Keywords

1 Introduction

With the continuous advancement of high-power electronic technology and high-power density electromechanical systems, More Electric Engine (MEE) technology has been propelled to the forefront of development [1]. Due to its capability to comprehensively optimize the efficiency and performance of engines, the MEE technology has garnered significant attention from developed countries worldwide [2,3,4]. The electric fuel pump which plays a crucial role as a component of the More Electric Engine, due to their advantages such as high power density, rapid response, and precise flow rate control over a wide range, have been widely used in the fuel systems of turbofan engines in the field of unmanned aerial vehicles, cruise missiles, and other weapon systems [5]. Therefore, researching low-cost, high-precision, and highly reliable electric fuel pumps is a focal point for achieving domestic production in China's turbofan engine fuel systems. Domestic research on fuel pumps has primarily focused on conventional aviation engines, with limited attention to their application in small-scale turbofan engines.

In the field of aerospace engines, the efficient and reliable operation of electric fuel systems is of paramount importance. These systems are responsible for delivering fuel to meet the demanding requirements of aircraft propulsion. However, traditional one-way valves used in electric fuel systems have been associated with significant power losses and difficulties in quickly blocking fuel reverse backflow, leading to inefficiencies and potential hazards during engine operation.

To address these challenges, this study proposes a novel design of a pump boost valve specifically tailored for electric fuel systems in aerospace engines [6]. The main valve spool is designed as a baffle structure, and a backflow damping mechanism is incorporated to enhance the valve's performance. The primary objective of this design is to achieve efficient flow distribution between the main and auxiliary fuel circuits during the engine startup phase, thereby reducing ineffective power loss and improving overall system efficiency.

The proposed pump boost valve design aims to overcome the limitations of traditional one-way valves by introducing the baffle spool to effectively block reverse fuel backflow and implementing the backflow damping mechanism to regulate the valve's dynamic and static characteristics. Furthermore, the study explores the influence of key parameters such as spring stiffness, spool diameter, and backflow damping hole on the static and dynamic characteristics of the electric fuel pump.

The findings of this research contribute to the advancement of electric fuel systems in aerospace engines by addressing the challenges associated with power losses and fuel reverse backflow. The proposed pump boost valve design offers a promising solution to improve the efficiency and reliability of electric fuel systems. By optimizing the valve's static and dynamic characteristics, this study provides valuable insights for the design and optimization of electric fuel systems in aerospace applications.

2 Design Principles of Boost Valve

2.1 Working Principle of Traditional Boost Valve

As shown in Fig. 1, the electric fuel pump consists of a gear pump, a main fuel pressure valve, an overflow valve, and a motor. The motor is directly connected to the gear pump [7], driving it to rotate and supply fuel to the fuel system. When the motor speed is low, the pressure in front of the pressure valve is insufficient to push open the valve core, and at this time, the auxiliary fuel circuit supplies fuel separately. As the motor speed increases, the pressure in front of the pressure valve exceeds the opening pressure of the valve, allowing both the main fuel circuit and the auxiliary fuel circuit to supply fuel simultaneously. When the speed reaches a certain value, the auxiliary fuel circuit is manually closed, and at this point, the main fuel circuit supplies fuel alone.

Fig. 1
A diagram of a conventional electric fuel pump highlights various components including the motor, gear pump, boost valve, and the main and auxiliary fuel circuit nozzles.

Schematic diagram of a conventional electric fuel pump

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The traditional fuel pump employs a one-way valve as the boost valve [8]. In order to enhance the power-to-weight ratio and reliability of aviation engines, modern electric fuel pump systems incorporate two fuel circuits: the auxiliary circuit and the main circuit. The main circuit exhibits relatively lower flow resistance compared to the auxiliary circuit. During the engine startup phase, there exists a certain flow distribution relationship between the main and auxiliary circuits. Typically, a boost valve is installed in the main circuit to satisfy the aforementioned flow distribution relationship, as depicted in Fig. 1. Once the engine startup is complete, the auxiliary circuit is closed, and the engine is supplied with fuel solely through the main circuit.

However, the presence of a high-flow-resistance boost valve in the main circuit results in significant power losses for the electric fuel pump. This not only doubles the required input power for the motor but also severely impacts the endurance of the aircraft. Furthermore, when the motor ceases rotation, there is a risk of reverse backflow of fuel. The conventional one-way valve structure of the boost valve encounters difficulties in promptly blocking the fuel flow, thereby affecting the normal operation of the engine fuel system.

2.2 New Structure and Working Principle of the Novel Boost Valve

In order to address the issues associated with conventional solutions, a new boost valve needs to be investigated [9]. This valve core should be capable of maintaining a certain flow distribution relationship between the main fuel circuit and the auxiliary fuel circuit, without causing significant pressure loss when the main fuel circuit supplies a high flow rate. The schematic diagram of the new structure of the boost valve for the electric fuel pump is shown in Fig. 2. This boost valve introduces a completely redesigned valve core.

Fig. 2
A diagram of an electric fuel pump depicts various components namely the motor, gear pump, and boost and overflow valves. The main fuel pump is connected to the boost valve and the auxiliary fuel path is connected to the gear pump and boost valve.

Schematic diagram of the electric fuel pump

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The boost valve consists of an inlet, an outlet, a return port, a housing, a valve seat, a valve core, and a spring assembly. The valve seat is designed in a nozzle structure, while the valve core adopts a baffle structure. The valve core is installed inside the boost valve, with one end connected to one end of the spring assembly and the other end forming a throttle orifice with the valve seat, which acts as a nozzle baffle. The other end of the spring assembly is connected to the base of the housing.

During the engine starting phase, the throttle port formed by valve seat 2 and valve core 3 remains closed, and the starting fuel circuit is supplied independently as Fig. 3. As the fuel pressure increases, it overcomes the spring force and hydraulic pressure acting on the end face of the boost valve outlet core, causing a certain opening in the throttle port formed by valve seat 2 and valve core 3. The fuel flows through the throttle port and exits through the boost valve outlet 6, achieving flow matching between the starting fuel circuit and the main fuel circuit.

Fig. 3
A diagram of a boost valve structure depicts various components such as the valve body, valve seat, valve core, two return oil damping ports, fuel pump inlet, and boost valve return port.

Schematic diagram of boost valve structure

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The fuel medium in the chamber where the boost valve spring assembly 4 is located flows back to the fuel pump inlet 5 through the boost valve return port 7, passing through the return oil damping port 4. The role of the return oil damping port 4 is to provide damping for the movement of the valve core 3, improving the dynamic characteristics and robustness of fuel flow control in the electric fuel pump system.

After the engine has completed the starting phase, the starting fuel circuit is closed, and all fuel from the boost valve outlet 6 must pass through the boost valve inlet 5. At this point, only the main fuel circuit supplies fuel. As the motor speed increases, the area of the throttle port increases, and the damping at the throttle port decreases.

When the throttle port reaches its maximum opening, even if the motor speed continues to increase, the opening no longer changes. At this point, the throttle port is in its lowest resistance state. Compared to traditional boost valves, the pressure in the spring chamber of this boost valve is lower, facilitating the movement of the valve core to its extreme position.

When the electric fuel pump receives a parking command, the throttle port formed by the nozzle plate and valve closes rapidly under the action of the spring force and reverse fuel pressure, achieving a quick shutdown function. After closing, the throttle port maintains a high level of sealing.

3 Mathematical Modelling of Boost Valve

3.1 Mathematical Model of Traditional Boost Valve

Modelling using a cone valve as the spool of a check valve, denoted as valve A, as shown in Fig. 4 [10].

Fig. 4
A schematic of a check valve depicts a mechanical structure with labeled components including distances d P, d A, d R, d S, angles alpha, and pressures P 1, P 2. The components are interconnected in a complex system.

Check valve port and pressure on both sides

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$${d}_{a}={d}_{s}-2{x}_{v}\,\,{\text{sin}}\,\,\alpha \,\,{\text{cos}}\,\,\alpha$$
(1)
$${A}_{v}=\pi {x}_{v}{d}_{a}\,\,{\text{sin}}\,\,\alpha$$
(2)

As in Eqs. (1) and (2), \({d}_{a}\) is the diameter of the valve core at the flow section, \({d}_{s}\) is the diameter of the upstream channel in the valve port, \({x}_{v}\) is the valve port opening, α is the cone angle of the valve core, and \({A}_{v}\) is the cross-sectional area of the valve port. Equation (3) represents the flow equation of the valve port.

$$Q={C}_{d}{A}_{v}\sqrt{\frac{2({p}_{1}-{p}_{2})}{\rho }}$$
(3)

In the Eq. (3), \({C}_{d}\) is the flow coefficient, \(\rho\) is the density of the fuel, \({p}_{1}\) is the pressure in the upstream chamber of the valve port, and \({p}_{2}\) is the pressure in the downstream chamber of the valve port.

$${F}_{s}=2{C}_{v}{C}_{d}{A}_{v}({p}_{1}-{p}_{2})\,\,{\text{cos}}\theta$$
(4)

In the Eq. (4), \({F}_{s}\) represents the steady-state hydrodynamic force acting on the valve core, \({C}_{v}\) is the flow velocity coefficient ranging from 0.98 to 0.99, and \(\theta\) is the jet direction angle. The ideal jet angle is 69°.

$${F}_{1}=\frac{\pi }{4}{p}_{1}{({d}_{s}-2{x}_{v}\,\,{\text{sin}}\,\,\alpha \,\,{\text{cos}}\,\,\alpha )}^{2}$$
(5)
$${F}_{2}=\frac{\pi }{4}{p}_{2}({d}_{p}^{2}-{d}_{a}^{2})$$
(6)

In the Eqs. (5) and (6), \({F}_{1}\) represents the pressure exerted on the valve core due to the action of the upstream fluid, while \({F}_{2}\) represents the pressure exerted on the valve core due to the action of the downstream fluid. The parameter \({d}_{p}\) refers to the diameter of the cylindrical section of the valve core.

The driving force on the valve core is determined by the pressure in the front chamber of the pressure relief valve. The driving force on the valve core will overcome the inertial force, spring force, and steady-state fluid dynamic force acting on the valve core. Neglecting transient fluid dynamic forces, the differential equation that governs the force balance on the valve core during dynamic processes is given by:

$${F}_{1}=m\frac{{d}^{2}x}{d{t}^{2}}+{K}_{1}{(x+x}_{0})+{F}_{s}+{F}_{2}$$
(7)

In the Eq. (7), \({x}_{0}\) represents the compression of the spring when the valve opening is zero, and \({K}_{1}\) is the spring stiffness.

3.2 Mathematical Model of the New Boost Valve

The main difference between this boost valve and the one-way valve is that the valve core is changed from a cone valve to a flat plate structure, and there is damping in the spring chamber to create a certain back pressure. We refer to this valve as Valve B, as shown in Fig. 3.

To analyse the dynamic and static characteristics of the new boost valve, a mathematical model is established based on its structural parameters and operating principles. The mathematical model takes into account the forces acting on the valve spool, including the inertial force, spring force, steady-state fluid dynamic force, and transient fluid dynamic force.

$$Q={C}_{d}\pi D{x}_{v}\sqrt{\frac{2({p}_{1}-{p}_{2})}{\rho }}$$
(8)

In the Eq. (8), \(D\) represents the diameter of the pressure acting surface in the front chamber of the pressure relief valve. The steady-state hydrodynamic force acting on the valve spool is.

$${F}_{s1}=2{C}_{v}{C}_{d}A({p}_{1}-{p}_{2})\,\,{\text{cos}}\,\,\theta$$
(9)

The driving force of the valve spool is determined by the pressure in the front chamber of the boost valve. It overcomes the inertial force, spring force, and steady-state fluid dynamic force acting on the spool. Neglecting the transient fluid dynamic force, the differential equation that describes the force equilibrium of the spool during the dynamic process is given by [11].

$${p}_{1}A=m\frac{{d}^{2}x}{d{t}^{2}}+{K}_{1}{(x+x}_{0})+{F}_{s1}+{p}_{2}{A}_{0}$$
(10)

In the Eq. (10), \({A}_{0}\) represents the effective area of the pressure acting on the spring chamber of the boost valve. \(m\) denotes the equivalent mass of the moving components of the valve, taking into account the mass of the valve spool and the spring.

The mathematical model provides insights into the dynamic behaviour of the new boost valve, allowing for the analysis of its response characteristics and performance optimisation. By solving the differential equation, the dynamic response of the valve spool can be obtained under different operating conditions and structural parameters, facilitating the design and evaluation of the new boost valve.

Next, this paper will discuss the simulation and analysis of the dynamic and static characteristics of the new boost valve based on the established mathematical model.

4 Simulation and Comparative Analysis of Static and Dynamic Characteristics of Traditional and New Boost Valves in AMESim

In this section, we will build the mathematical models of the traditional boost valve, referred to as Valve A in Fig. 4, and the new boost valve, referred to as Valve B in Fig. 3, in the AMESim simulation environment. By utilizing the simulation results, we will compare the static and dynamic characteristics of these two different boost valves. The key simulation parameters are shown in Table 1.

Table 1 Critical simulation parameters
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4.1 Comparison of Static Characteristics of Boost Valves

First, we compared the static characteristics of these two valves. The static characteristics primarily include the flow-pressure curve and the flow-valve position curve. By simulating under different operating conditions and plotting the corresponding curves, we can observe the performance differences between the two valves.

Figure 5 shows the comparison of the pressure- flow curves between Valve A and Valve B. By comparing the curves, we can observe that Valve B has a higher flow rate at the same pressure, indicating that Valve B has better flow control capability. The curve of Valve A is smoother, indicating that it can maintain a more stable flow output across different pressure ranges. By comparing the two sets of curves, we find that the new type of booster valve has lower pressure losses at the same flow rate. This means that using the new type of booster valve in the fuel system can reduce energy consumption and heat loss in the system.

Fig. 5
A graph plots inlet pressure in megapascal versus flow rate in liters per hour for the performance of two valves. Valve A starts at (400.6, 067) and ends at (2200.6, 0.86) and valve B starts at (390.6, 0.64) and ends at (2200.6, 0.69). Values are estimated.

Pressure-flow comparison chart

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Figure 6 illustrates the comparison of the flow-valve position curves between Valve A and Valve B. From the graph, it can be observed that at the same valve position, Valve B exhibits a significantly higher flow rate compared to Valve A, indicating that Valve B is capable of providing a greater flow output under the same control signal. Furthermore, the curve of Valve B is steeper, indicating that it is more sensitive to small adjustments in the valve position and possesses higher responsiveness.

Fig. 6
A graph plots flow in liters per hour versus spool position in millimeters for two valves. Valve A starts at (0.12, 400) and ends at (0.69, 2300) and valve B starts at (0.16, 410) and ends at (0.91, 2300). Values are estimated.

Flow-valve spool position comparison chart between new type boost valve and traditional boost valve

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4.2 Comparison of Dynamic Characteristics of the Boost Valve

By inputting a unit step velocity into the electric fuel pump system, the unit step response of the flow rate through the boost valve is obtained, as shown in Fig. 7. It can be observed that the traditionally designed boost valve, Valve A, exhibits significant overshoot with a steady-state accuracy of 1.3% and a settling time of 41 ms. In contrast, the new-type boost valve, Valve B, has a much smaller overshoot of only 2.7%, a steady-state accuracy of 1.4%, and a settling time of 40 ms. From the comparison, it is evident that Valve A has a significant overshoot, while both valves demonstrate similar steady-state accuracy and settling time. This indicates that the new-type boost valve has better dynamic performance compared to the traditionally designed boost valve, providing a smoother operation during startup.

Fig. 7
A graph plots flow in liters per hour versus time in seconds. The valves start at (1.00, 0) and end at (1.35, 2.25). Valves depict a significant initial spike at (1.10, 6.6) for A and (1.10, 2.25) for B before stabilizing. Values are estimated.

Comparison chart of dynamic characteristics between new type boost valve and traditional boost valve

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4.3 Analysis of Simulation Results for Valve Closing Speed

In the simulation experiment, we recorded the variations of the valve position over time for the conventional boost valve and the new boost valve. The closing speed of Valve A was measured to be 2.35 mm/s, while Valve B exhibited a closing speed of 2.55 m/s. It is evident that the new boost valve demonstrates a significant advantage in terms of closing speed. It can close the valve more rapidly, reducing the possibility of backflow and liquid reflux. This contributes to the improved stability and response speed of the fuel supply system. Through quantitative analysis of the simulation data, we calculated the valve closing time for both the conventional boost valve and the new boost valve. The results clearly indicate that the new boost valve exhibits significantly shorter closing time, highlighting its superiority in terms of rapid response and backflow prevention.

Based on the analysis of the simulation results, we can draw the following conclusions: Firstly, the new boost valve demonstrates a clear advantage in terms of pressure loss. Compared to the conventional boost valve, it can minimize the energy loss in the system, thereby improving the efficiency and energy utilization of the fuel system. Secondly, the new boost valve exhibits a remarkable improvement in valve closing speed. It can close the valve more rapidly, effectively preventing backflow and liquid backflow, thus enhancing the stability and response speed of the system. Considering comprehensive analysis, the new boost valve demonstrates excellent performance in terms of pressure loss and valve closing speed. This makes it as an ideal choice for the electric fuel pump system, capable of improving the system’s operational efficiency and stability.

However, it is important to note that the simulation experiments were conducted under ideal conditions, and there may be other factors and constraints in practical systems. Therefore, further experimental validation and engineering optimization are required before applying the new boost valve to real-world systems. In conclusion, the simulation results and analysis presented in this chapter validate the improvements achieved by the new boost valve in terms of pressure loss and valve closing speed. This provides strong theoretical and experimental evidence for the application and promotion of the new boost valve.

4.4 Comparison of Boost Valve Simulation and Experimental Results

The new boost valve was applied to an electric fuel pump, and a prototype of the electric fuel pump was constructed for bench testing. The pressure-flow characteristic curve of the electric fuel pump under no-load conditions was measured, and the experimental results were compared with the simulation results, as shown in Fig. 8. The maximum error was 8.6%, and the average error was 1.9% according to the Mean Absolute Error (MAE) as in Eq. (11). Therefore, the experimental results largely validated the correctness of the simulation model.

Fig. 8
A graph plots inlet pressure in megapascal and error percent versus flow rate in liters per hour. The graph has three lines labeled experimental results, simulation results with a slowly increasing trend, and error line with a rapidly decreasing trend followed by a linear movement.

Comparison of experimental and simulation results for boost valve pressure-flow curves

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$$MAE=\frac{1}{m}{\sum }_{i=1}^{m}\left|{y}_{i}-f({x}_{i})\right|$$
(11)

5 Analysis and Optimization of Factors Influencing Boost Valve Static and Dynamic Characteristics

5.1 Influence of Spring Stiffness on Boost Valve Static and Dynamic Performance

Without changing the preloading force of the regulating spring, only the stiffness coefficient is varied to 6N/mm, 7N/mm, and 8N/mm, respectively. From Fig. 9, it can be observed that as the stiffness coefficient increases, the inlet pressure increases at the same flow rate [12].

Fig. 9
A graph plots inlet pressure in megapascals versus flow rate in liters per hour. The graph has three lines labeled K = 6, 7, and 8 Newtons per millimeter, marked from the bottom left to the top right in an increasing trend.

Comparison of pressure-flow curves for boost valves with different spring stiffness

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By applying a step input of full flow rate, the dynamic response curves of the boost valve under three different spring stiffness values are obtained, as shown in Fig. 10. It can be observed that the curves almost overlap, indicating that the influence of spring stiffness on the dynamic performance is minimal, except for a slight variation in the steady-state value of the inlet pressure.

Fig. 10
A graph plots flow in liters per hour versus time in seconds. The graph has three lines labeled K = 7000, 8000, and 6000 Newtons per millimeter. The lines have a sharp rise at (1.0, 0) and stabilize with a linear movement at (1.1, 2.1). Values are estimated.

Comparison chart of dynamic characteristics of boost valves with different spring stiffness

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5.2 Influence of Main Spool Diameter on Boost Valve Static and Dynamic Performance

The diameter of the main spool has a significant impact on the static characteristics of the boost valve, as shown in Fig. 11. Three different main spool diameters of 5 mm, 10 mm, and 15 mm are considered. As the main spool diameter increases, the inlet pressure gradually decreases at the same flow rate.

Fig. 11
A graph plots inlet pressure in megapascal versus flow rate in liters per hour. The graph has three lines labeled D = 5, 10, and 15 millimeters. As the diameter increases, the inlet pressure decreases at a given flow rate. The 5 millimeter diameter maintains a steady high pressure across all flow rates.

Pressure-flow curve at different main valve spool diameters

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In terms of dynamic characteristics, an increase in the main spool diameter results in a decrease in the output pressure during dynamic response, as shown in Fig. 12. When the main spool diameter is 5 mm, there is a significant overshoot. As the spool diameter increases, the overshoot, settling time, and steady-state accuracy all decrease. Considering the design requirements of the electric fuel pump and the static characteristics, it is important to select an appropriate main spool diameter.

Fig. 12
A graph plots flow in liters per hour versus time in seconds. The spool diameters 10, 15, and 5 millimeter, start at (1.00, 0) and end at (1.45, 2.25). The spool diameters depict a significant initial spike at (1.01, 3.0) for 5 m m and (1.01, 2.25) for 10 and 15 millimeters before stabilizing. Values are estimated.

Comparison chart of dynamic characteristics of boost valves with different spool diameter

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5.3 Influence of Return Damping Orifice Diameter on Static and Dynamic Performance of the Boost Valve

By varying the diameter of the return damping orifice, it is possible to alter the back pressure in the spring chamber, thereby affecting the static and dynamic performance of the electric fuel pump. As shown in Fig. 13, increasing the diameter of the return damping orifice reduces the back pressure in the spring chamber, resulting in a lower opening pressure of the boost valve. Having a certain back pressure ensures that the valve core closes faster when the electric fuel pump stops working, preventing backflow of the fuel.

Fig. 13
A graph plots inlet pressure in megapascal versus flow rate in liters per hour. The graph has three lines labeled d = 3, 4, and 5 millimeters. The lines depict that as the flow rate increases, the inlet pressure initially decreases from mid-left and then rises to the top right.

Comparison of pressure-flow curves of boost valves at different orifice diameters

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The step response of the electric fuel pump flow under different damping orifice diameters is shown in Fig. 14. It can be observed that changing the diameter of the damping orifice has a minimal impact on the system’s dynamic response.

Fig. 14
A graph plots flow in liters per hour versus time in seconds. The diameters 3, 4, and 5 millimeters, start at (1.00, 0) and end at (1.35, 2.25). The diameters depict a significant initial spike at (1.01, 2.25) before stabilizing. Values are estimated.

Comparison of flow Step response of boost valves at different orifice diameters

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6 Conclusion

In conclusion, through the study and comparison of the static and dynamic characteristics of the traditional and new-type boost valves in the electric fuel pump system, the following conclusions can be drawn. The new-type boost valve exhibits better flow control capability and lower pressure loss. In terms of dynamic performance, the new-type boost valve demonstrates faster response time, smaller overshoot, and higher steady-state accuracy. Factors such as spring stiffness, main valve core diameter, and damping hole diameter have certain influences on the performance of the boost valve. However, the damping hole diameter has minimal effect on the system's dynamic response. Overall, the new-type boost valve shows excellent performance in reducing pressure loss, improving response speed, and enhancing stability. It provides valuable insights for the design and optimization of electric fuel pump systems. Further research is needed to validate and optimise the application of the new-type boost valve in practical systems.