# Numerical Study on Pipeline Pressure Surge of the Large Aircraft Fuel System

Authors: Yi Tu; Xuanren Chen; Liang Yin; Qiuyun Zheng; Yu Zeng
Journal: Shock and Vibration
 (2022)

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## Abstract

The sudden closure of the refueling valve during the refueling process will cause the water hammer phenomenon in the pipeline of the large aircraft fuel system and produce pressure waves propagating along the pipeline. In serious cases, it will cause severe damage to the pipeline. The pressure surge in the pipeline can be affected by many design factors. In this study, the numerical modeling method of the large aircraft fuel system is studied using the Flowmaster program, and the accuracy of steady and transient state analysis of the simulation method is verified by experimental data. Based on this numerical method, a complete system-level simulation model of the large aircraft fuel system was established. Using this model, the effects of valve closure speed, diameter of the refueling main pipe, and refueling volume flow rate on pipeline pressure surge during the refueling process are investigated. The results indicate that all three factors have a significant impact on the pipeline pressure surge of the fuel system. The effect of the valve closing speed and the pipe diameter on the pressure surge of the pipeline is nonlinear and gradually weakened with the decrease of valve speed and the increase of pipe diameter, while the effect of refueling volume flow rate on the pipeline pressure surge is approximately linear.


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## Body

## 1. Introduction

Large aircraft typically use multiple engines, and the design of the fuel system must ensure that the system can reliably provide fuel to the engines under various possible working conditions. To make full use of the aircraft structural space, the fuel feed system of large aircraft is equipped with multiple fuel tanks, which are distributed in different locations of the aircraft wing. The fuel tanks are connected to engines, refueling ports, and other tanks through intricate piping system components to ensure the independent fuel feeding capacity of each fuel tank for all engines. The composition and regulation of the fuel system are becoming increasingly complex. As a complex fluid pipeline system, the operation of the fuel system of large aircraft is accompanied by rapid valve closure, pump failure, or unexpected pipeline damage, which will lead to a dramatic change of the fluid velocity inside the pipeline and cause a pressure wave to propagate along the pipeline. This water hammer will affect the pipe wall and cause vibration and noise in the pipeline. In serious cases, it can damage pipelines and valves and affect aircraft safety. The rapid reduction of pressure will also cause cavitation in the system and affect the service life of fuel system pipes and valves. The instantaneous surge in pipeline pressure caused by the rapid shutdown of the refueling valve in the pressure refueling process is the most serious. For the design of the fuel system, these influencing factors should be analyzed and evaluated according to the requirements of the operating conditions of the system.The fuel system of commercial aircraft is a complex pipe network system involving numerous components such as pipes, pumps, valves, fuel tanks, and control devices. Various operating cases need to be analyzed and evaluated in the process of system design, including pressure refueling, engine feeding, emergency fuel jettison, fault state analysis, and so on. Most of the operating conditions of the aircraft fuel system have long duration times and involve a relatively large number of operating components, which put forward high requirements for the efficiency of the numerical analysis platform. Commonly used fuel system software simulation platforms include Flowmaster [1, 2], EASY5 [3], AMESim [4,5], and MATLAB/Simulink [6, 7]. Flowmaster possesses superior convergence properties in complex system simulation analysis because of its linearization numerical solution method [8]. Li et al. established the simulation model of aircraft fuel system based on Flowmaster and conducted transient and steady-state analysis of the aircraft fuel system [9]. Kang et al. investigated the temperature rise of the engine feeding system in constant and variable fuel pump speed using the Flowmaster program. Their results demonstrated that the accuracy of the simulation model was primarily affected by the performance curve of the pump component [10]. Yi et al. conducted the steady state and transient analysis of the scramjet fuel supply system using Flowmaster software and analyzed the transient response caused by the sudden closing of the control valve [11]. Su Qian simulated and analyzed the aircraft integrated fuel heat management system with Flowmaster platform [12]. Jiang et al. established a simulation platform to analyze the intermittent fault in the aircraft fuel system based on Flowmaster program [13]. Ng and Tan analyzed the fuel system dynamical behavior during aircraft in-flight refueling using Flowmaster software [14].Flowmaster is also widely used in the analysis and research of pressure shock waves in pipeline systems. Zuo et al. conducted a comparative study of the single-phase water hammer phenomenon in the pump pipeline system between Flowmaster and their developed program. Their results demonstrate that these two methods have good consistency in the analysis of water hammer effect [15]. Liu et al. simulated the water hammer phenomenon occurring in the air conditioning chilled water system of high-rise buildings using Flowmaster program and used the simulation platform to optimize the design and weaken the water hammer effect of the system [16]. Feng et al. investigated the flow fluctuation and water hammer effect of the auxiliary feedwater system of Daya Bay Second-generation Nuclear Power Station using Flowmaster software for the valve closure operation process [17]. Zhou et al. developed a multiscale modeling method of shock wave propagation caused by coal and gas outbursts using numerical simulations in 1D and 3D. Their research results show the suitability and fidelity of Flowmaster one-dimensional simulation in system-level pressure shock wave transient analysis [18, 19].It can be seen from the previous literature review that the Flowmaster program has been used in the analysis of the aircraft fuel system and water hammer phenomenon simulation of the fluid system. However, most of the existing modeling and simulation methods for aircraft fuel systems are based on the simplification of the system. The efficiency and convergence are achieved by reducing the number of system components. It is not consummate enough for engineers to carry out comprehensive system design and optimization. This study mainly studies the efficient and accurate numerical analysis method of the large aircraft fuel system and investigates the influence factors such as closure speed of the refueling valve, diameter of the refueling pipeline, and refueling speed on the pipeline surge pressure using the established system simulation model. The method and research conclusion of this study can provide a reference of large aircraft fuel system design, which can shorten the product development time and test times, and reduce the production cost [20].


## 2. System Introduction

Figure1 shows a schedule of the A320 fuel system. There are five tanks in the aircraft, including one center tank, two inner tanks, and two outer tanks. The fuel system provides functions that supply fuel in the correct quantities to the fuel tanks during refueling and supplying fuel to the engines and the auxiliary power unit (APU). The maximum fuel storage capacity of all tanks is 18728 kg, including 6427 kg of the center tank, 5435 kg of each inner tank, and 691 kg of each outer tank. There are two fuel pumps in the center tank and each inner tank, respectively, to supply fuel to the engines from the tanks. There are sequence valves at the outlet of the inner wing tank pumps, which ensure that when all pumps are running, the center pumps will deliver the fuel preference. A cross feed valve is used for the fuel feeding pipeline to allow both engines to be fed from one side tank or one engine to be fed from both side tanks. The outer tanks do not supply fuel directly to the engine. There are two transfer valves mounted in each wing to permit fuel transfer from the outer to the inner tank when the fuel consumption of the inner tank is down to 750 kg. Low pressure shut-off valves are used to disconnect the engine from the fuel pipeline, which is controlled by the engine master switch or engine fire pushbutton.Figure 1
Schedule of the fuel system of A320 aircraft.


## 3. System Modeling

The software Flowmaster V2019 was used to establish the components and system model. The fuel system simulation model requires not only the realization of the pressure and flow distribution calculation of the whole pipe network system but also the transient analysis of system pressure surges. Accordingly, the mathematical models of the components need to consider the relationship between the pressure drop and the flow rate and capture the main contributing factors influencing the pipeline system pressure surge.


### 3.1. Tank Modeling

The fuel tank has multiple output ports, each of which serves as a pressure boundary for the system pipeline to which it is connected. The interface layout of the tank model is illustrated in Figure2. The port pressure value is affected by the atmospheric pressure of the fuel surface of the tank, the total fuel mass, the height of the port, and the port flow resistance.Figure 2
Interface layout of the fuel tank.Taking port 1 as an example, when the height of the liquid levelL ≥ h1, the outlet pressure of port 1 is calculated by (1):(1)P1=Pg+ρ1gL+Z−K1m˙122ρ1A12.AsL < h1, the liquid can only flow into the tank, and the mass flow rate m˙1=0 in the case of outflow. The outlet pressure of port 1 is calculated by (2):(2)P1=Pg+ρ1gh1+Z−K1m˙122ρ1A12,where Pg is the liquid surface pressure; ρ1 is the liquid density; L is the level of liquid above the tank base; K1 is the flow loss coefficient used to calculate the pressure loss at the tank port; A1 is the cross-sectional area of port 1; K1m12/2ρ1A12 represents the pressure drop that occurs at the port 1. The boundary pressure of other ports is calculated similarly to that of port 1.The fuel storage of the tank of three branches is calculated according to the continuity equation (3):(3)m˙1+m˙2+m˙3=−ρdVdt.


### 3.2. Pipe Model

The pipe model not only needs to calculate the pressure loss as the fluid flows through the pipeline but also needs to analyze the pressure surge caused by the water hammer effect in the pipeline.


#### 3.2.1. Pipe Flow Resistance Model

Darcy formula is used to calculate the steady flow resistance of the pipeline as (4) shown:(4)ΔP=fLdρV22,where the friction factor f uses the Colebrook–White model and is calculated in sections according to the Re (Reynolds number) range of the flow as shown in (5) below.(5)f=64Re,Re≤2000,0.25lgk/3.7d+5.74/Re0.92,Re≥4000,Re2000−1.64Re+0.5−0.25Re/2000lgk/3.7d+5.74/Re0.92,4000>Re>2000.


#### 3.2.2. Pressure Surge Analysis Model in the Transient Simulation

In this simulation model of the fuel system, the constant cross-section area for each pipe is assumed. Since the velocity of the fluid in the pipe is a small value relative to the velocity of the pressure wave propagation, the momentum equation (6) and the continuity (7) can be established. Using the method of characteristics, the pipe is divided into a number of internal reaches with a length δx equal to the distance traveled by a pressure wave during one time step δt as shown in Figure 3. Therefore, δx=a⋅δt and the internal node number N can be calculated by (8):(6)Aδpδx+ρgAsinθ=−δm˙δt−fm˙m˙2ρdA,(7)δPδt=ρa2δm˙ρAδx,(8)N=La.δt−1,where A is the cross-section area of the pipe, θ is the inclined angle of the pipeline, d is the hydraulic diameter of the pipe, and a is the propagation velocity [10] of the wave calculated by (9):(9)a=K/ρρ1/K+D/EδΨ,where K is the bulk modulus of the liquid, which characterizes the compressibility of the liquid; ρ is the liquid density; E is the elastic modulus of the pipe material; D is the hydraulic diameter of the pipe; δ is the pipe wall thickness; μ is the Poisson’s ratio of the pipe material; and Ψ is the fixed coefficient of the pipe. Ψ = 1 − 0.5μ as one end of the pipe is fixed. Ψ = 1 − μ2 as both ends of the pipe are fixed. Ψ = 1 when the pipe is freely retractable.Figure 3
Internal node distribution of the pipe model.


### 3.3. Pump Model

The pump is the moving part of the fuel system, generating a pressure head in the circulation pipeline to provide the driving force for the fuel distribution system. This component is based on the pressure head and flow rate curve of the design state and scaled according to different working speeds. The relationship between the pressure head, volume, flow rate, and rotational speed of the pump satisfies the similarity law, as shown in (10) and (11):(10)QQ0=NN0,(11)HH0=N2N02,where Q is the volume flow rate, N is the rotational speed, and H is the head of the pump defined by (12):(12)H=P2−P1ρg+z2−z1,where P1 and P2 are the inlet and outlet static pressures, respectively, z1 and z2 are the heights of the centerline of the inlet and outlet pipe connected to the pump relative to the reference plane.


### 3.4. Valve Model

Ball valves are widely used as shut-off valves and regulating valves in fuel systems. The valve model can directly use the manufacturer performance curve provided by the valve supplier to calculate the loss coefficientK in different valve positions. With the loss coefficient data, the total pressure loss of the valve can be calculated by (13):(13)ΔP=KρQ22A2,where ΔP is the total pressure loss through the valve, A is the flow area of the valve, ρ is the fluid density, and Q is the fluid volume flow rate.


## 3.1. Tank Modeling

The fuel tank has multiple output ports, each of which serves as a pressure boundary for the system pipeline to which it is connected. The interface layout of the tank model is illustrated in Figure2. The port pressure value is affected by the atmospheric pressure of the fuel surface of the tank, the total fuel mass, the height of the port, and the port flow resistance.Figure 2
Interface layout of the fuel tank.Taking port 1 as an example, when the height of the liquid levelL ≥ h1, the outlet pressure of port 1 is calculated by (1):(1)P1=Pg+ρ1gL+Z−K1m˙122ρ1A12.AsL < h1, the liquid can only flow into the tank, and the mass flow rate m˙1=0 in the case of outflow. The outlet pressure of port 1 is calculated by (2):(2)P1=Pg+ρ1gh1+Z−K1m˙122ρ1A12,where Pg is the liquid surface pressure; ρ1 is the liquid density; L is the level of liquid above the tank base; K1 is the flow loss coefficient used to calculate the pressure loss at the tank port; A1 is the cross-sectional area of port 1; K1m12/2ρ1A12 represents the pressure drop that occurs at the port 1. The boundary pressure of other ports is calculated similarly to that of port 1.The fuel storage of the tank of three branches is calculated according to the continuity equation (3):(3)m˙1+m˙2+m˙3=−ρdVdt.


## 3.2. Pipe Model

The pipe model not only needs to calculate the pressure loss as the fluid flows through the pipeline but also needs to analyze the pressure surge caused by the water hammer effect in the pipeline.


### 3.2.1. Pipe Flow Resistance Model

Darcy formula is used to calculate the steady flow resistance of the pipeline as (4) shown:(4)ΔP=fLdρV22,where the friction factor f uses the Colebrook–White model and is calculated in sections according to the Re (Reynolds number) range of the flow as shown in (5) below.(5)f=64Re,Re≤2000,0.25lgk/3.7d+5.74/Re0.92,Re≥4000,Re2000−1.64Re+0.5−0.25Re/2000lgk/3.7d+5.74/Re0.92,4000>Re>2000.


### 3.2.2. Pressure Surge Analysis Model in the Transient Simulation

In this simulation model of the fuel system, the constant cross-section area for each pipe is assumed. Since the velocity of the fluid in the pipe is a small value relative to the velocity of the pressure wave propagation, the momentum equation (6) and the continuity (7) can be established. Using the method of characteristics, the pipe is divided into a number of internal reaches with a length δx equal to the distance traveled by a pressure wave during one time step δt as shown in Figure 3. Therefore, δx=a⋅δt and the internal node number N can be calculated by (8):(6)Aδpδx+ρgAsinθ=−δm˙δt−fm˙m˙2ρdA,(7)δPδt=ρa2δm˙ρAδx,(8)N=La.δt−1,where A is the cross-section area of the pipe, θ is the inclined angle of the pipeline, d is the hydraulic diameter of the pipe, and a is the propagation velocity [10] of the wave calculated by (9):(9)a=K/ρρ1/K+D/EδΨ,where K is the bulk modulus of the liquid, which characterizes the compressibility of the liquid; ρ is the liquid density; E is the elastic modulus of the pipe material; D is the hydraulic diameter of the pipe; δ is the pipe wall thickness; μ is the Poisson’s ratio of the pipe material; and Ψ is the fixed coefficient of the pipe. Ψ = 1 − 0.5μ as one end of the pipe is fixed. Ψ = 1 − μ2 as both ends of the pipe are fixed. Ψ = 1 when the pipe is freely retractable.Figure 3
Internal node distribution of the pipe model.


## 3.2.1. Pipe Flow Resistance Model

Darcy formula is used to calculate the steady flow resistance of the pipeline as (4) shown:(4)ΔP=fLdρV22,where the friction factor f uses the Colebrook–White model and is calculated in sections according to the Re (Reynolds number) range of the flow as shown in (5) below.(5)f=64Re,Re≤2000,0.25lgk/3.7d+5.74/Re0.92,Re≥4000,Re2000−1.64Re+0.5−0.25Re/2000lgk/3.7d+5.74/Re0.92,4000>Re>2000.


## 3.2.2. Pressure Surge Analysis Model in the Transient Simulation

In this simulation model of the fuel system, the constant cross-section area for each pipe is assumed. Since the velocity of the fluid in the pipe is a small value relative to the velocity of the pressure wave propagation, the momentum equation (6) and the continuity (7) can be established. Using the method of characteristics, the pipe is divided into a number of internal reaches with a length δx equal to the distance traveled by a pressure wave during one time step δt as shown in Figure 3. Therefore, δx=a⋅δt and the internal node number N can be calculated by (8):(6)Aδpδx+ρgAsinθ=−δm˙δt−fm˙m˙2ρdA,(7)δPδt=ρa2δm˙ρAδx,(8)N=La.δt−1,where A is the cross-section area of the pipe, θ is the inclined angle of the pipeline, d is the hydraulic diameter of the pipe, and a is the propagation velocity [10] of the wave calculated by (9):(9)a=K/ρρ1/K+D/EδΨ,where K is the bulk modulus of the liquid, which characterizes the compressibility of the liquid; ρ is the liquid density; E is the elastic modulus of the pipe material; D is the hydraulic diameter of the pipe; δ is the pipe wall thickness; μ is the Poisson’s ratio of the pipe material; and Ψ is the fixed coefficient of the pipe. Ψ = 1 − 0.5μ as one end of the pipe is fixed. Ψ = 1 − μ2 as both ends of the pipe are fixed. Ψ = 1 when the pipe is freely retractable.Figure 3
Internal node distribution of the pipe model.


## 3.3. Pump Model

The pump is the moving part of the fuel system, generating a pressure head in the circulation pipeline to provide the driving force for the fuel distribution system. This component is based on the pressure head and flow rate curve of the design state and scaled according to different working speeds. The relationship between the pressure head, volume, flow rate, and rotational speed of the pump satisfies the similarity law, as shown in (10) and (11):(10)QQ0=NN0,(11)HH0=N2N02,where Q is the volume flow rate, N is the rotational speed, and H is the head of the pump defined by (12):(12)H=P2−P1ρg+z2−z1,where P1 and P2 are the inlet and outlet static pressures, respectively, z1 and z2 are the heights of the centerline of the inlet and outlet pipe connected to the pump relative to the reference plane.


## 3.4. Valve Model

Ball valves are widely used as shut-off valves and regulating valves in fuel systems. The valve model can directly use the manufacturer performance curve provided by the valve supplier to calculate the loss coefficientK in different valve positions. With the loss coefficient data, the total pressure loss of the valve can be calculated by (13):(13)ΔP=KρQ22A2,where ΔP is the total pressure loss through the valve, A is the flow area of the valve, ρ is the fluid density, and Q is the fluid volume flow rate.


## 4. Numerical Method Validation

The experimental data in Yafei Chen’ research [21] was used to verify the simulation method. The schematic of the experimental system is illustrated in Figure 4, and the simulation model adopts the same component parameters as the test system. The pipe material is stainless steel, with a density of 7900 kg/m3 and an elastic modulus is 194 GPa. The fluid medium of the test system is water at 20°C, and its bulk modulus is 2.18 GPa. The water hammer velocity a is calculated by (9), and the result is 1433 m/s. The absolute pressure at the outlet of the test system is 101.325 kPa, and the absolute pressure of the water source is 131.723 kPa. The valve opening curve of the experimental data is added to the simulation model by the component signal generator as shown in Figure 4.Figure 4
Schematic of the experimental system.The corresponding simulation model is built using the Flowmaster program as shown in Figure5. The inlet and outlet of the water tank were modeled as a constant pressure inlet and a constant pressure outlet. Since the experimental test time is very short (8 s) and the volume of the water source tank in the test system is big enough, the pressure boundary at the inlet and outlet of the system can be considered almost unchanged. Figure 5 shows the mass flow rate analysis result of this pipeline with value 1.124 kg/s in the steady state under experimental test conditions and the error of which is 2.18% compared to the experimental test data 1.1 kg/s.Figure 5
The simulation model of experimental system based on flowmaster.Figure6 shows a comparison between the experimental data and the simulation results. It can be seen from the comparison results that the peak value of the prevalve node pressure is moderately smaller than the experimental data, and the appearance time of the peak value lags behind the experimental data by about 0.3 s. As for the outlet pressure of the control valve, the simulation results have a peak value slightly larger than the experimental data. Various reasons lead to the difference between the experimental data and the simulation results, among which the flow resistance characteristics when the valve approximates wholly close have a greater impact on the pressure wave. Furthermore, the experimental measurement errors (the accuracy of the instruments) are also the possible causes of simulation and calculation errors. Nevertheless, the overall trend and the magnitude of the peak error indicate that the prediction of the water hammer effect of the liquid piping system using the Flowmaster transient analysis is feasible and reliable.Figure 6
Comparison between simulation results and experimental data.


## 5. Simulation Results and Discussion

The system-level simulation model of the A320 aircraft fuel system is built as shown in Figure7. The system model consists of fuel tanks, fuel tank pumps, refueling and feeding pipes, transfer valves, low-pressure shut-off valves, check valves, fuel filters, flow and pressure boundaries, and control modules for valves and pumps. Using the system simulation model, the transient simulation of the pressure refueling and engine feeding process can be carried out to understand the pressure and flow distribution during the system operation. The simulation model can also be used to evaluate the pressure surges of the pipeline system during the system control process, such as the sudden closure of regulating valves and speed up or fault shutdown of the fuel pumps.Figure 7
Simulation model of fuel system based on flowmaster.


### 5.1. Simulation of Fuel System Refueling and Feeding Process

#### 5.1.1. Refueling Process

The transient simulation was conducted for the refueling process of the fuel system using the established model in Figure7. Fuel is supplied to the fuel tanks through the refueling port on the right side. In this analysis case, the flow source boundaries of the left engine, the right engine, and APU were set to 0 m3/s. The refuel shut-off valve of the left refuel port was set to complete close. The constant pressure refueling method was used for this case and the refueling pressure was set to 2.4 bar. The initial fuel mass for all 5 tanks is 0 kg.The simulation results of the fuel mass changes of each fuel tank during the refueling process are shown in Figure8. As can be seen from the results, the refueling speed of the right inner and outer tanks is slightly higher than that of the left tanks. This is because the tanks of the right wing are closer to the refueling port, and the corresponding pipe flow resistance is lower. The refueling sequence of the whole system is to refuel the outer wing fuel tanks first, then refuel the inner wing fuel tanks through the transfer valve between the inner and outer fuel tanks after full fuel, and finally refuel the central fuel tank. It takes 1197 s to fill all tanks at a constant refueling pressure of 2.4 bar. It can be seen from the curves that the refueling speed is slightly slowed down, but not significant with the increase in the fuel storage capacity of the tanks. This is because the height of the fuel liquid level of the tank increases and the output pressure of the fuel tank branch increases due to the fuel gravity.Figure 8
The fuel mass result of the tanks during the refueling process.It can be seen from the tank mass curve in Figure8 that when t = 500 s, the left and right outer fuel tanks have been filled up, and the left and right inner tanks are still in the process of refueling. At this time, the transfer valves between the outer tanks and the inner tanks have been opened, and the fuel is transferred into the inner tanks through the outer tanks. Figure 9(a) shows the mass flow rate and pressure distribution of the whole system at t = 500 s. It can be seen that the mass flow rate exists only in the flow path from the refueling port to the inner tanks in this moment. The fuel pressure is high and evenly distributed in the main refueling pipe and gradually decreases with the pressure at the inner tank port along the flow path.Figure 9
Flow and pressure distribution of the system in refueling cases. (a) t = 500 s, (b)t = 1000 s.
(a)(b)Figure9(b) shows the mass flow rate and pressure distribution of the whole system at t = 1000 s. As can be seen from the tank fuel mass curve, all inner and outer tanks have been filled up at this time, and the center tanks are in the process of refueling. The flow rate of the refueling port at t = 1000 s is larger than that at t = 500 s as the mass flow rate result is shown, and this result is also supported by Figure 8, in which the gradient of the tank fuel mass curve of the center tank is clearly larger than that of the inner tank. This is because the flow resistance of the flow path from the refueling port to the left and right inner fuel tanks is larger than that to the center tank.


#### 5.1.2. Engine Feeding Process

All fuel tanks are fully loaded at the beginning of the engine feeding process. The left and right refueling ports are disconnected by setting the refueling valve fully closed. The fuel consumption for each engine was set to 0.55 kg/s, the cross-feed valve was set full closed, and all tank pumps were set to operate at normal speed.Figure10 shows the fuel mass result of the tanks during the feeding process. As can be seen from this figure, the feeding sequence of the fuel tanks is as follows: the fuel in the central tank is used first, and then the fuel in the inner wing tank is consumed. When the fuel of each inner tank is consumed to less than 750 kg, the transfer valve between the inner and outer fuel tank will open, and the fuel in the outer tank is allowed to be transferred into the inner tank. As can be seen from the fuel mass curve, this process starts at t = 14400 s. During this process, the fuel mass of the outer tanks decreases rapidly, while the fuel mass of the inner tank increases. This process ends when all fuel in the outer tank is transferred to the inner tank. After that, the fuel mass in the inner tank continues to decrease due to fuel consumption.Figure 10
The fuel mass result of the tanks during engine feeding process.In this simulation, the entire engine fuel feeding process lasts for 17,310 s. The simulation results also show that in this normal fuel feeding process, the fuel mass curves of the left and right fuel tanks almost coincide, and the fuel consumption speed of both side tanks keeps equal, which means that the current system design can well ensure the balance of fuel consumption in the left and right fuel tanks and maintain the center of gravity of the aircraft during flight.Figure11 shows the pressure and mass flow rate distribution of the fuel system at t = 5000 s and t = 10,000 s during the feeding process. It can be seen from the figures that each engine is supplied by one fuel pump in the center tank at t = 5000 s, and only fuel in the center tank is consumed at this time. The mass flow rate exists only in the flow path from the center tank to the left and right engines. The pressure distribution result in Figure 11(a) also shows that in the engine feeding process, the fuel feeding circuit is completely isolated from the refueling circuit by the refuel valves and defuel cross valves. The fuel pumps increase the output pressure of the fuel tank, leading to the pressure of the main feeding pipeline being significantly higher than that of the outlet ports of the center fuel tank.Figure 11
Flow and pressure distribution of the system in engine feeding cases. (a) t = 5000 s. (b) t = 10,000 s.
(a)(b)Each engine is supplied by two pumps in its own side inner wing tank att = 10,000 s, and the fuel in the inner tanks is consumed at this point of time. Mass flow rate exists only in the flow path from the inner tanks to the left and right engines as shown in Figure 11(b). Comparing the pressure distribution results in Figures 11(a) and 11(b), it can be seen that through the system parameters design, the fuel feed pressure maintains good consistency whether the fuel is supplied by one center tank pump or by two inner tank pumps.


### 5.2. Analysis of Pipeline Pressure Surge in Fuel System

Based on the fuel system simulation model illustrated in Figure7, the pipeline surge pressure for refueling case was investigated, which is the most severe condition for pipeline surge pressure of the aircraft fuel system. In the process of pressure refueling, the refueling valves automatically close when the tanks contain the preselected load or when the fuel sensors detect that the tank is fully loaded. In the case of a sudden closing of the refueling valve, the fuel flow rate in the pipeline will change sharply, resulting in instantaneous pressure surges inside the pipeline. The magnitude of this pressure surge is affected by a variety of system design factors, including the closure speed of the refueling shut-off valve, the size of the refueling pipeline, and the refueling flow rate.


#### 5.2.1. Effect of Valve Speed on Pipeline Pressure Surge

In this analysis, the right-wing refueling port is used for refueling the tanks with a constant volume flow rate of 0.025 m³/s, the main refueling pipe diameter of the system is 0.08 m, and the other parameter settings are the same as those in Section4. The left fuel tank refueling valve begins to close with a specific speed at t = 1 s during this refueling process. In this analysis, the valve opening changes linearly, and the valve speed is defined by the time it takes (1, 1.5, 2, 2.5 s) for the valve from fully open to fully close. In this section, the effect of valve speeds on pipeline surge pressure is studied.Figure12 shows the pressure surge at the inlet node of the left refueling valve in different valve closing speed cases. It can be seen from the figure that the sudden closing of the refueling valve during the refueling process will induce water hammer surge in the pipeline, and the peak value of the pressure declines with the increase of the valve closing time. The wave amplitude in the pipeline continues to weaken with the advance of time and gradually tends to be steady. After stability, this node pressure reaches the same steady-state value. This is because the valve closing speed only affects the transient processes. As the refueling valve is completely closed, the steady-state parameters of the fuel system for these four simulation cases are still the same.Figure 12
The valve inlet pressure in the case of different valve closure times.Figure13 shows the maximum surge pressure as a function of the valve closure time. As can be seen, the valve speed has a significant impact on the peak surge pressure of the pipeline. When the closing time of the valve increases from 0.25 s to 3 s, the maximum surge pressure can be reduced from 14.7 bar to 3.15 bar. However, this effect is gradually weakened with the decrease of the valve speed (increase of valve closure time), which means that as the valve speed decreases to a certain value, the influence of its change on the maximum pipeline impact pressure of the system is no longer considerable.Figure 13
Effect of valve speed on maximum pipeline pressure surge.


#### 5.2.2. Effect of Pipe Diameter on Pipeline Surge Pressure

In this analysis, the right-wing refueling port is used to refuel the tanks with a constant volume flow rate 0.025 m³/s, the valve closure time is specified as 0.5 s, four different pipe diameters (0.08, 0.1, 0.12, 0.14 m) of the refueling main pipe are chosen for this simulation case. The remaining parameter settings are the same as Section4. During this refueling process, the left fuel tank refueling valve begins to close at t = 1 s.Figure14 shows the pressure surge at the node of the left refueling valve inlet under different pipe diameters. As can be seen from the figure, increasing the pipe diameter results in gradually declining peak values of the internal pipe pressure wave. This is because, under the same refueling volume flow rate, the fluid velocity inside the pipeline decreases as the pipe diameter increases, which leads to a decrease of the kinetic energy carried by the same mass of fuel. The pressure results also show that as the diameter of the main pipe increases, the time for the pressure wave to stabilize will become shorter.Figure 14
The valve inlet pressure in the case of different pipe diameters.Figure15 shows the maximum surge pressure as a function of the diameter of the refueling pipeline. It can be seen from the figure that the water hammer surge pressure inside the pipeline can be alleviated by increasing the diameter of the pipeline, as the pipeline diameter increases from 0.06 m to 0.16 m, the maximum surge pressure can be reduced from 17.18 bar to 2.91 bar, however this mitigation trend is gradually weakened. From the perspective of engineering design for aircraft fuel system, the increase of pipe diameter conveys many benefits, which can reduce the flow resistance in steady state and alleviate the water hammer surge pressure of the system. However, the increase in pipe diameter increases the weight of the whole system, which is an important factor to consider in aircraft system design. Therefore, the determination of pipe diameter needs to be evaluated and weighed comprehensively according to various influencing factors.Figure 15
Effect of pipe diameter on maximum pipeline pressure surge.


#### 5.2.3. Effect of Refueling Flow Rate on Pipeline Surge Pressure

To study the effect of refueling flow rate on pipeline surge pressure, four different refueling volume flow rates (0.2, 0.025, 0.03, 0.035 m3/s) are considered for this comparative study. The refueling port on the right wing is used to refuel the tanks in this analysis. The diameter of the main refueling pipe is set as 0.1 m. During this refueling process, the refueling valve of the left fuel tank begins to close at t = 1 s with the closure time specified as 0.5 s. The remaining parameter settings are the same as Section 4.Figure16 shows the analysis results of the pressure fluctuation of the node at the valve inlet location under the refueling volume flow rate (0.2, 0.025, 0.03, 0.035 m3/s). As shown in the results, the amplitude of the pressure wave increases with the increase in refueling speed. This is because the fluid velocity inside the pipeline will increase with the rise of the refueling volume flow rate as the pipe diameter is kept consistent, and the kinetic energy of the fuel will increase synchronously. The increasing fluid velocity will also lead to an increase in the flow resistance of the pipeline and the steady-state pressure at the valve inlet location.Figure 16
The valve inlet pressure in the case of different refueling flow rate.Figure17 shows the variation of the maximum pipeline surge pressure with the refueling volume flow rate. It can be seen from the figure that the increase in pipeline surge pressure caused by the increase in refueling speed is almost linear, as the refueling volume flow rate increases from 0.015 m3/s to 0.04 m3/s, the maximum surge pressure will rise from 4.16 bar to 8.02 bar. From a time efficiency point of view, faster refueling speed is better. However, the rising refueling speed will increase the flow resistance of the entire pipeline system, resulting in the requirement of higher refueling pressure or larger pipe diameter in the system design, which will bring weight cost to the aircraft design. Therefore, the refueling speed must also be thoroughly weighed according to the system design requirements.Figure 17
Effect of refueling speed on maximum pipeline pressure surge.


## 5.1. Simulation of Fuel System Refueling and Feeding Process

### 5.1.1. Refueling Process

The transient simulation was conducted for the refueling process of the fuel system using the established model in Figure7. Fuel is supplied to the fuel tanks through the refueling port on the right side. In this analysis case, the flow source boundaries of the left engine, the right engine, and APU were set to 0 m3/s. The refuel shut-off valve of the left refuel port was set to complete close. The constant pressure refueling method was used for this case and the refueling pressure was set to 2.4 bar. The initial fuel mass for all 5 tanks is 0 kg.The simulation results of the fuel mass changes of each fuel tank during the refueling process are shown in Figure8. As can be seen from the results, the refueling speed of the right inner and outer tanks is slightly higher than that of the left tanks. This is because the tanks of the right wing are closer to the refueling port, and the corresponding pipe flow resistance is lower. The refueling sequence of the whole system is to refuel the outer wing fuel tanks first, then refuel the inner wing fuel tanks through the transfer valve between the inner and outer fuel tanks after full fuel, and finally refuel the central fuel tank. It takes 1197 s to fill all tanks at a constant refueling pressure of 2.4 bar. It can be seen from the curves that the refueling speed is slightly slowed down, but not significant with the increase in the fuel storage capacity of the tanks. This is because the height of the fuel liquid level of the tank increases and the output pressure of the fuel tank branch increases due to the fuel gravity.Figure 8
The fuel mass result of the tanks during the refueling process.It can be seen from the tank mass curve in Figure8 that when t = 500 s, the left and right outer fuel tanks have been filled up, and the left and right inner tanks are still in the process of refueling. At this time, the transfer valves between the outer tanks and the inner tanks have been opened, and the fuel is transferred into the inner tanks through the outer tanks. Figure 9(a) shows the mass flow rate and pressure distribution of the whole system at t = 500 s. It can be seen that the mass flow rate exists only in the flow path from the refueling port to the inner tanks in this moment. The fuel pressure is high and evenly distributed in the main refueling pipe and gradually decreases with the pressure at the inner tank port along the flow path.Figure 9
Flow and pressure distribution of the system in refueling cases. (a) t = 500 s, (b)t = 1000 s.
(a)(b)Figure9(b) shows the mass flow rate and pressure distribution of the whole system at t = 1000 s. As can be seen from the tank fuel mass curve, all inner and outer tanks have been filled up at this time, and the center tanks are in the process of refueling. The flow rate of the refueling port at t = 1000 s is larger than that at t = 500 s as the mass flow rate result is shown, and this result is also supported by Figure 8, in which the gradient of the tank fuel mass curve of the center tank is clearly larger than that of the inner tank. This is because the flow resistance of the flow path from the refueling port to the left and right inner fuel tanks is larger than that to the center tank.


### 5.1.2. Engine Feeding Process

All fuel tanks are fully loaded at the beginning of the engine feeding process. The left and right refueling ports are disconnected by setting the refueling valve fully closed. The fuel consumption for each engine was set to 0.55 kg/s, the cross-feed valve was set full closed, and all tank pumps were set to operate at normal speed.Figure10 shows the fuel mass result of the tanks during the feeding process. As can be seen from this figure, the feeding sequence of the fuel tanks is as follows: the fuel in the central tank is used first, and then the fuel in the inner wing tank is consumed. When the fuel of each inner tank is consumed to less than 750 kg, the transfer valve between the inner and outer fuel tank will open, and the fuel in the outer tank is allowed to be transferred into the inner tank. As can be seen from the fuel mass curve, this process starts at t = 14400 s. During this process, the fuel mass of the outer tanks decreases rapidly, while the fuel mass of the inner tank increases. This process ends when all fuel in the outer tank is transferred to the inner tank. After that, the fuel mass in the inner tank continues to decrease due to fuel consumption.Figure 10
The fuel mass result of the tanks during engine feeding process.In this simulation, the entire engine fuel feeding process lasts for 17,310 s. The simulation results also show that in this normal fuel feeding process, the fuel mass curves of the left and right fuel tanks almost coincide, and the fuel consumption speed of both side tanks keeps equal, which means that the current system design can well ensure the balance of fuel consumption in the left and right fuel tanks and maintain the center of gravity of the aircraft during flight.Figure11 shows the pressure and mass flow rate distribution of the fuel system at t = 5000 s and t = 10,000 s during the feeding process. It can be seen from the figures that each engine is supplied by one fuel pump in the center tank at t = 5000 s, and only fuel in the center tank is consumed at this time. The mass flow rate exists only in the flow path from the center tank to the left and right engines. The pressure distribution result in Figure 11(a) also shows that in the engine feeding process, the fuel feeding circuit is completely isolated from the refueling circuit by the refuel valves and defuel cross valves. The fuel pumps increase the output pressure of the fuel tank, leading to the pressure of the main feeding pipeline being significantly higher than that of the outlet ports of the center fuel tank.Figure 11
Flow and pressure distribution of the system in engine feeding cases. (a) t = 5000 s. (b) t = 10,000 s.
(a)(b)Each engine is supplied by two pumps in its own side inner wing tank att = 10,000 s, and the fuel in the inner tanks is consumed at this point of time. Mass flow rate exists only in the flow path from the inner tanks to the left and right engines as shown in Figure 11(b). Comparing the pressure distribution results in Figures 11(a) and 11(b), it can be seen that through the system parameters design, the fuel feed pressure maintains good consistency whether the fuel is supplied by one center tank pump or by two inner tank pumps.


## 5.1.1. Refueling Process

The transient simulation was conducted for the refueling process of the fuel system using the established model in Figure7. Fuel is supplied to the fuel tanks through the refueling port on the right side. In this analysis case, the flow source boundaries of the left engine, the right engine, and APU were set to 0 m3/s. The refuel shut-off valve of the left refuel port was set to complete close. The constant pressure refueling method was used for this case and the refueling pressure was set to 2.4 bar. The initial fuel mass for all 5 tanks is 0 kg.The simulation results of the fuel mass changes of each fuel tank during the refueling process are shown in Figure8. As can be seen from the results, the refueling speed of the right inner and outer tanks is slightly higher than that of the left tanks. This is because the tanks of the right wing are closer to the refueling port, and the corresponding pipe flow resistance is lower. The refueling sequence of the whole system is to refuel the outer wing fuel tanks first, then refuel the inner wing fuel tanks through the transfer valve between the inner and outer fuel tanks after full fuel, and finally refuel the central fuel tank. It takes 1197 s to fill all tanks at a constant refueling pressure of 2.4 bar. It can be seen from the curves that the refueling speed is slightly slowed down, but not significant with the increase in the fuel storage capacity of the tanks. This is because the height of the fuel liquid level of the tank increases and the output pressure of the fuel tank branch increases due to the fuel gravity.Figure 8
The fuel mass result of the tanks during the refueling process.It can be seen from the tank mass curve in Figure8 that when t = 500 s, the left and right outer fuel tanks have been filled up, and the left and right inner tanks are still in the process of refueling. At this time, the transfer valves between the outer tanks and the inner tanks have been opened, and the fuel is transferred into the inner tanks through the outer tanks. Figure 9(a) shows the mass flow rate and pressure distribution of the whole system at t = 500 s. It can be seen that the mass flow rate exists only in the flow path from the refueling port to the inner tanks in this moment. The fuel pressure is high and evenly distributed in the main refueling pipe and gradually decreases with the pressure at the inner tank port along the flow path.Figure 9
Flow and pressure distribution of the system in refueling cases. (a) t = 500 s, (b)t = 1000 s.
(a)(b)Figure9(b) shows the mass flow rate and pressure distribution of the whole system at t = 1000 s. As can be seen from the tank fuel mass curve, all inner and outer tanks have been filled up at this time, and the center tanks are in the process of refueling. The flow rate of the refueling port at t = 1000 s is larger than that at t = 500 s as the mass flow rate result is shown, and this result is also supported by Figure 8, in which the gradient of the tank fuel mass curve of the center tank is clearly larger than that of the inner tank. This is because the flow resistance of the flow path from the refueling port to the left and right inner fuel tanks is larger than that to the center tank.


## 5.1.2. Engine Feeding Process

All fuel tanks are fully loaded at the beginning of the engine feeding process. The left and right refueling ports are disconnected by setting the refueling valve fully closed. The fuel consumption for each engine was set to 0.55 kg/s, the cross-feed valve was set full closed, and all tank pumps were set to operate at normal speed.Figure10 shows the fuel mass result of the tanks during the feeding process. As can be seen from this figure, the feeding sequence of the fuel tanks is as follows: the fuel in the central tank is used first, and then the fuel in the inner wing tank is consumed. When the fuel of each inner tank is consumed to less than 750 kg, the transfer valve between the inner and outer fuel tank will open, and the fuel in the outer tank is allowed to be transferred into the inner tank. As can be seen from the fuel mass curve, this process starts at t = 14400 s. During this process, the fuel mass of the outer tanks decreases rapidly, while the fuel mass of the inner tank increases. This process ends when all fuel in the outer tank is transferred to the inner tank. After that, the fuel mass in the inner tank continues to decrease due to fuel consumption.Figure 10
The fuel mass result of the tanks during engine feeding process.In this simulation, the entire engine fuel feeding process lasts for 17,310 s. The simulation results also show that in this normal fuel feeding process, the fuel mass curves of the left and right fuel tanks almost coincide, and the fuel consumption speed of both side tanks keeps equal, which means that the current system design can well ensure the balance of fuel consumption in the left and right fuel tanks and maintain the center of gravity of the aircraft during flight.Figure11 shows the pressure and mass flow rate distribution of the fuel system at t = 5000 s and t = 10,000 s during the feeding process. It can be seen from the figures that each engine is supplied by one fuel pump in the center tank at t = 5000 s, and only fuel in the center tank is consumed at this time. The mass flow rate exists only in the flow path from the center tank to the left and right engines. The pressure distribution result in Figure 11(a) also shows that in the engine feeding process, the fuel feeding circuit is completely isolated from the refueling circuit by the refuel valves and defuel cross valves. The fuel pumps increase the output pressure of the fuel tank, leading to the pressure of the main feeding pipeline being significantly higher than that of the outlet ports of the center fuel tank.Figure 11
Flow and pressure distribution of the system in engine feeding cases. (a) t = 5000 s. (b) t = 10,000 s.
(a)(b)Each engine is supplied by two pumps in its own side inner wing tank att = 10,000 s, and the fuel in the inner tanks is consumed at this point of time. Mass flow rate exists only in the flow path from the inner tanks to the left and right engines as shown in Figure 11(b). Comparing the pressure distribution results in Figures 11(a) and 11(b), it can be seen that through the system parameters design, the fuel feed pressure maintains good consistency whether the fuel is supplied by one center tank pump or by two inner tank pumps.


## 5.2. Analysis of Pipeline Pressure Surge in Fuel System

Based on the fuel system simulation model illustrated in Figure7, the pipeline surge pressure for refueling case was investigated, which is the most severe condition for pipeline surge pressure of the aircraft fuel system. In the process of pressure refueling, the refueling valves automatically close when the tanks contain the preselected load or when the fuel sensors detect that the tank is fully loaded. In the case of a sudden closing of the refueling valve, the fuel flow rate in the pipeline will change sharply, resulting in instantaneous pressure surges inside the pipeline. The magnitude of this pressure surge is affected by a variety of system design factors, including the closure speed of the refueling shut-off valve, the size of the refueling pipeline, and the refueling flow rate.


### 5.2.1. Effect of Valve Speed on Pipeline Pressure Surge

In this analysis, the right-wing refueling port is used for refueling the tanks with a constant volume flow rate of 0.025 m³/s, the main refueling pipe diameter of the system is 0.08 m, and the other parameter settings are the same as those in Section4. The left fuel tank refueling valve begins to close with a specific speed at t = 1 s during this refueling process. In this analysis, the valve opening changes linearly, and the valve speed is defined by the time it takes (1, 1.5, 2, 2.5 s) for the valve from fully open to fully close. In this section, the effect of valve speeds on pipeline surge pressure is studied.Figure12 shows the pressure surge at the inlet node of the left refueling valve in different valve closing speed cases. It can be seen from the figure that the sudden closing of the refueling valve during the refueling process will induce water hammer surge in the pipeline, and the peak value of the pressure declines with the increase of the valve closing time. The wave amplitude in the pipeline continues to weaken with the advance of time and gradually tends to be steady. After stability, this node pressure reaches the same steady-state value. This is because the valve closing speed only affects the transient processes. As the refueling valve is completely closed, the steady-state parameters of the fuel system for these four simulation cases are still the same.Figure 12
The valve inlet pressure in the case of different valve closure times.Figure13 shows the maximum surge pressure as a function of the valve closure time. As can be seen, the valve speed has a significant impact on the peak surge pressure of the pipeline. When the closing time of the valve increases from 0.25 s to 3 s, the maximum surge pressure can be reduced from 14.7 bar to 3.15 bar. However, this effect is gradually weakened with the decrease of the valve speed (increase of valve closure time), which means that as the valve speed decreases to a certain value, the influence of its change on the maximum pipeline impact pressure of the system is no longer considerable.Figure 13
Effect of valve speed on maximum pipeline pressure surge.


### 5.2.2. Effect of Pipe Diameter on Pipeline Surge Pressure

In this analysis, the right-wing refueling port is used to refuel the tanks with a constant volume flow rate 0.025 m³/s, the valve closure time is specified as 0.5 s, four different pipe diameters (0.08, 0.1, 0.12, 0.14 m) of the refueling main pipe are chosen for this simulation case. The remaining parameter settings are the same as Section4. During this refueling process, the left fuel tank refueling valve begins to close at t = 1 s.Figure14 shows the pressure surge at the node of the left refueling valve inlet under different pipe diameters. As can be seen from the figure, increasing the pipe diameter results in gradually declining peak values of the internal pipe pressure wave. This is because, under the same refueling volume flow rate, the fluid velocity inside the pipeline decreases as the pipe diameter increases, which leads to a decrease of the kinetic energy carried by the same mass of fuel. The pressure results also show that as the diameter of the main pipe increases, the time for the pressure wave to stabilize will become shorter.Figure 14
The valve inlet pressure in the case of different pipe diameters.Figure15 shows the maximum surge pressure as a function of the diameter of the refueling pipeline. It can be seen from the figure that the water hammer surge pressure inside the pipeline can be alleviated by increasing the diameter of the pipeline, as the pipeline diameter increases from 0.06 m to 0.16 m, the maximum surge pressure can be reduced from 17.18 bar to 2.91 bar, however this mitigation trend is gradually weakened. From the perspective of engineering design for aircraft fuel system, the increase of pipe diameter conveys many benefits, which can reduce the flow resistance in steady state and alleviate the water hammer surge pressure of the system. However, the increase in pipe diameter increases the weight of the whole system, which is an important factor to consider in aircraft system design. Therefore, the determination of pipe diameter needs to be evaluated and weighed comprehensively according to various influencing factors.Figure 15
Effect of pipe diameter on maximum pipeline pressure surge.


### 5.2.3. Effect of Refueling Flow Rate on Pipeline Surge Pressure

To study the effect of refueling flow rate on pipeline surge pressure, four different refueling volume flow rates (0.2, 0.025, 0.03, 0.035 m3/s) are considered for this comparative study. The refueling port on the right wing is used to refuel the tanks in this analysis. The diameter of the main refueling pipe is set as 0.1 m. During this refueling process, the refueling valve of the left fuel tank begins to close at t = 1 s with the closure time specified as 0.5 s. The remaining parameter settings are the same as Section 4.Figure16 shows the analysis results of the pressure fluctuation of the node at the valve inlet location under the refueling volume flow rate (0.2, 0.025, 0.03, 0.035 m3/s). As shown in the results, the amplitude of the pressure wave increases with the increase in refueling speed. This is because the fluid velocity inside the pipeline will increase with the rise of the refueling volume flow rate as the pipe diameter is kept consistent, and the kinetic energy of the fuel will increase synchronously. The increasing fluid velocity will also lead to an increase in the flow resistance of the pipeline and the steady-state pressure at the valve inlet location.Figure 16
The valve inlet pressure in the case of different refueling flow rate.Figure17 shows the variation of the maximum pipeline surge pressure with the refueling volume flow rate. It can be seen from the figure that the increase in pipeline surge pressure caused by the increase in refueling speed is almost linear, as the refueling volume flow rate increases from 0.015 m3/s to 0.04 m3/s, the maximum surge pressure will rise from 4.16 bar to 8.02 bar. From a time efficiency point of view, faster refueling speed is better. However, the rising refueling speed will increase the flow resistance of the entire pipeline system, resulting in the requirement of higher refueling pressure or larger pipe diameter in the system design, which will bring weight cost to the aircraft design. Therefore, the refueling speed must also be thoroughly weighed according to the system design requirements.Figure 17
Effect of refueling speed on maximum pipeline pressure surge.


## 5.2.1. Effect of Valve Speed on Pipeline Pressure Surge

In this analysis, the right-wing refueling port is used for refueling the tanks with a constant volume flow rate of 0.025 m³/s, the main refueling pipe diameter of the system is 0.08 m, and the other parameter settings are the same as those in Section4. The left fuel tank refueling valve begins to close with a specific speed at t = 1 s during this refueling process. In this analysis, the valve opening changes linearly, and the valve speed is defined by the time it takes (1, 1.5, 2, 2.5 s) for the valve from fully open to fully close. In this section, the effect of valve speeds on pipeline surge pressure is studied.Figure12 shows the pressure surge at the inlet node of the left refueling valve in different valve closing speed cases. It can be seen from the figure that the sudden closing of the refueling valve during the refueling process will induce water hammer surge in the pipeline, and the peak value of the pressure declines with the increase of the valve closing time. The wave amplitude in the pipeline continues to weaken with the advance of time and gradually tends to be steady. After stability, this node pressure reaches the same steady-state value. This is because the valve closing speed only affects the transient processes. As the refueling valve is completely closed, the steady-state parameters of the fuel system for these four simulation cases are still the same.Figure 12
The valve inlet pressure in the case of different valve closure times.Figure13 shows the maximum surge pressure as a function of the valve closure time. As can be seen, the valve speed has a significant impact on the peak surge pressure of the pipeline. When the closing time of the valve increases from 0.25 s to 3 s, the maximum surge pressure can be reduced from 14.7 bar to 3.15 bar. However, this effect is gradually weakened with the decrease of the valve speed (increase of valve closure time), which means that as the valve speed decreases to a certain value, the influence of its change on the maximum pipeline impact pressure of the system is no longer considerable.Figure 13
Effect of valve speed on maximum pipeline pressure surge.


## 5.2.2. Effect of Pipe Diameter on Pipeline Surge Pressure

In this analysis, the right-wing refueling port is used to refuel the tanks with a constant volume flow rate 0.025 m³/s, the valve closure time is specified as 0.5 s, four different pipe diameters (0.08, 0.1, 0.12, 0.14 m) of the refueling main pipe are chosen for this simulation case. The remaining parameter settings are the same as Section4. During this refueling process, the left fuel tank refueling valve begins to close at t = 1 s.Figure14 shows the pressure surge at the node of the left refueling valve inlet under different pipe diameters. As can be seen from the figure, increasing the pipe diameter results in gradually declining peak values of the internal pipe pressure wave. This is because, under the same refueling volume flow rate, the fluid velocity inside the pipeline decreases as the pipe diameter increases, which leads to a decrease of the kinetic energy carried by the same mass of fuel. The pressure results also show that as the diameter of the main pipe increases, the time for the pressure wave to stabilize will become shorter.Figure 14
The valve inlet pressure in the case of different pipe diameters.Figure15 shows the maximum surge pressure as a function of the diameter of the refueling pipeline. It can be seen from the figure that the water hammer surge pressure inside the pipeline can be alleviated by increasing the diameter of the pipeline, as the pipeline diameter increases from 0.06 m to 0.16 m, the maximum surge pressure can be reduced from 17.18 bar to 2.91 bar, however this mitigation trend is gradually weakened. From the perspective of engineering design for aircraft fuel system, the increase of pipe diameter conveys many benefits, which can reduce the flow resistance in steady state and alleviate the water hammer surge pressure of the system. However, the increase in pipe diameter increases the weight of the whole system, which is an important factor to consider in aircraft system design. Therefore, the determination of pipe diameter needs to be evaluated and weighed comprehensively according to various influencing factors.Figure 15
Effect of pipe diameter on maximum pipeline pressure surge.


## 5.2.3. Effect of Refueling Flow Rate on Pipeline Surge Pressure

To study the effect of refueling flow rate on pipeline surge pressure, four different refueling volume flow rates (0.2, 0.025, 0.03, 0.035 m3/s) are considered for this comparative study. The refueling port on the right wing is used to refuel the tanks in this analysis. The diameter of the main refueling pipe is set as 0.1 m. During this refueling process, the refueling valve of the left fuel tank begins to close at t = 1 s with the closure time specified as 0.5 s. The remaining parameter settings are the same as Section 4.Figure16 shows the analysis results of the pressure fluctuation of the node at the valve inlet location under the refueling volume flow rate (0.2, 0.025, 0.03, 0.035 m3/s). As shown in the results, the amplitude of the pressure wave increases with the increase in refueling speed. This is because the fluid velocity inside the pipeline will increase with the rise of the refueling volume flow rate as the pipe diameter is kept consistent, and the kinetic energy of the fuel will increase synchronously. The increasing fluid velocity will also lead to an increase in the flow resistance of the pipeline and the steady-state pressure at the valve inlet location.Figure 16
The valve inlet pressure in the case of different refueling flow rate.Figure17 shows the variation of the maximum pipeline surge pressure with the refueling volume flow rate. It can be seen from the figure that the increase in pipeline surge pressure caused by the increase in refueling speed is almost linear, as the refueling volume flow rate increases from 0.015 m3/s to 0.04 m3/s, the maximum surge pressure will rise from 4.16 bar to 8.02 bar. From a time efficiency point of view, faster refueling speed is better. However, the rising refueling speed will increase the flow resistance of the entire pipeline system, resulting in the requirement of higher refueling pressure or larger pipe diameter in the system design, which will bring weight cost to the aircraft design. Therefore, the refueling speed must also be thoroughly weighed according to the system design requirements.Figure 17
Effect of refueling speed on maximum pipeline pressure surge.


## 6. Conclusion

The numerical modeling method for the transient analysis of the large aircraft fuel system is studied using the Flowmaster program. The accuracy of the method was verified by comparing the analysis results of the steady and transient state with experimental data. A simulation model of the entire large aircraft fuel system is established using this method, and the transient analysis of the water hammer effect during the pressure refueling process for different refueling valve closure times (1, 1.5, 2, 2.5s), main pipe diameters (0.08, 0.1, 0.12, 0.14 m), and refueling volume flow rates (0.2, 0.025, 0.03, 0.035 m3/s) is conducted using this simulation model. The following conclusions were reached:(1)
The closure speed of the refueling valve is the key factor affecting the amplitude of the pipeline pressure wave, as the valve closure time increases from 0.25 s to 3 s, the maximum surge pressure can be reduced from 14.7 bar to 3.15 bar. However, this effect is weakened with the decrease of the valve speed.(2)
The increase in the pipe diameter of the refueling pipeline can reduce the peak value of the pipeline wave pressure caused by the water hammer effect. This effect is nonlinear and gradually weakens with the increase in pipeline diameter.(3)
The increase in refueling volume flow rate will significantly increase the pressure surge in the pipeline, and this effect is approximately linear.The modeling method and analysis conclusion in this study can provide a reference for engineering design, modeling, and system performance evaluation of large aircraft fuel systems. Based on this system simulation model, it can efficiently complete the system simulation evaluation under numerous operating conditions with different component parameters and realize the optimization of system parameters, which is of great significance to system design.



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*Source: 7529857-2022-05-04.xml*