performance, being subject to strict regulations and rules, in this case, CS-23. The system can be broken into smaller parts or subsystems, each with specific functions, such as feeding the engines, transferring and managing fuel quantities, and refueling/defueling. A common architecture might include several tanks integrated into the wing structure, which are connected by flapper valves that allow fuel to be transferred by gravity. The fuel transfer can be aided by the scavenge jet pumps, which extract fuel from the auxiliary tanks and discharge it into the main feed tank or collector tank, keeping it always full of fuel. The high complexity of the global system creates the need for modeling and simulation, and the next section will introduce the reader to fundamental concepts related to system modeling, focusing on fluid systems. 20 Chapter 3 Aircraft Fuel System Modeling In general, a system is a combination of components that work together to achieve a specific goal. The systems can be seen as isolated parts of the universe which are studied separately from its environment [11]. The system interacts with its environment like the aircraft fuel system interacts with the outside air pressure. In the literature, generally, there are two groups of system variables: the system inputs and outputs. The first group is not dependent on what happens within the system (the outside air temperature in the case of a fuel system), while the second group depends (e.g. outlet fluid pressure generated by a centrifugal boost pump). The system outputs are of primary interest to engineers. The system can be described by states or state variables. For instance, the fuel system can be partially described by one of its tanks’ volume, which is a state variable. Systems can be discrete or dynamic; when state variables continuously change over time, the system is called dynamic. A schematic of a dynamic system with its input and outputs is represented in figure 14. The big advantage of system modeling comes from the easy, time and cost-saving way of acquiring technical data from the system’s behavior. The data obtained by tests made with physical prototypes are, of course, very valuable, but most of the time, it is too costly and time-consuming. Actually, neither the physical experiments nor the simulations are 100% accurate. The physical experiments rely on the sensor’s and setup accuracy, while the computational model simulations rely on the accuracy of mathematical models and equation solvers. These never correspond to reality, but if the mathematical models are accurate enough, they can be very important in any engineering project. Inputs Outputs Dynamic system (parameter, state variables) … … Figure 14: Dynamic system representation. 21 3.1 Fluid system modeling basics The aircraft fuel system is a physical system that integrates fluid, mechanical, thermal, and electric systems. In this thesis, the focus is on the fluid mechanical part of the system. Hence, the model built only uses fluid system model building blocks. The fluid system is often compared to an electric circuit because the basic governing laws are the same. While electric circuits have electrical resistance, capacitance, and inductance, fluid systems have fluid resistance, capacitance, and inertance. Examples of fluid resistance include orifices, valves, nozzles, and pipe friction. The fluid resistor can be any element that dissipates fluid energy when it flows across it. This energy loss is translated into the pressure to drop. The elemental equation that expresses the amount of pressure drop ∆Prequired to force a unit of flow rate Qthrough the resistor is: Q=1 R∆P(3) Where the resistor is characterized by its resistance factor R. The fluid capacitor can be considered an energy storage in the form of liquid with potential energy. The fluid capacitance Ccan be expressed by: C=∆V ∆P(4) where ∆V ∆Pis the volume variation per unit of pressure change, meaning that the more volume the system can store for the same amount of pressure difference, the more capacitance it has. The fluid inertance, on the other hand, is the ability to resist acceleration. Considering a very long pipe, the mass of liquid that is flowing through it has a lot of momentum, and therefore, to stop this flow from coming out of this pipe, a big deceleration is required because the long pipe element introduces high inertance to the system. The inertance Ican be described by the following equation: ∆P=IdQ dt (5) Where ∆Pis the pressure drop required to stop the fluid flow with a flow rate of Qfrom moving through the inertor element. Additionally, fluid systems may also include fluid sources. The fluid source can be a pressure or a flow rate source, for example, and they are frequently used to set boundary conditions in fluid systems. For instance, an ideal flow rate source can generate a constant flow rate regardless of the pressure difference required. In summary, a fluid system can have several components, such as pumps, control valves, and tanks, and each of these components can be modeled as the building blocks presented so far. For complex fluid systems with complex components, the mathematical modeling will 22 look more complex as well. Most of the analyses of fluid systems rely on pressure and flow rate information. Therefore, it is important to understand how they relate to each other. One important equation is the one that defines the pressure of the fluid at a given point as a function of liquid height: Ph=ρgh (6) Where ρis the fluid’s density, gthe gravitational acceleration, and hthe liquid level. Another important fluid mechanics equation is Bernoulli’s equation (7). This equation states that the total pressure energy contained in a fluid particle along a streamline is conserved if no additional work is applied to it. P+ρU2 2+ρgh =Cte (7) The first term in this equation is the fluid’s static pressure, which is the pressure related to the forces acting on the fluid. The second term is the dynamic pressure, which is associated with the fluid’s kinetic energy, and the third term is the hydrostatic pressure, which is related to the fluid’s gravitational potential energy. To understand this principle, a fictitious scenario involving a fuel system can be analyzed (Figure 15). Considering that two fuel tanks are connected through a pipe, where there is a shutoff valve, initially closed. The tanks have different fuel levels (H1and H2), and at some point, the shutoff valve is open. Considering that there is no pressure loss due to friction (∆PL= 0), the Bernoulli’s equation can be applied as follows: P1+ρU2 1 2+ρgH1=P2+ρU2 2 2+ρghp+ ∆PL(8) where P1is equal to the ambient pressure P0and P2is equal to the ambient pressure plus the pressure caused by the mass of liquid above point 2, which can be calculated using equation 6: P2=P0+ρg(H2−hp)(9) By combining equation 9 with 8, a new expression can be written: P0+ρU2 1 2+ρgH1=P0+ρg(H2−hp) + ρU2 2 2+ρgh + ∆PL(10) Considering the tank is very large, the fluid velocity at point 1 can be considered zero. Assuming there is no pressure drop due to friction, the ∆Ploss term can be considered zero. So, some terms canceled out:   P0+  ρU2 1 2+ρgh1=  P0+ρg(H2−hp) + ρU2 2 2+ρghp+  ∆PL(11) 23 the increase in kinetic energy will be compensated by a reduction in pressure (in this case the hydrostatic pressure). Figure 20: Venturi principle schematic. A Jet pump is constructed in a way that there is a reduction in pressure at the suction port because of the reduction in the cross-sectional area. A schematic of a jet pump is shown in figure 21, where it can be seen that the cross-sectional area reduces close to the nozzle, and a suction effect will be created that will induce the fluid to flow inside the throat and exchange momentum with the motive fluid. The discharge flow is the sum of the motive and induced flow. Regarding the geometric parameters of the pump, two important ratios are of great importance when modeling its behavior: the diffuser inlet-to-outlet ratio r1and the nozzle-to-throat ratio r2: r1=Ath Ad (22) r2=An Ath (23) where Ath,Adand Anare the cross-sectional areas of the throat, diffuser outlet, and nozzle, respectively. One of the most important quantities to define is the induced flow, sometimes called secondary flow. This parameter can be modeled with the following equation: q2=Anc √1 + Ken r2 ρ(p2−p0)(24) where Anis the nozzle area, Ken is the hydraulic loss coefficient at the throat entry, p2and p0are the pressures at the suction port and throat inlet, respectively. The factor cis a function of the throat and nozzle cross-sectional areas, expressed by: 30 Throat Induced flow (2) Diffuser Nozzle Discharge flow (3) Mo�ve flow (1) Figure 21: Jet pump schematic. c=1−r2 r2 (25) As seen, the secondary flow rate depends a lot on the geometric parameters of the pump and motive flow rate. Typical values for jet pump efficiency range from 15 to 35% [13], and this efficiency can vary a lot depending on the pressure drop at the discharge port, as will be explained in the model analysis chapter. An important parameter to evaluate the jet pump’s performance is the pressure ratio, described by: N=Pd−Pi Pm−Pd (26) where Pd,Pi, and Pmare the discharge, induced, and motive port pressures, respectively. Besides the pressure ratio, a very important parameter is the flow ratio, which can be calculated by: M=QS Qm (27) where QSand Qmare the suction and motive flow rates. The value of the flow ratio generally ranges from 0.5 to 2.5. For instance, a jet pump with a motive flow rate of 1 liter per minute can induce 2 liters per minute if it has a flow ratio of 2. The efficiency of the jet pump depends both on the flow ratio and the pressure ratio, so with Nand Mthe pump’s efficiency can be calculated: η=NM (28) As will be shown in later sections, the jet pump is an extremely sensitive device in terms of flow and pressure variation of its neighborhood, so its operating range needs to be carefully studied so it can meet its output requirements. 31 3.6 Valves and orifices Valves and orifices are also essential blocks when modeling fluid circuits. Their main function is to add pressure drop to the system, and this can be useful to control the amount of fuel that goes to the engine or interrupt refuel flow when the aircraft fuel tanks reach the desired level. The orifice equation states that the flow through a pipe is proportional to the square root of the pressure drop across the orifice [14]. Q=CoAp(2g∆P)/ρ(29) where Qis the flow rate, Cois the orifice coefficient, Ais the orifice area, gis the gravitational acceleration, ∆Pis the pressure drop across the orifice, and ρis the fluid’s density. The valves are more complex components, which can be of various types, including shutoff valves, check valves, flow control valves, and crossfeed valves. The multi-way directional valves (3 or more ways) are not covered here since they were not used in the fuel system modeling. The shutoff and flow control valves are considered two-way directional valves because they enable the flow from port A to B and vice versa. These valves are modeled as a variable orifice, which can be controlled by a linear spool. The spool actively controls the orifice area, consequently controlling the pressure drop across it, so in the shutoff scenario, the spool position can go from totally open (x = 5 mm) to totally closed (x = 0 mm) for example, while in the flow control scenario, the spool position has to be adjusted to achieve the required flow rate. The check valves are slightly different, as they only enable the fluid to flow in one direction, so they are classified as one-directional valves. In the context of a fuel system, check valves can act as flapper valves, which let the fuel flow from one tank to another by gravity in the direction of the wing root only. Check valves can also be placed before the suction inlet of the jet pumps, preventing the fuel from flowing back to the auxiliary tank. 3.7 Chapter summary This chapter introduced the reader to simple concepts about fluid circuits and fluid mechanics, where some equations were presented, such as Bernoulli’s equation, which was further applied to a simple example of fuel transfer between tanks. Later in the chapter, the fundamentals of dynamic system modeling were presented, including common simulation solver types. Finally, the key components of the fuel system, such as tanks, pumps, and valves, were briefly discussed from a modeling perspective. 32 Chapter 4 Model Development A significant part of this work was dedicated to developing the system model, which became a tool to perform simulations and understand the system from another perspective. This section is divided into three subsections: software selection, model objectives, and model building. Usually, the works related to system modeling and simulation address the validation of the model [15, 16, 17, 18, 19], which supports the reliability and accuracy of the model by comparing the model results with real-world data, or even with theoretical predictions based on analytical equations. In the context of this master’s thesis, the validation process was not strictly necessary. However, this opens space for future work, where the model results presented in Chapter 5 can be compared with the previous works used as reference for this project and add value to the current model. 4.1 Software Selection Extensive research was conducted as part of this thesis to identify a software tool suitable for system modeling of Aircraft fuel systems. Several different tools are available for system modeling, such as OpenFOAM, OpenModelica, and MATLAB/Simulink. Each of these tools has its own unique features. For example, OpenFOAM requires 3D geometry input and uses 3D Computational Fluid Dynamics (CFD) solvers to calculate pressure, temperature, and flow rate, which demands high computational power. On the other hand, Flowmaster is a general-purpose 1D computational fluid dynamics (CFD) code that allows users to choose pre-modeled components and connect them as required without needing 3D geometry input. Conversely, MATLAB is a high-level programming language that usually comes with Simulink as an extension. With its add-on Simscape, users can model systems in a component-based modeling approach involving multiple physical domains and integration capabilities. With so many software tools available, it is easy to become overwhelmed. To begin, a list of potential candidates was created, which included: • MATLAB/Simulink + Simscape; 33 • Simscenter Amesim; • OpenFOAM; • COMSOL Multiphysics; • Easy5; • Flowmaster; • OpenModelica; • Modelon Impact; • AxStream; • Altair Activate. From the list above, only 4 programs were found in the literature, with Flowmaster leading the list with 6 papers mentioning its applicability to aircraft fuel system models [20, 21, 22, 15, 16, 23], followed by MATLAB/Simulink [24, 25, 17, 26, 27], and finally Simcenter Amesim [28, 18, 29] and Easy5 [30, 31, 32] appearing in the same number of published articles 2. The software from the list not mentioned in the literature could also be used as a tool for this project, but one key factor for the software selection for this thesis was the amount of previous work already published. Among the criteria for selecting software, cost, availability of online documentation, and versatility were also relevant. Flowmaster lacks capabilities in modeling other physical domains since it is focused on fluid mechanical circuits, which makes it a less versatile option. MATLAB/Simulink, on the other hand, is already a very well-known software applied in many engineering fields. MATLAB itself is just a programming language, but Simulink can be acquired as an integrated product that works simultaneously with MATLAB. Additionally, Simulink has an add-on called ”Simscape” which brings the versatility of modeling systems in various physical domains, such as hydraulic, electrical, thermal, magnetic, and mechanical. From an industry perspective, although the model presented here explores only the fluid mechanical area, the final objective remains integrating this system with the electrical and mechanical systems linked to it, thus the need for a more versatile option. In this field, MATLAB proved to be an excellent option, being used in almost 30% of the published articles and having extensive online documentation and support available for its tools. 34 Table 2: Number of times the software was identified in the literature. Software Count % MATLAB/Simulink 5 29% Simscenter Amesim 3 18% Flowmaster 6 35% EASY 5 3 18% TOTAL 17 100% 4.2 Model Objectives Until now, the model objectives and requirements were mentioned superficially. In a more detailed way, the model should be built so that the user can quickly identify the fuel’s physical properties, such as fluid flow rate and pressure in different system locations at different time instants. To define the model requirements, it is important to first state where it starts and ends, in other words, the system’s boundaries. Here, the focus will be on the airframe part of the fuel system and not on the engine part, where the highpressure boost pump is located [33]. So, the end of the fluid circuit will be at the border (Airframe-Engine), well represented by the dotted line in figure 22. Figure 22: Fuel control system. 35 4.3 Building the model To start building a model, it is important first to have a reference architecture, including the components needed and the connections between them. Based on the gathered knowledge about reference fuel systems from the same airplane category, some premises for the model were: • Does not include center tank; • Does not include Auxiliary Power Unit (APU); • Includes 2 engines, one in each wing; • Includes at least one centrifugal boost pump for each wing; • Contains 3 tanks in each wing, including a collector cell; • Has a single port for refueling/defueling; • Includes a crossfeed valve; • Uses at least one scavenge jet pump. Besides the premises presented, for a complete representation of the system, it should be capable of simulating the critical functions of a fuel system, as presented in chapter two. These are fuel storage, engine feed, fuel transfer, refueling/defueling, and being able to crossfeed fuel from one wing to the other. The jettison function, although present in many systems, is not considered mandatory in this category of aircraft, so it was left aside. With these assumptions, a schematic of the reference fuel system system was built, serving as a guide for further model development, shown in the figure 23. 4.3.1 Feed System The feed system model is the most basic model of a fuel system, including at least one tank, a booster pump, the feed line, and the engine fuel system inlet, which can be considered as a fluid reservoir. Figure 24 shows one example of the first models built to represent the feed system. The figure shows the tank connected to a centrifugal pump, acting as a booster pump, which will increase the pressure of the fluid to reach the engines. The check valve is included in the feed line to prevent fluid from flowing in the opposite direction. With this initial model, the user is already capable of simulating the feed function and observing the values of pressure and flow rates being delivered to the engine. 36 Engine feed Transfer Refuel/Defuel Scavenge Ejector Pump Booster Pumps Engine S.O.V Refuel S.O.V Defuel valves Crossfeed valve Flapper valves Refueling port Check valve Outboard Tank Inboard Tank Collector Tank Figure 23: Reference fuel system schematic. The centrifugal pumps must be capable of providing enough fuel to the engines in the most critical phase, which is the take-off phase. One way to calculate the required flow rate output is by One constraint in this system is that the centrifugal pump’s speed should not be controlled, meaning it operates with a constant shaft angular velocity during the simulation time. This brings the need to use a flow control valve so the fuel consumption by the engine can vary over time. In the model presented here, the flow can be controlled by a flow control valve or completely interrupted by a shutoff valve. The control over the valves is an input signal, which can be defined by the user as a 2-D array (time and data vectors), where the data represents the valve’s spool position at a given time. This is important to simulate the engine demand, which will differ in each flight phase. Creation of nodes Simscape does not have, by default, a straightforward way to check how fluid properties vary in each location of the system. To overcome this, subsystems were created inside Simscape, which function as the system’s nodes. A node represents the connection between two components, and inside the node, the user can check the properties such as mass/volumetric flow rate and pressure. These subsystems, called nodes, were built using flow rate and pressure sensor components from the Simscape Isothermal Liquid (IL) library (25), and their implementation enables the user to check the fluid properties in any location of the system. The node has an input port A, where is the expected fluid ”inlet,” and a port B, the ”outlet”. If, for some reason, the value of the flow rate on this node is negative, the user can imply that the fluid is flowing 37 Figure 24: Basic feed system. Figure 25: Node structure. 38 Figure 26: Example of how the nodes are used. in the opposite direction. Each node also includes a display block for quick check, which is useful for stationary analysis, because it can hold the values of the parameters calculated in the last time step of the simulation. Additionally, a scope block is included to see the variation of the state variable over time, and finally, a ”To Workspace” block, which sends the time and data vectors in 2-D array form to MATLAB workspace with the name of the node, so this data can be manipulated in a MATLAB script if needed. One example can be when the user wants to calculate the pressure drop value locally, for instance, across a check valve component 26. For this, the node’s information is sent to the workspace, and considering the expected direction of the flow (A→B), the pressure upstream is subtracted from the downstream pressure, thus resulting in the localized pressure drop. 4.3.2 Transfer System With a single-wing feed system correctly built and performing as expected, the transfer system can be integrated into it by adding more tanks, valves, and a scavenge jet pump. The tanks added to this system represent the outboard, inboard, and collector tanks. The new configuration of the system appears in figure 27, where the feed system incorporated another centrifugal pump, which operates in parallel to the one in the previous model. This additional pump must work mainly as a backup pump, as required in most fuel systems. In extreme cases, when the fuel flow to the engine is higher than expected, both booster pumps might operate together. The new model also incorporates a jet pump, which has the function of transferring fuel from the inboard tank to the collector tank, thus keeping it always full as fuel is being consumed by the engine. The booster pumps usually supply more fuel flow rate than the engine requires, resulting in extra fuel. This excess energy can be bypassed at the engine interface and be re-directed to another part of the system and be used as the motive flow for the jet pump. The bypassed flow is directed to the motive port of the jet pump, resulting in a secondary flow coming out of the inboard tank. 39 Figure 34: Complete system. but in the last model, each feed line has a branch that connects it to the refuel gallery, enabling the feed pumps to pump fuel out of the tanks. For this case, the engine shutoff valves must be closed, and the defuel valves shutoff valves open so fuel is directed to the refuel/defuel gallery. The final model appears in figure 34, but in the appendix B, it is shown with higher resolution. 4.3.5 Model limitations At the end of this chapter, it must be noted that the model has some limitations and might not apply to every study regarding the identification of physical properties inside the fuel system. The model encompasses several pre-modeled components, and they are integrated based on architectures observed in the referenced articles. The fuel system model considered the liquid phase, however, since the tanks are also filled with air, the gas phase must be included in the modeling for more accurate simulations, also because the air pressure in the tank ullage will determine how close the fuel is to evaporate. Additionally, the architecture proposed in this thesis uses a jet pump that takes fluid from the feed line as a motive source, and this might not apply to every architecture, causing the study of the jet pump sensitivity to be less relevant. It should be noted that the model’s simulation results were not validated by comparing them to experimental data. As a result, the only measure that can be obtained is from the solver configuration used in Simulink, which was the ode15. 46 4.4 Chapter summary This section covered the methodology of the thesis, from software selection to the final model architecture. MATLAB is a very popular software in various engineering applications, while Simulink is an additional product from Mathworks, which uses a block diagram approach for modeling systems. Inside Simulink, the Simscape add-on can be used to model fluid systems with its extensive library of physical components, making it a suitable option for the task. At the beginning of the model development, a reference architecture was presented, and the first step was to model the feed system; then, the transfer system was integrated, including more tanks, a scavenge jet pump and inclined pipe components to model the dihedral angle effect. Later, adding the crossfeed valve, modeled as a shutoff valve, enabled the connection of the right and left sides of the system. The refueling gallery was integrated into the system as the last modeling stage. 47 Chapter 5 Model Simulations and Analysis The final part of this work was dedicated to using the model capabilities to study some issues that are present in the fuel system. Some of the simulations are presented to demonstrate the model’s capabilities and flexibility, while other studies bring relevant insights for system engineers. In this section, some issues are studied, such as the sensitivity of the jet pump to its geometric parameters and position in the system, the influence of the dihedral angle on the fuel transfer, the imbalance caused by single-sided pressure refueling, the ”water hammer” phenomenon during refueling and finally an engine failure scenario in which the crossfeed valve impact is analyzed. 5.1 Jet Pump Sensitivity Analysis The scavenge jet pump brings a lot of advantages for being a low-cost device with no moving parts and, therefore, extremely reliable. One drawback is that this pump is very sensitive to some parameters, such as the motive flow rate, nozzle area, nozzle-to-throat ratio, throat-to-diffuser ratio, and outlet and inlet pressure. These parameters can significantly affect the efficiency and how much fuel is drawn from the inboard tank and discharged into the collector tank. This is important to verify since the collector tank must always be full. To keep the collector tank always full, the flow rate that goes out needs to be replenished by the inboard tank, and this is accomplished by the scavenge jet pump, as seen from the figure 35. The flow rate measured at the jet pump’s discharge port should be at least equal to the flow rate drawn from the collector tank to feed the engine. If the discharge of the jet pump is greater than the flow going out of the collector tank, the additional fluid can return to the inboard tank through a return line. Mathematically, this condition can be expressed as: Qin ≥Qout (32) In which Qin and Qout are the flow rates in and out of the collector tank. Based on figure 35, the equation 48 Collector tank Inboard tank Engine interface Return line Figure 35: Scavenge jet pump and collector tank flow balance. 32 can be written as: Qd≥Qf+Qm(33) Where Qfis the engine feed flow rate, Qdand Qmare the discharge and motive flow rates of the jet pump, respectively. Considering that the discharge flow rate is the sum of the motive flow with the induced flow Qi, the equation (33) becomes:  Qm+Qi≥Qf+ Qm(34) The motive flow is canceled out of the equation, and the requirement for the jet pump is written as a function of the induced flow: Qi≥Qf(35) To ensure that the induced flow is at least the same as the maximum engine feed flow rate, the jet pump performance needs to be studied. The jet pump’s efficiency is the product of the flow ratio by the pressure ratio, and in the case of the scavenge jet pump, the flow ratio is more important to meet the requirement imposed by equation 35. The flow ratio can be affected by several factors, and in this study, seven of them were analyzed. Some of the analyzed parameters were already presented in earlier chapters, namely the geometric parameters of the pump as nozzle area, nozzle-to-throat ratio, and diffuser inlet-to-outlet ratio. The other variables that 49 Throat Diffuser Nozzle Figure 36: Jet Pump study variables. might impact the flow ratio are the lengths of the pipes in each jet pump port, as identified by L1,L2,L3 in figure 36. In the schematic, each port is connected to a pipe component, and each pipe might have a different length, depending on the position of the jet pump in the system. The different pipe lengths will lead to different pressure drops due to friction, affecting the flow ratio. The last parameter to evaluate is the engine demand, which varies during flight. As discussed earlier, the motive flow is the bypassed portion of the flow that is pumped to the feed lines, and since the engine demand varies, the bypassed flow used to power the jet pump will change as well, which might impact its performance. A sensitivity analysis was conducted to understand how each variable is correlated to the system output, namely, the flow ratio. The approach taken was to generate random values in a given range for each parameter, following a uniform distribution (Table 3). Table 3: Parameter range specification for random values generation. Parameter Min Max Type of distribution Nozzle area [m2] 1.00E-05 1.00E-04 Uniform Ratio1 0.1 0.4 Ratio2 0.1 0.4 L1[m] 0.01 2L2[m] L3[m] Engine Demand [L/min] 0.8 5.3 The number of values generated for each parameter was set to 50, resulting in 50 different simulations, 50 [h] 0 0.5 1 L1 0 0.2 0.4 0.6 0.8 FlowRatio 0 0.5 1 L2 0 0.5 1 L3 0 0.5 1 engine_demand 0 2e-05 4e-05 nozzle_area 0.1 0.15 ratio_1 0.1 0.15 ratio_2 Figure 37: Sensitivity analysis for all 7 variables. producing 50 different flow ratios. Each parameter range was defined based on common values found for smaller aircraft fuel system applications. In the table, the variables ratio_1and ratio_2refer to the nozzle-to-throat ratio and diffuser inletto-outlet ratio, respectively. After simulating, the flow ratio is plotted against each variable, as shown in figure 37, where the first sensitivity analysis results are shown. The variables with higher correlation can be identified by looking at the line created by the linear regression from the plotted results. The first sensitivity analysis demonstrated that the flow ratio ranges between almost zero to about 2 within the results of the simulations performed, indicating an extremely high variability. From the variables plotted, the nozzle is the only one that presents an evident correlation to the output, while the others do not illustrate any specific bias. The correlation values are presented in the tornado plot from figure 38. The tornado plot shows that the jet pump’s nozzle area highly affects the flow ratio. The correlation between these two variables is negative, indicating that smaller nozzle areas must produce higher flow ratios. Considering the optimal value for the nozzle area being 1e-5 (m2), a further step was taken by analyzing the sensitivity of the flow ratio when the nozzle area was fixed. A second sensitivity analysis was performed by removing the variation of the nozzle area and generating 50 more random values for the remaining parameters. The second sensitivity study is shown in figure 39. The figure indicates that when removing the nozzle area, the flow ratio values fluctuate between 0.9 and 2.4, which is still a significant variation. From the plots observed, the linear fit from most of the data does not show any trend, except for ratio_1, which illustrates a strong negative correlation. By computing the statistics from these results, a second tornado plot was created, appearing in figure 40. After analyzing the tornado plot, it is clear that, up to this point, only the geometric parameters have been significant in maximizing the flow ratio. Nevertheless, the dominance of the ratio_1might have 51 ratio 1 Engine demand L1 ratio 2 L3 Flow Ratio -1 -0.5 0 0.5 1 Parameter Influence nozzle area Correlation L2 Figure 38: Tornado plot of the sensitivity analysis for all variables. 0 0.5 1 L1 0.8 1 1.2 1.4 1.6 1.8 2 2.2 2.4 FlowRatio 0 0.5 1 L2 0 0.5 1 L3 0 0.5 1 engine_demand 0.1 0.15 ratio_1 0.1 0.15 ratio_2 Figure 39: Sensitivity analysis excluding the nozzle area. 52 Correlation -1 -0.5 0 0.5 1 L2 ratio 2 engine demand L3 L1 ratio 1 Flow Ratio Parameter Influence Figure 40: Tornado plot of the sensitivity analysis excluding the nozzle area. hidden the influence of the other parameters, motivating another sensitivity analysis to be conducted while excluding the ratio_1variable from the analysis by setting it to constant. The next study considered the nozzle area and the nozzle-to-throat ratio fixed at 1e-5 m2and 0.1, respectively. The remaining parameters used a new set of random values, generated again with the same specifications previously presented. The results are plotted in figure 41: 0 0.5 1 L1 1.8 2 2.2 2.4 2.6 2.8 3 3.2 FlowRatio 0 0.5 1 L2 0 0.5 1 L3 0 0.2 0.4 engine_demand 0.1 0.15 ratio_2 Figure 41: Sensitivity analysis excluding nozzle area and ratio_1. The last sensitivity analysis shows that the flow ratio ranges approximately from 1.9 to 3.1, but most of the values appear between 1.9 and 2.5. The higher values of the flow ratio resulted from the lowest 53 Correlation Engine demand L1 ratio 2 L3 L2 Flow Ratio -1 -0.5 0 0.5 1 Parameter Influence Figure 42: Tornado plot of the sensitivity analysis excluding nozzle area and ratio_1). values of L1,L2, and L3, which agrees with the hypothesis that the pressure drop in the lines affects the amount of flow drawn from the inboard tank. Although this hypothesis may sound obvious, the lengths of the lines have different impacts on the system’s output. The plots show that the length of the pipe at the discharge port L3has a significant negative correlation with the flow ratio, suggesting that when the pump is placed far from the collector tank inlet, it will affect the flow ratio produced. The tornado plot in figure 42 shows the parameter’s influence, and unlike the previous graphs, here, 2 variables show a significant correlation, namely L3and L2. As per the previous analyses, it is evident that a careful study of the placement of the jet pump can greatly benefit in achieving an optimized jet pump performance. In this scenario, where the flow ratio must be high enough to maintain the collector tank at its maximum capacity, the strategy for optimizing its performance should involve placing it as close as possible to the collector tank. The study also indicates that the engine demand does not significantly influence the flow ratio. Therefore, the flow ratio during flight is expected to remain constant regardless of the fuel consumption rate. As a last step, a fourth sensitivity analysis was performed, excluding the higher correlation variable from the previous study, which was the length of the discharge pipe (L3). From the remaining parameters, the parameter L2shows a higher correlation with the output, but since the range of values for the generated flow ratio was only about 0.25, this last analysis is not explored. In summary, the sensitivity analyses conducted on the jet pump system have provided valuable insights into the key factors influencing the flow ratio. It became evident that the nozzle area is the most influential parameter, and the nozzle-to-throat ratio also plays a significant role when determining the flow ratio, both 54 with a negative correlation. Furthermore, the placement of the jet pump relative to the collector tank, specifically the lengths of the discharge and suction pipes (L3and L2), also demonstrates a noteworthy influence on the flow ratio. The results suggest that optimizing jet pump performance involves carefully considering nozzle geometry and the spatial arrangement of the jet pump in relation to the collector tank. Importantly, these findings indicate that engine demand does not significantly impact the flow ratio, providing stability in fuel supply during flight. As the analysis evolves, a comprehensive understanding of these factors will guide the design and operation of jet pump systems for optimal performance and efficiency. 5.2 Dihedral angle effect on fuel transfer Another interesting study can be done with the model, focusing on the transfer system, observing the tank levels and mass variation with the inclusion of a wing dihedral angle. The effect caused by the dihedral angle on the fuel transfer, although not obvious, plays an important role in the design of the fuel system, namely the amount of scavenge jet pumps used. By adding a dihedral angle on the wings, the fuel will transfer inboards faster, which, in turn, creates head differences, and these results are explored here by analyzing fuel tank level variation over the flight phases for different wing dihedral angles. The first case considered that the airplane has no wing dihedral (Γ = 0), the engine demand is an input signal based on normalized data for a common flight mission profile, and the total simulation time is around 2.2 hours. Figure 43 shows the graph for the valve spool position of the flow control valve, placed before the engine fuel system inlet, to simulate the imposed engine throttle. The flight phases are represented by the fuel consumption variation over time, simplified by step functions, where the cruise is the predominant phase during the simulation. Initially, the tank levels are set to complete (98% of its maximum capacity). As expected, the collector tank level (Figure 44) is maintained during the entire flight. This happens because the jet pump is always drawing fuel from the inboard tank and discharging it into the collector tank, thus decreasing the level of the inboard tank over time. As the inboard tank empties, the head difference between the inboard and outboard tank increases, which generates a fuel flow toward the root of the wing. However, a minimum head difference must first be created for the fuel to overcome the flapper valve cracking pressure and be transferred from the outboard to the inboard, which only happens about 0.25 hours. The graph shows that the inboard tank will empty before the outboard tank, creating a significant 55 Figure 50: Valve characteristics. (c) 0 5 10 15 20 25 30 35 40 45 50 0 2 4 Spool (mm) (a) Spool position (Valve closure = 1 sec) 0 5 10 15 20 25 30 35 40 45 50 380 400 OB volume (m) (b) Outboard Volume (Valve closure = 1 sec) 0 5 10 15 20 25 30 35 40 45 50 Time (seconds) 1 1.5 Pressure (bar) Pressure (Valve closure = 1 sec) Figure 51: Simulation with valve closure time of 1 second. (a) Valve spool position, (b) Outboard tank volume, (c) Pressure in the middle of the refuel gallery. 62 has a similar behavior as in the previous simulation. For the simulation with a closure time of 0.25 s, the pressure already shows an oscillating profile, where the pressure signal takes much longer to stabilize at 1 bar. The absolute pressure has reached almost 4 bar, and the minimum value was about 0.5 bar. The results for 0.2 s of closure time show a dramatic increase in the pressure spikes, going up to 9 bar, creating a dangerous situation for the refueling system. The simulations performed demonstrated that the quicker the valve closes, the stronger the shock waves produced, but other parameters, such as the refueling pressure, may also affect the pressure variation. One last case was studied, considered to be the worst case scenario, where the refueling pressure was increased from 2.8 to 4 bar, and the simulation results show that the pressure peaks can reach 12 bars (Figure 53). Besides the high-pressure peaks, the oscillation reaches very low-pressure values, going below the Jet-A fuel vapor pressure, which is about 0.2 bar at 38 ºC. This is significant especially right after the valve closure, where the pressure fell close to zero and this causes the fuel to cavitate. In the current simulation, the cavitation effects are not explored, since the chosen simscape library only supports one-phase liquid simulations, ignoring the formation of fuel vapor and further mixing with the liquid fuel. If this effect was considered, the pressure profile would appear more irregular, due to the vapor bubbles collapsing due to the pressure oscillation, creating additional shock waves. However, this does not invalidate the pressure amplitude results obtained, whose accuracy depends mainly on pipe discretization and solver configurations. Nevertheless, it is important to note that cavitation is a major problem in many fluid systems, especially in an aircraft fuel system where not only the pipe and pumping equipment can be damaged due to cyclic vapor bubbles collapse, but also because the pumps should be able to provide an uninterrupted flow of fuel to the engines, which is not possible if vapor cavities are formed within the tank. 5.5 Crossfeed valve When dealing with twin-engine aircraft, an engine crossfeed system is required so that fuel from the left wing collector tank can feed the right wing engine, and vice versa. This is particularly important during engine failure scenarios when one of the engines is shut down. In an engine failure scenario, fuel from only one engine is being consumed, and the crossfeed system enables the fuel from both right and leftwing tanks to feed one single engine. If this doesn’t happen, the center of gravity of the plane will shift sidewards as fuel is being consumed just by one side, creating an unwanted rolling moment. 63 20 21 22 23 24 25 26 27 28 29 30 Time (seconds) 0 1 2 3 4 5 6 Valve spool position (m) Closure time = 0.25 s Closure time = 0.2 s Closure time = 0.5 s (a) Refueling shutoff valve spool position over time. 20 21 22 23 24 25 26 27 28 29 30 Time (seconds) 0 1 2 3 4 5 6 7 8 9 Absolute pressure (bar) Closure time = 0.25 s Closure time = 0.2 s Closure time = 0.5 s (b) Absolute pressure inside the pipeline varying over time. Figure 52: Comparison of the dynamic behavior of the fluid inside the pipeline for different valve closure times. 64 0 5 10 15 20 25 30 35 40 45 50 Time (seconds) 0 1 2 3 4 5 6 7 8 9 10 Absolute pressure (bar) Worst case scenario (Higher refueling pressure) P(max) =9.72 bar P (min) = 0.109 bar Figure 53: Worst case scenario. 0 20 40 60 80 100 120 140 Time (minutes) 0 2 4 6 Volumetric flow rate (L/min) Engine demand Figure 54: Right engine fuel consumption during flight. The model developed for this thesis is also capable of simulating engine failure scenarios, as well as valve faults. The probability of having two failures like this simultaneously is very low, but for demonstration of the model capabilities, this is studied. The simulation considers an engine failure in the left wing at around 33 minutes. The fuel demand for both engines is an input signal that tries to represent the flight phases’ usual fuel consumption. These phases can be identified from the graph in figure 54, where the take-off phase and initial climb happen around 10 and 20 minutes when the engine is configured for maximum power and from 20 minutes onwards, the plane would fly at cruise speed. At t = 33 minutes, the left engine fails, and since the airplane lost half of its thrust capacity, it is assumed that the remaining engine will be configured for maximum power again to keep flying at a constant altitude, so the fuel consumption rate returns to 6 L/min. Regarding the tank levels, at the moment of failure, the left collector tank level decreases slightly, 65 0 20 40 60 80 100 120 140 Time (minutes) 0.18 0.2 0.22 0.24 0.26 0.28 0.3 0.32 Fuel tank levels (m) (L) Collector tank (L) Inboard tank (L) Outboard tank (R) Collector tank (R) Inboard tank (R) Outboard tank Figure 55: Tank levels variation. Continuous and dashed lines for left and right wing tanks, respectively. 0 20 40 60 80 100 120 140 Time (minutes) 800 900 1000 1100 1200 1300 Fuel tank mass (kg) Left wing fuel mass Right wing fuel mass Figure 56: Total wing fuel mass variation. while the other tanks stay at a constant level until the end of the simulation (Figure 55). This is related to the scavenge jet pump, which, after the failure, is no longer able to pump fuel to the collector tank, given that the motive flow has been interrupted. In normal conditions, the collector tank always receives more fuel than it needs, and the additional fuel returns to the inboard tank through a connection at the top of the collector tank. Now, without this additional fluid from the jet pump, the left collector tank level stays exactly at the height of the return line, which is about 0.3 m. However, the right engine keeps consuming fuel from the right collector tank, then causing the fuel levels of the inboard and outboard tanks to drop. In this situation, the airplane’s center of gravity will shift towards the left side since the wings’ mass difference increases over time, as shown in figure 56. The main purpose of this simulation is to demonstrate the model’s flexibility in terms of simulation, despite the unlikely scenario of an engine and crossfeed valve failure. Nevertheless, larger commercial aircraft that need approval from the regulatory authority for ETOPS (Extended Twin OPerationS) must include two redundant crossfeed valves in the system design, to minimize the probability of two combined failures, as this case illustrated. 66 0 20 40 60 80 100 120 140 Time (minutes) 0.18 0.2 0.22 0.24 0.26 0.28 0.3 0.32 Fuel tank levels (m) (L) Collector tank (L) Inboard tank (L) Outboard tank (R) Collector tank (R) Inboard tank (R) Outboard tank Figure 57: Tank levels variation. Continuous and dashed lines for left and right wing tanks, respectively. 0 20 40 60 80 100 120 140 Time (minutes) 800 900 1000 1100 1200 1300 Fuel tank mass (kg) Left wing fuel mass Right wing fuel mass Figure 58: Total wing fuel mass variation. A second case is studied with this model, considering a normal crossfeed valve operation in case of an engine failure. For this simulation, the boundary conditions and input signals are maintained from the previous study, except for the crossfeed valve control signal, which opens the valve seconds after the engine failure was detected. The time of failure was maintained at 33 min, and figure 57 shows the tank levels variation. The graph shows that at the time of failure, the left collector tank falls and rapidly recovers since the motive flow for the left jet pump was interrupted for some seconds. By analyzing the mass variation over time, in figure 58, it can be seen that if the crossfeed opens seconds after the failure, the wing’s mass from both sides will remain balanced. Although the flow rates going out from both collector tanks are the same, this model can still be useful for designing the crossfeed valve and connections between feed lines since fuel flow is not always split equally, as demonstrated in the refueling imbalance case. 67 5.6 Chapter summary A critical part of this thesis relies on the model analysis, where various features of the model are explored with simulations. This section presented some of the model capabilities, exploring the jet pump performance, dihedral angle effect on fuel transfer, refuel flow imbalance, water hammer phenomenon, and crossfeed valve impact on failure scenarios. The scavenge jet pump has a highly non-linear behavior, varying significantly with its geometric parameters and the system’s boundary conditions. The sensitivity analysis performed demonstrated that the nozzle area, length of the discharge pipe, and nozzle-to-throat area ratio are extremely influential for its performance in this type of application. Additionally, the dihedral angle of the wings creates an additional head to the outboard tanks which helps to transfer fuel inboards, eliminating the need for another scavenge jet pump at the outboard tanks. Moreover, the refueling process was simulated and a flow imbalance was identified due to pressure differences in the flow distribution. The transient behavior of the flow at the end of the refueling process was also studied, considering different valve closure times and identifying the best and worst-case scenarios. Lastly, the simulated engine failure highlights the importance of the crossfeed valve in the system’s architecture, indicating the tank’s level and mass variation over time post-failure. The results presented are a way of showing the capabilities of the model built and bringing relevant insights on fuel system behavior in terms of fuel tank levels, mass, fuel flow rate, and pressure distribution along the system. 68 Chapter 6 Conclusions and Future Works 6.1 Conclusions This work aimed to develop a small aircraft fuel system generic model, which later should serve as a tool to develop comprehensive studies on the fluid-mechanical behavior of the system by analyzing flow rate and pressure variations in different locations under various conditions. The fuel system is complex and essential, comprising several non-linear aspects, and the model of such a system has shown itself to be crucial for understanding the system’s response to certain inputs and flight scenarios, as well as identifying potential problems with the used configuration or improvements to be made. There is an extensive market for computational tools capable of modeling and simulating aircraft fuel systems, so the research on software and previous works turned out to be critical for the quality of the model. A general architecture for the fuel system was proposed, which aimed to include an additional degree of complexity compared to previous works in the field, so the wing dihedral and a scavenge jet pump were added to the model, creating more possibilities in terms of simulation. The simulations performed were related to the engine feed and refueling processes, which included components and overall system performance. One of the studies was related to the jet pump, which demonstrated that the induced flow rate created depends mostly on the pump’s geometric parameters but is significantly affected by the discharge and suction line lengths, emphasizing the importance of optimizing the jet pump location in the system. The engine feed process was also studied in combination with the fuel storage and transfer functions, simulating the impact of the dihedral angle on fuel transfer, highlighting that an additional scavenge jet pump may not be needed for positive wing dihedral. Still related to the engine feed process, an engine failure was imposed on the system, and the crossfeed valve impact was observed, showing its critical role in the fuel system. Additionally, the refueling process was simulated, revealing important issues in the design, such as the flow imbalance caused by the different pressure drops along the different flow paths caused by the single-sided pressure refueling approach. The design solutions for this case were mentioned, and 69 the necessary pressure drop was calculated to balance the flow distribution within the refueling gallery. A last study regarding the refueling process was the pressure surge in the pipeline at the end of the refueling process, verifying pressure peaks of almost 10 bar for valve closure times of 0.1 seconds. The simulations performed have shown some of the model and software capabilities and limitations and how this can be explored for early aircraft fuel system design assessment. The studies performed with the model encouraged the development of a scientific article that was accepted for publication in the journal ” Technologia i Automatyzacja Montażu ”. The article entitled ”A Simulation Model for Small Aircraft Fuel System Model Analysis” includes a more focused analysis of two of the studies, namely the dihedral angle effect on fuel transfer and the jet pump sensitivity analysis [35]. Nonetheless, it is imperative to highlight some of the model limitations, such as the absence of the gas phase within the model, which in reality would correspond to the tank ullage and small quantities of fuel vapor, meaning that the fuel venting system and cavitation phenomenon cannot be simulated. Additionally, the model was built using the isothermal liquid library from Simscape, so the temperature variable is neglected in every simulation, making the model most suited for analyzing problems where only flow rate and pressure variations are significant. Additionally, the tanks are considered open to the atmosphere, indicating that the inner pressure will always equal 1 atm. This implies that the fuel volume can reach higher values than what is specified as its maximum capacity. Finally, it is important to state that the model was not validated carefully comparing it to experimental data, and its simulation results were only visually compared to those in the existing scientific publications. Based on the lessons learned from this work, the main takeaways are that an aircraft’s fuel system is highly complex and diverse, and its development and certification require proper modeling and simulation. The fuel system’s functions are often critical, and it needs to be well integrated and designed to ensure the aircraft functions properly as a whole. The best approach to modeling a system is to keep it simple while generating results that are as close to reality as possible, requiring little computational power. Achieving this requires a thorough understanding of the system in question, its governing laws, and extensive knowledge of modeling techniques. 6.2 Future Works Several promising avenues for future work can significantly enhance the modeling and simulation of aircraft fuel systems. In the current thesis, the modeling primarily focused on the simulation of liquid fuel, with the cavitation process omitted from the water hammer analysis. Future research could create a more 70 comprehensive model by incorporating both liquid and gas phases within the same system. This extension allows for a more accurate representation of water hammer effects. It also opens the door to modeling complex interactions, such as those in vent lines, where the behavior of fuel and air can be jointly simulated. Moreover, the quest for accuracy can lead to a crucial phase of model validation using real-world data. Conducting experiments and gathering data from operational aircraft fuel systems will enable researchers to refine and validate the model, ensuring that it faithfully replicates the behavior of actual systems under varying conditions. Furthermore, integrating the fuel system model with automation systems, controllers, and avionics systems represents a compelling area for future research. By merging the fuel system model with the broader aircraft control and monitoring infrastructure, it becomes possible to develop advanced control strategies, predictive maintenance algorithms, and safety protocols to enhance aircraft fuel systems’ overall performance and reliability. These future research endeavors offer opportunities to improve the precision and comprehensiveness of aircraft fuel system modeling and potentially advance the aviation industry’s technology, safety, and environmental sustainability to new heights. 71 83 shaft_speed_1=0; %[rpm] 84 shaft_speed_2=0; %[rpm] --> (backup pump) 85 86 87 %Scavenge Ejector Pump 88 nozzle_area = 7e-5; %[m^2] 89 ratio1=0.25; 90 ratio2=0.25; 91 92 93 %% DIHEDRAL ANGLE 94 95 dihedral = 2; %[degree] 96 tank_L=3; %[m] --> considering the half wingspan divided into 3 equal parts with same length 97 transfer_pipe_elevation = -tank_L*sin(deg2rad(dihedral)); %( minus) because the elevation from A to B is negative 98 99 if dihedral == 0 100 transfer_pipe_length=0.1047; 101 else 102 transfer_pipe_length=-transfer_pipe_elevation; 103 end 104 105 %the length of the pipe needs to be as short as possible to avoid ficticious high pressure drops 106 107 %% TANK PARAMETERS 108 %Tank volume coefficient (1 is full , 0 is empty) 109 110 if scenario ==2 %refueling scenario 111 tank_k=0; % percentage of total capacity 112 else 113 tank_k=0.98; 114 end 115 116 %flapper valve height [m] 117 118 if scenario ==1 %engine feed 119 fp_height = 0.01; 120 end 121 122 if scenario ==2 %refueling 123 fp_height =0.01; 124 end 125 126 sec_flow_port_height = 0.01; %[m] -> port where the jet pump takes fluid from the inboard tank 78 127 128 %tank height vectors 129 outboard_heights = [fp_height , .1]; 130 inboard_heights = [sec_flow_port_height .3 fp_height fp_height ]; 131 collector_heights= [0.3 0.1 fp_height 0.01]; 132 133 %% VALVES/ORIFICES 134 135 %PRESSURE COMPENSATED 3-WAY FLOW CONTROL VALVE (P_C_valve) 136 137 pc_min_spool_position=0; %[mm] 138 pc_spool_range =10; %[mm] 139 140 pc_orifice_A=5e-5; %[m^2] (controls the flow to the engines) 141 pc_orifice_pressure=26; %[psi] 142 pc_regulation_range=2; %[psi] 143 pc_valve_area=1e-3; %[m^2] 144 145 %normal check valves 146 cv_crack_p=1; %[psi] 147 cv_max_pressure_diff =1.1* cv_crack_p; %[psi] 148 cv_A= 1e-3; %[m^2] 149 150 %flapper valve 151 fp_crack_p =0.01; %[psi] 152 fp_max_pressure_diff =1.1* fp_crack_p; %[psi] 153 fp_valve_A=1e-2; %[m^2] 154 155 %JET PUMP suction check valve (scv) 156 scv_crack_pressure =800*9.81*0.3; %[Pa] --> full tank provides the cracking pressure 157 scv_max_pressure_diff=scv_crack_pressure+10; %[Pa] 158 scv_A=1e-2; %[m^2] 159 160 %JET PUMP discharge check valve (dcv) 161 dcv_crack_pressure =1; %[psi] 162 dcv_max_pressure_diff=dcv_crack_pressure*1.1; %[psi] 163 dcv_A=1e-2; %[m^2] 164 165 %collector return line Check valve (rcv) 166 rcv_crack_p=800*9.8*0.0015; %[Pa] 167 rcv_max_pressure_diff=800*9.8*0.0015+1; %[Pa] 168 rcv_A=1e-2; %[m^2] 169 170 %SHUTOFF VALVES general variable 171 spool_position_range=5; %[mm] 172 max_spool_position =5; %[mm] 79 173 SOV_orifice_A=1e-3; %[m^2] 174 175 %Refuel SOV 176 L_refuel_SOV_A = 1e-3; %[m^2] --> refuel SOV orifice area 177 R_refuel_SOV_A = 1e-3; %[m^2] --> refuel SOV orifice area 178 179 %Xfeed valve 180 xfeed_valve_A=1e-2; %[m^2] --> 1e-3 will cause flow imbalance ( to be adjusted ...) 181 182 %refuel imbalance flow restriction optimization 183 delta_p = 0.7; %[psi] 184 185 %% fuel consumption varying over time [consumption x flight phase] 186 187 steady = 1; %(1 for steady fuel consumption , 0 to define a varying engine consumption) 188 189 if steady == 1 190 Engine_demand = timeseries(double (1*[1.3 1.3] ') , [Ts*0 Ts *1]'); 191 elseif steady==0 192 Engine_demand = timeseries(double (1*[0 0 1.3 1.3 0 0]'), [ Ts*0 Ts*0.1 Ts*0.1+30 Ts*0.9 Ts *0.9+30 Ts*1]'); 193 else 194 fprintf('Error defining timeseries object') 195 end 196 197 %refuel flow rate function (constant) 198 refuel_q = timetable(seconds([0 Ts]'), 1*[40 40]'); 199 200 201 %% CORRECTION FUNCTIONS --> When dihedral angle =! 0 202 203 %{ 204 data = readcell('correction_functions.xlsx '); 205 206 %--> this code calculates the error between expected value and the 207 simulated value for tank levels with non zero wing dihedral 208 209 %Extract the time vector (tout) and data vectors (g1, g2, g3) from the cell array 210 211 time = cell2mat (data (2:end , 1)); 212 g1=cell2mat(data (2:end , 2)); 213 g2=cell2mat(data (2:end , 3)); 80 214 g3=cell2mat(data (2:end , 4)); 215 216 g1=timeseries(g1, time); %collector 217 g2=timeseries(g2, time); %inboard 218 g3=timeseries(g3, time); %outboard 219 %} 220 221 %% END OF SCRIPT A.2 Model output function 1clc 2 3%% OUTPUT VARIABLES 4%------------------------------------------------- 5%----------- This script was built improve the workflow , by calculating and printing the interest variables in the output window. 6 7 8%% JET PUMPS MEASURED VARIABLES 9 10 %flow rates 11 jet_q_d=squeeze(out.node18_q);%jet discharge 12 jet_q_d =3.79* jet_q_d(end); 13 jet_q_i=squeeze(out.node16_q); %jet induced 14 jet_q_i =3.79* jet_q_i(end); 15 jet_q_m=squeeze(out.node19_q); %jet motive 16 jet_q_m =3.79* jet_q_m(end); %liters per minute 17 %pressures 18 jet_p_m=squeeze(out.node19_p); 19 jet_p_m=jet_p_m(end); 20 jet_p_i=squeeze(out.node16_p); 21 jet_p_i=jet_p_i(end); 22 jet_p_d=squeeze(out.node18_p); 23 jet_p_d=jet_p_d(end); 24 25 %TO ENGINE 26 delivered_q=out.node2_q(end); %engine feed flow rate 27 extra_q=out.node10_q(end); %extra feed line flow rate 28 29 %pressures 30 delivered_p=out.node6_p(end); %engine inlet pressure 31 32 %Gravity flows 33 inb2col_q=out.node23_q(end); %flow from inboard to collector though flapper valve 81 34 out2inb_q=out.node20_q(end); %flow from outboard to inboard though flapper valve 35 36 %% TANKS 37 38 %INBOARD TANK 39 back_to_inboard_q=out.node17_q(end); %remaining flow back to inboard tank 40 41 %COLLECTOR TANK 42 col_q_in = jet_q_d + inb2col_q; %flow in the collector tank 43 col_q_out=out.node7_q(end); %flow out of the collector tank 44 45 %pressures 46 47 48 %% PRESSURE DROPS (PUMPS , PIPES) 49 50 pumps pressure gain 51 boost_pump1_p_gain = out.node4_p(end)-out.node1_p(end); 52 boost_pump2_p_gain = out.node5_p(end)-out.node3_p(end); 53 jet_pump_p_gain_23 = out.node18_p(end)-out.node16_p(end); 54 jet_pump_p_gain_13 = out.node18_p(end)-out.node19_p(end); 55 56 pipes pressure drop 57 feed_line_delta_p = (out.node9_p(end)-out.node6_p(end)); 58 bypass_line_delta_p = (out.node10_p(end)-out.node13_p(end)); 59 bypass_inboard_line_delta_p=(out.node27_p(end)-out.node17_p(end )); 60 motive_line_delta_p=(out.node26_p(end)-out.node19_p(end)); 61 scav_line_delta_p=out.node11_p(end)-out.node15_p(end); 62 total_pipes_delta_p=(feed_line_delta_p+bypass_line_delta_p+ bypass_inboard_line_delta_p+motive_line_delta_p+ scav_line_delta_p); 63 64 transfer pipes pressure drop 65 out_inb_pipe_delta_p = out.node22_p(end)-out.node20_p(end); 66 inb_col_pipe_delta_p = out.node8_p(end)-out.node23_p(end); 67 68 %% VALVES 69 70 check valves pressure drops 71 boost_pump1_CV_delta_p=out.node4_p(end)-out.node29_p(end); 72 boost_pump2_CV_delta_p=out.node5_p(end)-out.node28_p(end); 73 bypass_CV_delta_p=out.node13_p(end)-out.node14_p(end); 74 jet_pump_CV_delta_p=out.node18_p(end)-out.node11_p(end); 75 76 %% JET PUMP PARAMETERS 82 77 78 %JET PUMP CALCULATIONS 79 N=(jet_p_d -jet_p_i)./(jet_p_m -jet_p_d); %pressure ratio 80 eta=(jet_q_i./jet_q_m).*N; %jet pump efficiency 81 82 83 %% PRINT RESULTS 84 %---------------------------------------- 85 86 87 %Delivered flow rate and pressure 88 fprintf('\n---------STATIONARY ANALYSIS: Delivered flow rate [ gpm] and pressure [psi]: \n\n') 89 90 if scenario ==1 91 fprintf('\n Case number = %0.0f (ENGINE FEED)\n\n', scenario); 92 elseif scenario ==2 93 fprintf('\n Case number = %0.0f (REFUELING)\n\n', scenario) ; 94 end 95 96 97 fprintf('Delivered flow rate: %0.2f\n', delivered_q); 98 fprintf('Delivered pressure: %0.2f\n', delivered_p); 99 100 %Tank flow rates (in and out) 101 fprintf('\n--------- Tank flow rates (in and out) [gpm]: \n\n') ; 102 fprintf('Flow out of the collector: %0.2f\n', col_q_out); 103 104 %Pressure gain or drop (Pumps) 105 fprintf('\n\n--------- Pressure gain/drop (Pumps): [psi] \n\n') 106 fprintf('Boost pump 1 pressure gain: %0.2f \n', boost_pump1_p_gain); 107 %fprintf('Boost pump 2 pressure gain: %0.2f \n', boost_pump2_p_gain); 108 fprintf('jet pump pressure gain (2-3): %0.2f\n', jet_pump_p_gain_23); %23 -> from induced port (2) to discharge (3) port 109 110 fprintf('\njet pump pressure drop (1-3) due to orifice: %0.2f\n ', -jet_pump_p_gain_13); %13 -> from motive port (1) to discharge (3) port 111 112 %Pressure drops (PIPES) 113 fprintf('\n\n--------- Pressure drops (PIPES): [psi] \n\n') 114 fprintf('Pressure drop (feed line): %0.2f\n', feed_line_delta_p ); 83 115 fprintf('Pressure drop (bypass line): %0.2f\n', bypass_line_delta_p); 116 fprintf('Pressure drop (bypass line back to inboard): %0.2f\n', bypass_inboard_line_delta_p); 117 fprintf('Pressure drop (motive line): %0.2f\n', motive_line_delta_p); 118 fprintf('Pressure drop (scavenge transfer line): %0.2f\n', scav_line_delta_p); 119 fprintf('\nTotal pressure drop in the pipes: %0.2f\n', total_pipes_delta_p); 120 121 %pressure drop (TRANSFER LINES) 122 fprintf('\n\n--------- Pressure drops (TRASNFER PIPES): [psi] \ n\n') 123 fprintf('Pressure drop (Outboard to Inboard): %0.2f\n', out_inb_pipe_delta_p); 124 fprintf('Pressure drop (Inboard to Collector): %0.2f\n', inb_col_pipe_delta_p); 125 fprintf('\n These are pressure gains instead (elevation increases the pressure at the outlet.\n') 126 127 %Pressure drops (CHECK VALVES) 128 fprintf('\n\n--------- Pressure drops (CHECK VALVES): [psi] \n\ n') 129 fprintf('Pressure drop (boost pump 1 check valve): %0.2f\n', boost_pump1_CV_delta_p); 130 fprintf('Pressure drop (boost pump 2 check valve): %0.2f\n', boost_pump1_CV_delta_p); 131 fprintf('Pressure drop (bypass line check valve): %0.2f\n', bypass_CV_delta_p); 132 fprintf('Pressure drop (Jet pump outlet check valve): %0.2f\n', jet_pump_CV_delta_p); 133 134 %Jet Pump INFO 135 fprintf('\n\n------ Jet pump (RESULTS) ------\n\n') 136 137 fprintf('Motive flow [lpm]: %0.2f \n', jet_q_m); 138 fprintf('Induced flow [lpm]: %0.2f \n', jet_q_i); 139 fprintf('Discharge flow [lpm]: %0.2f \n', jet_q_d); 140 141 fprintf('\nPressure ratio: %0.2f \n', N); 142 fprintf('Efficiency: %0.2f \n', eta); 143 144 %Collector tank info 145 fprintf('\n\n--------- Collector tank info \n\n') 146 147 148 %Total pressure drops 84 149 fprintf('\n\n------------ Total pressure drops [psi] \n\n') 150 fprintf('Pressure drop - extra flow until collector tank inlet: %0.2f \n', out.node10_p(end)-out.node15_p(end)+ jet_pump_p_gain_13); 151 152 153 %% CORRECTION FUNCTION --> for dihedral angle =! 0 154 155 %this block calculates the real tank levels based on the error calculated for non zero dihedral simulations. 156 157 %{ 158 f1_t = squeeze(out.collector1_level); %collector tank 1 159 g1_t =0.3* tank_k -f1_t; 160 f2_t = squeeze(out.inboard1_level); %inboard tank 1 161 g2_t =0.3* tank_k -f2_t; 162 f3_t = squeeze(out.outboard1_level); %outboard tank 1 163 g3_t =0.3* tank_k -f3_t; 164 165 %Exporting Correction Functions to Excel --> g(t) 166 167 writecell ([{'Time ', 'g1(t)', 'g2(t)', 'g3(t) '}; num2cell([out. tout , g1_t , g2_t , g3_t])], 'correction_functions.xlsx '); 168 %} 85 Appendix B Fuel System Model information Figure 59: Fuel system model building blocks from Simscape Isothermal Liquid Library 86 Figure 60: Fuel System Complete Model