A mimicking technique of back pressure in the hardware-in-the-loop simulation of a fuel control unit

Abstract

In the hardware-in-the-loop (HIL) simulation of the fuel control unit (FCU) for aero-engines, the back pressure has a great impact on the metered fuel, thus influencing the confidence of the simulation. During the practical working process of an aero-engine, the back pressure of the FCU is influenced by the combined effect of the pressure of the combustion chamber, the resistance of the spray nozzles, and the resistance of the distribution valve. There is a need to study the the mimicking technique of FCU back pressure. This paper models the fuel system of an aero-engine so as to reveal the impact of FCU back pressure on the metered fuel and come up with a scheme to calculate the equivalent FCU back pressure. After analyzing the requirements for mimicking the pressure, an automatic regulating facility is designed to adjust the FCU back pressure in real time. Finally, experiments are carried out to verify its performance. Results show that the mimicking technique of back pressure is well suited for application in HIL simulation. It is able to increase the confidence of the simulation and provide guidance to the implementation of mimicking the FCU back pressure.

Keywords

Back pressure hardware-in-the-loop simulation fuel control unit aero-engine mimicking technique

1. Introduction

Hardware-in-the-loop (HIL) simulation enables the operation and testing of actual components of a system along with virtual computer-based simulation models of the rest of the system in real time.^1,2 In this way, the quality of testing is enhanced, thus shortening the design cycle and improving the reliability of the tested components.

The fuel control unit (FCU) is a fuel-metering device that regulates the fuel flow to the engine in accordance with the pilot’s demand, ambient environmental conditions, and other related factors. It is a crucial part of engine control system. Usage of HIL simulation for testing the aero-engine FCU has been reported in several researches for different purposes. Montazeri-Gh et al.^3,4 investigated the complex interaction between the FCU hardware and overall aircraft performance, while Karpenko and Sepehri⁵ objectively tested novel fault tolerant control and diagnostics algorithms for fluid power actuators. Principles of the fuel control are presented by Tudosie,⁶ among which the type with constant fuel differential pressure and an adjustable fuel window is most widely used. However, the performance of the electro-hydraulic FCU can be influenced by changes in the characteristics of the operating environment and by changes in the system parameters.³ As a result, whether the differential pressure across a fuel-metering valve could maintain constant remains a question. You et al.⁷ investigated the influence of fluctuant inlet pressure on the characteristics of the FCU for a ramjet. Gaudet⁸ presented an approach for controlling fuel flow in which the differential pressure across a fuel-metering valve is regulated by simultaneously varying the pump displacement and a small amount of bypass flow.

In the practical fuel system of an aero-engine, fuel is injected into combustion chambers through the FCU, fuel distribution valve, and spray nozzles. So, the back pressure of the FCU is equal to the sum of the back pressure of the spray nozzles, which is the outlet pressure of the engine compressor or the burner pressure, and the pressure drop of the fuel distribution valve as well as the spray nozzles. However, they both change with the operating state of the aero-engine. According to some researches,^9,10 fuel regulated by the FCU is closely related to its back pressure. Regulating effects differ even in cases of the same metering valve opening but with different back pressure, which influences the confidence of the simulation. So, it is necessary to adjust the back pressure of the FCU in real time. A common way to simulate the pressure is to use a throttle valve with either a fixed orifice or a manually adjusted orifice. It is readily apparent that its real-time performance cannot be guaranteed, which brings about new approaches. One of them is to simulate the atmospheric environment of the combustion chamber. This approach requires complicated devices that are of high cost. A much simpler way is to design an automatically adjusted valve that regulates the back pressure of the FCU according to the real-time engine state.

In this paper, mimicking technique of back pressure that is used in HIL simulations of FCUs for aero-engines is studied. In Section 2, the mathematical model and AMESim model of the fuel system are established, which reveal the working principle of each component. Then, the effect of the FCU back pressure on metered fuel is investigated with the AMESim model in Section 3. Also, decisive factors of FCU back pressure and its calculation scheme are discussed in this part. Afterwards, requirements for simulating back pressure are put forward and an automatic regulating facility is finally designed in Section 4. Finally, in Section 5, experiments are conducted to verify the performance of the facility and its application in the HIL simulation.

2. Modeling of the fuel system

In order to know how the FCU works, how its back pressure changes, and how it influences the metered fuel, each component of the fuel system should be analyzed. Taking a certain turbofan engine, for example, its fuel system includes a gear pump, FCU, fuel distribution valve, and spray nozzle, while the FCU includes a metering valve, a pressure drop valve, a fuel return valve, and a pressure rising valve, shown in Figures 1 and 2. The gear pump is driven by a high-pressure turbine after changing shaft speed by the gearbox. It generates flow with enough power to overcome pressure induced by the load at the pump outlet. The electro-hydraulic servo valve controlled by the electronic control unit (ECU) changes the pressure of the control chamber of the metering valve, thus changing its displacement, which is then acquired by an LVDT displacement sensor and sent to the ECU for closed-loop control.¹¹ There is a linear relationship between the opening area and the displacement of the metering valve. The pressure drop valve senses the pressure at the inlet and outlet of the metering valve and adjusts the control fuel pressure of the fuel return valve, so as to adjust the displacement of the return valve, therefore adjusting the quantity of return fuel. If the pressure difference increases as the pump speed rises or the opening of the metering valve becomes smaller, the pressure drop valve feels the change of pressure difference and moves upwards, decreasing the control fuel pressure of the return valve. This leads to the upward movement of the return valve, resulting in the increase of return fuel and therefore the decrease of metered fuel. In consequence, the pressure difference is approximately held constant. Given this, fuel passing through the metering valve is only decided by its opening area, which means that the ECU is able to control the fuel quantity by controlling the displacement of the metering valve. The pressure increasing and the shut off valve act like “hydraulic resistance,” increasing the fuel pressure. Fuel metered by the FCU is then distributed by the fuel distribution valve and sprayed into the combustion chambers.

Figure 1.

Components of the fuel system. PRSOV: pressure raising and shut off valve.

Figure 2.

Schematic diagram of the fuel system. PRSOV: pressure raising and shut off valve; FCU: fuel control unit.

2.1. Mathematical model

2.1.1. Gear pump

The relationship between the fuel $Q$ generated by the gear pump and its rotational speed $n$ is given by the following equation:

Q = l \cdot n,

(1)

where $l$ represents the fuel per rotation of the pump.

2.1.2. Fuel-metering valve

The metering valve is the key component of the FCU, shown in Figure 1. It controls the fuel through the combustion chamber, called the metered fuel and denoted by $Q_{fm}$ , which can be calculated with the following equation:

Q_{fm} = μ_{fm} A_{fm} \sqrt{\frac{2 (p_{1} - p_{2})}{ρ}},

(2)

where $μ_{fm}$ is the flow coefficient, $A_{fm}$ is the opening of the metering valve, and $ρ$ is the fuel density. $p_{1}$ and $p_{2}$ are the pressure at the inlet and outlet of the metering valve, respectively.

2.1.3. Pressure drop valve

The pressure drop valve maintains the difference of $p_{1}$ and $p_{2}$ , whose structure is shown in Figure 3. $p_{1}$ and $p_{2}$ act on the right- and left-hand sides of the pressure drop valve, respectively. Force caused by the pressure difference balances the force of spring that is located in the left chamber of pressure drop valve when in a steady state, which yields the following:

(p_{1} - p_{2}) A_{pd} = k_{pd} x_{pd},

(3)

where $A_{pd}$ is the spool area of the pressure drop valve, $k_{pd}$ is the spring stiffness and, $x_{pd}$ is the spring compression.

Figure 3.

Structure of the pressure drop valve.

2.1.4. Fuel return valve

The fuel return valve transmits the spare fuel to the inlet of the gear pump, whose structure is shown in Figure 4. There is a center hole in the return valve, through which a portion of the inlet fuel of the metering valve flows into the pressure drop valve and then combines with the outlet fuel of the metering valve, forming a “hydraulic potentiometer” whose working medium is the inlet fuel of the metering valve.¹² Fuel that flows through the center hole, denoted by $Q_{fo}$ , can be computed as follows:

Q_{fo} = μ_{fo} A_{fo} \sqrt{\frac{2 (p_{1} - p_{pd})}{ρ}},

(4)

where $μ_{fo}$ is the flow coefficient, $p_{pd}$ is the pressure, and $A_{fo}$ is the area of the center hole. The fuel stated above joins the outlet fuel from the metering valve. So, it can also be calculated as follows:

Q_{fo} = μ_{fo} C_{pd} x_{pd} \sqrt{\frac{2 (p_{pd} - p_{2})}{ρ}},

(5)

where $C_{pd}$ is the perimeter of the pressure drop valve.

Figure 4.

Structure of the fuel return valve.

$p_{1}$ and $p_{pd}$ are applied to the right- and left-hand sides of the fuel return valve, respectively. The valve moves under these pressures so as to control its opening toward the inlet of the gear pump and therefore control the return fuel. When in a steady state, the force caused by the pressure difference balances the force of spring that is located in the left chamber of the return valve, which yields the following:

(p_{1} - p_{pd}) A_{fr} = k_{fr} x_{fr},

(6)

where $A_{fr}$ is the spool area of the fuel return valve, $k_{fr}$ is the spring stiffness, and $x_{fr}$ is the spring compression. Fuel that returns to the inlet of the gear pump is given as follows:

Q_{fr} = μ_{fr} C_{fr} x_{fr} \sqrt{\frac{2 (p_{1} - p_{0})}{ρ}},

(7)

where $μ_{fr}$ is the flow coefficient, $C_{fr}$ is the perimeter of the valve, and $p_{0}$ is the low pressure.

Considering the fuel continuity, there is the following:

Q_{fm} + Q_{fr} + Q_{fo} = Q .

(8)

2.1.5. Pressure raising and shut off valve

The pressure raising and shut off valve, abbreviated as PRSOV, works as a “hydraulic resistance,” increasing the fuel pressure and shutting off the fuel sometimes. Figure 5 displays its structure. $p_{2}$ and $p_{pr}$ act on the left- and right-hand sides of the PRSOV, respectively. Force caused by the pressure difference balances the force of the spring that is located in the chamber of the PRSOV when in a steady state, which gives the following:

(p_{2} - p_{pr}) A_{pr} = k_{pr} x_{pr},

(9)

where $A_{pr}$ is the spool area of the PRSOV, $k_{pr}$ is the spring stiffness, and $x_{pr}$ is the spring compression. Metered fuel flows through the PRSOV as follows:

Q_{fm} = μ_{pr} C_{pr} x_{pr} \sqrt{\frac{2 (p_{2} - p_{3})}{ρ}},

(10)

where $μ_{pr}$ is the flow coefficient, $C_{pr}$ is the perimeter of the valve, and $p_{3}$ is the outlet fuel pressure of the PRSOV.

Figure 5.

Structure of the pressure raising and shut off valve.

2.1.6. Fuel distribution valve and spray nozzles

The fuel distribution valve distributes fuel into two kinds of combustion chambers, the first called the pre-burner and the second called main combustion chamber,¹³ represented by $Q_{fd, s}$ and $Q_{fd, m}$ , respectively. Then the spray nozzles atomize the fuel and spray it into the combustion chambers.¹⁴ They can usually be treated as fixed orifices.

2.1.7. Steady-state model of the fuel system

Based on the equations stated above, the model that relates one variable to another can be derived. Take the inlet fuel pressure of the metering valve, $p_{1}$ , and the pressure of combustion chamber, $p_{b}$ , for example. Other models can be achieved in the same manner.

Substituting (3) into (5), then:

Q_{pd} = \frac{μ_{pd} C_{pd} A_{pd} (p_{1} - p_{2})}{k_{pd}} \sqrt{\frac{2 (p_{pd} - p_{2})}{ρ}} .

(11)

Inserting (11) into (4) leads to the following:

K_{1} \sqrt{(p_{1} - p_{pd})} = K_{2} (p_{1} - p_{2}) \sqrt{(p_{pd} - p_{2})},

(12)

where $K_{1} = μ_{fo} A_{fo} \sqrt{\frac{2}{ρ}}, K_{2} = \frac{μ_{pd} C_{pd} A_{pd}}{k_{pd}} \sqrt{\frac{2}{ρ}}$ .

Substituting (6) into (7), then:

Q_{fr} = \frac{μ_{fr} C_{fr} A_{fr} (p_{1} - p_{pd})}{k_{fr}} \sqrt{\frac{2 (p_{1} - p_{0})}{ρ}} .

(13)

Inserting (2) and (13) into (8) and considering that $Q_{fo}$ is so small compared to $Q_{fm}$ and $Q_{fr}$ that it can be neglected for simplicity leads to the following:

K_{3} \sqrt{(p_{1} - p_{2})} + K_{4} (p_{1} - p_{pd}) \sqrt{(p_{1} - p_{0})} = Q,

(14)

where

K_{3} = μ_{fm} A_{fm} \sqrt{\frac{2}{ρ}}, K_{4} = \frac{μ_{fr} C_{fr} A_{fr}}{k_{fr}} \sqrt{\frac{2}{ρ}} .

Combining (12) with (14) and eliminating $p_{pd}$ , there is the following:

K_{3} \sqrt{(p_{1} - p_{2})} + K_{4} \frac{{K_{1}}^{2} {(p_{1} - p_{2})}^{3}}{{K_{1}}^{2} + {K_{2}}^{2} {(p_{1} - p_{2})}^{2}} \sqrt{(p_{1} - p_{0})} = Q .

(15)

This equation demonstrates the relationship between the inlet and outlet fuel pressure of the metering valve, namely, $p_{1}$ and $p_{2}$ , in steady state.

Given that fuel through the distribution valve and nozzle is continuous, the combined effect of the distribution valve and nozzle can be represented with an equivalent throttle facility, called “facility 1.” So, there is the following:

Q_{fm} = Q_{fd, m} + Q_{fd, s} = μ_{eq 1} A_{eq 1} \sqrt{\frac{2 (p_{3} - p_{b})}{ρ}},

(16)

where $μ_{eq 1}$ is the flow coefficient of facility 1 and $A_{eq 1}$ is its area.

Similarly, fuel through the PRSOV and facility 1 is continuous. We can use another equivalent facility, called “facility 2,” to express their joint effect. Substituting (9) into (10), then combining with (16):

Q_{fm} = μ_{eq 2} A_{eq 2} \sqrt{\frac{2 (p_{2} - p_{b})}{ρ}},

(17)

where $μ_{eq 2}$ is the flow coefficient of facility 2 and $A_{eq 2}$ is its area, and:

μ_{e q 2} A_{e q 2} = \frac{(μ_{p r} C_{p r} x_{p r}) (μ_{e q 1} A_{e q 1})}{\sqrt{{(μ_{p r} C_{p r} x_{p r})}^{2} + {(μ_{e q 1} A_{e q 1})}^{2}}} .

Equation (17) and (2) present the same thing, which yields the following:

p_{b} = p_{2} - K_{5} (p_{1} - p_{2}),

(18)

where

K_{5} = {(\frac{μ_{f m} C_{f m} x_{f m}}{μ_{e q 2} A_{e q 2}})}^{2} .

Solving (15) and (18), the relationship between $p_{1}$ and $p_{b}$ in steady state is finally obtained:

\begin{matrix} K_{3} \sqrt{\frac{p_{1} - p_{b}}{1 + K_{5}}} + \frac{K_{4} {K_{1}}^{2} {(p_{1} - p_{b})}^{3}}{{K_{1}}^{2} {(1 + K_{5})}^{3} + {K_{2}}^{2} (1 + K_{5}) {(p_{1} - p_{b})}^{2}} \\ \sqrt{(p_{1} - p_{0})} = Q . \end{matrix}

(19)

In brief, it can be clearly seen from Equation (15) that the pressure difference of the pressure drop valve will not always remain constant, resulting in the change of the metered fuel even in the case of fixed $A_{fm}$ . What is more, it is influenced by the nozzle back pressure in a complicated manner, since the model in (19) not only appears to be nonlinear but also has varying coefficients.

2.2. AMESim model

Since the mathematical model involves many variables and parameters, it is not likely to be comprehended intuitively and it is not convenient to get or display all variables, such as force, displacement, flow resistance, and so on. So, an AMESim model may facilitate the research. After analyses of the structure of each component, the model is established in Figure 6.^15,16

Figure 6.

AMESim model fuel system.

3. Effect of the fuel control unit back pressure on metered fuel

3.1. Effect of the nozzle back pressure on metered fuel

Firstly, the situation (denoted as situation 1) of the fixed opening of the metering valve (denoted as $A_{fm}$ ) but different nozzle back pressure, namely $p_{b}$ , are investigated, as shown in Figure 7. Increasing $p_{b}$ from 6 to 10 bar at 6 s and from 10 to 14 bar at 13 s, it can be seen from Figure 7(a) that both the inlet and outlet pressure of the metering valve, namely $p_{1}$ and $p_{2}$ , increase accordingly. Meanwhile, metered fuel decreases from 16.27 to 16.03 and 15.86 L/min respectively, shown in Figure 7(b). This is the consequence of the movement of the pressure drop valve. When $p_{b}$ becomes higher, $p_{2}$ becomes higher too, forcing the pressure drop valve to move rightward, thus loosening the spring, as depicted with a black line in Figure 7(c). As $p_{1}$ increases correspondingly, the spring force balances the pressure difference again, except for the reduction of spring compression, resulting in the decrease of $p_{1} - p_{2}$ , displayed with a red line. In conclusion, the metered fuel $Q_{fm}$ reduces with the increase of the nozzle back pressure $p_{b}$ , which demonstrates the necessity of our research. In order to obtain a similar $Q_{fm}$ in HIL simulations as in actual situations, it is recommended that the precision tolerance of $p_{b}$ be within 5%.

Figure 7.

Variables in situation 1. (Color online only.)

3.2. Relation between FCU back pressure and nozzle back pressure

First considering the case in Section 3.1, the FCU back pressure $p_{3}$ grows with the nozzle back pressure $p_{b}$ , shown as the red line and black lines, respectively, in Figure 7(d). However, their difference, depicted with the blue line, almost remains constant in this case. Then think about the situation (denoted as situation 2) of varying $A_{fm}$ and fixed $p_{b}$ , as we can see in Figure 8. Increasing $A_{fm}$ at 6 and 12.5 s in a ramp and sinusoidal manner, respectively, $Q_{fm}$ increases as expected. It can be seen that $p_{3}$ increases in the same manner simultaneously. In this regard, the difference between $p_{3}$ and $p_{b}$ arises owing to the change of pressure drop in the distribution valve and spray nozzles which is induced by the fuel change.

Figure 8.

$p_{3}$ and $Q_{fm}$ in situation 2.

3.3. Calculation scheme for FCU back pressure

The results gained in Section 3.2 are on the premise of fixed $A_{fm}$ or fixed $p_{b}$ , while actually both of them change in real time during operation of the engine.

From Equation (16), the total pressure drop of the fuel distribution valve and spray nozzles, denoted as $Δ p$ , can be obtained as follows:

Δ p = p_{3} - p_{b} = \frac{ρ {Q_{fm}}^{2}}{2 {(μ_{eq 1} A_{eq 1})}^{2}} .

(20)

It is readily apparent that $Δ p$ is proportional to the square of $Q_{fm}$ and inversely proportional to the square of $μ_{eq 1} A_{eq 1}$ . Suppose there is a steady point D, and let:

α = \frac{Δ p_{, D}}{{Q_{fm, D}}^{2}},

(21)

where the subscript D denotes the specific value of $Δ p$ and $Q_{fm}$ around point D. Then, (20) can be approximated as follows:

Δ p = α \cdot β \cdot {Q_{fm}}^{2},

(22)

where $β$ is termed the compensating factor, which serves to compensate the error introduced by $μ_{eq 1} A_{eq 1} .$ As $Q_{fm}$ increases, the distribution valve opens up and $x_{fd}$ is therefore enlarged, which leads to the increase of $μ_{eq 1} A_{eq 1}$ . So, $β$ ought to be reduced with the increase of $Q_{fm}$ . $β$ can be obtained from simulations, experiments or the approximate formula as follows:

β = {(\frac{Q_{fm, D}}{Q_{fm}})}^{m},

(23)

where m can be selected or adjusted based on actual situations, usually ranging from 1/12 to 1/2. $β$ is equal to 1 at steady point D.

Consider the situation in Section 3.2. Selecting a steady point where $Q_{fm, D}$ is 30.728 L/min, $Δ p_{, D}$ is 7.74 bar, then $α$ is equal to 8.216 × 10⁻³. Selecting m = 1/8, then $Δ p$ can be calculated with (22), as is depicted with the black and dashed line in Figure 9, while the red line is the simulated value of $Δ p$ in Section 3.2. The difference is so small that we can use Equation (22) to compute $Δ p$ . Hence, the FCU back pressure $p_{3}$ is gained:

p_{3} = α \cdot β \cdot {Q_{fm}}^{2} + p_{b} .

(24)

Figure 9.

Calculated fuel control unit back pressure. (Color online only.)

4. Mimicking scheme for fuel control unit back pressure

In this section, we talk about how to design a facility that regulates $p_{3}$ automatically while satisfying the requirements for HIL simulation. So, firstly, the requirements for simulating $p_{3}$ are discussed and then the regulating facility is schemed out.

4.1. Requirements for the mimicking of FCU back pressure

Starting with requirements for the settling time of $p_{3}$ , we should first investigate the operation process of the engine, that is, from idling state(speed) to maximum state(speed). A schematic demonstrating the closed-loop control of the engine speed is shown in Figure 10. It consists of two loops, an inner loop called the control loop of metered fuel and an outer loop called the control loop of rotational speed. The principle of the inner loop has been described in the foreword of Section 2. In the outer loop, the engine speed is collected and sent to the ECU for comparison with the instructed rotational speed, thus figuring out the instructed position of the metering valve and adjusting metered fuel through the inner control loop. Meanwhile, the rotational speed decides the fuel generated by the gear pump and the outlet pressure of the compressor influences the fuel metered by the FCU. It is believed that the settling time of $p_{3}$ corresponds to that of the rotational speed or metered fuel. In general, the speed settling time of an aero-engine from idling to maximum is around 5–6 s.^13,17 Therefore, the regulating facility should at least be able to follow the settling time of $p_{3}$ , that is, 5 s from idling to maximum. Furthermore, the bandwidth of the regulating facility should be wider than that of the fuel control loop, which is generally a value of 2–3 Hz.

Figure 10.

Schematic diagram of the engine speed control loop. ECU: electronic control unit.

So, integrated with Section 3, for the requirements for simulating $p_{3}$ , it is put forward that the precision tolerance of $p_{3}$ should be within 5%, the settling time of $p_{3}$ ought to be less than 5 s from idling to maximum, and the bandwidth of the regulating facility should be over 3 Hz.

4.2. Design of the automatic regulating facility

Coming next is the design of the automatic regulating facility based on the requirements described in Section 4.1. The working principle of the facility is shown in Figure 11. It is also comprised of two control loops. A throttle valve is installed at the outlet of the FCU, the opening of which can be adjusted by the valve rod. A motor is attached to the valve, turning the valve rod. The displacement of the rod, namely the position of the valve, is acquired by a permanent linear contactless displacement (PLCD) sensor, which is installed normal to the rod sent back to the controller. Fuel flows through the valve and thus generates pressure. The pressure is then collected by a pressure sensor and sent to the controller. Together with the instructed pressure calculated with Equation (24), an instructed position of the valve is figured out. Comparing it with the real position from the PLCD sensor, the deviation generates pulse signals that adjusts the valve rod so as to changes the valve opening, thereby regulating the fuel pressure. Finally, the automatic regulating facility comes out, as shown in Figure 12.

Figure 11.

Principles of the automatic regulating facility. PLCD: permanent linear contactless displacement.

Figure 12.

The automatic regulating facility. 1: motor; 2: rod; 3: magnetic ring; 4: valve; 5: permanent linear contactless displacement.

5. Hardware-in-the-loop simulation based on fuel control unit back pressure

Now that the automatic regulating facility of the FCU back pressure has been designed, it is time to carry out experiments for the purpose of validating its regulating ability and its application in HIL simulations. The test platform is as shown in Figure 13.

Figure 13.

Hardware-in-the-loop simulation test platform. 1: fuel tank; 2: booster pump 3: fuel control unit; 4: automatic regulating facility; 5: controller; 6: pressure transducer; 7: flow meter.

5.1. Validation of the regulating ability of FCU back pressure

Keeping the metered valve at the maximum opening and adjusting the instructed $p_{3}$ , the experimental result (denoted as situation 3) is exhibited in Figure 14. The black line in Figure 14(a) indicates the instructed $p_{3}$ and the red line represents the real $p_{3}$ . It is viewed that the real $p_{3}$ is able to keep up with the change of instructed $p_{3}$ . From the partially enlarged view, it can be seen that when the instructed $p_{3}$ is increased from 26.8 to 34.1 bar at 13.7 s, the real $p_{3}$ matches well with it in about 1 s, with a delay of 300 ms and no overshoot. The error of steady-state values is within 0.4 bar. As is seen in the experiments, the steady-state error is within 0.5 bar throughout the whole regulating process. So, the facility is able to satisfy the requirements of accuracy. Given that the regulation range of $p_{3}$ is from 10 to 50 bar, a variation of 7.3 bar is very large step and it only takes 1 s to settle down. So, the automatic regulating facility can satisfy the requirement for real-time simulations.

Figure 14.

Variables in situation 3. (Color online only.)

In addition, the black line in Figure 14(b) shows the change of $Q_{fm}$ as a result of the change of $p_{3}$ , shown by the red line. The result proves the conclusion in Section 3, that $Q_{fm}$ reduces with the increase of $p_{3}$ .

5.2. HIL simulation of a FCU based on the mimicking technique of back pressure

In order to apply the mimicking technique to practice and verify its performance, a HIL simulation (denoted as situation 4) is carried out. Adjusting the instructed rotational speed from idling to maximum step by step, with the blue dashed line in Figure 15(a), the real engine speed shown with the red line varies correspondingly and settles down in complete agreement. Beyond doubt this is a result of the change of metered fuel, displayed with a black line. $Q_{fm}$ brings about the change of operation state, including $p_{3}$ , which is the instructed $p_{3}$ , shown with a black line in Figure 15(b). Then the automatic regulating facility reacts, leading to the change of real $p_{3}$ , shown with a red line. We can see that the real $p_{3}$ follows the instruction as desired. In turn, the back pressure influences the metered fuel. It can be seen from the enlarged view in Figure 15(a) that when instructed speed increases from 86.6% to 92.8% at 40.15 s, the real speed follows in 0.8 s. The $Q_{fm}$ also settles down in 0.9 s. From the enlarged view in Figure 15(b), the instructed $p_{3}$ increases from 23.9 to 29.1 bar in 0.5 s and only jitters on a very small scale. The real $p_{3}$ responds with a delay of about 150 ms and no remarkable overshoot. The settling time is about 0.8 s with a steady-state error of nearly 0.1 bar. Throughout this simulation, the settling time for a large step change of $p_{3}$ is no more than 1 s and its steady error is within 2%.

Figure 15.

Variables in situation 4. (Color online only.)

6. Conclusion

This paper studies the mimicking technique of back pressure, which is used in HIL simulations of FCUs for aero-engines. Firstly, it establishes models of the fuel system, which reveals the working principle of each component. Then, the effect of FCU back pressure on metered fuel is investigated with the AMESim model, and it is found that the metered fuel reduces with the increase of back pressure. Afterwards, the determinants of FCU back pressure are discussed, thus coming up with the calculation scheme for its application in HIL simulations. After that, the mimicking scheme for FCU back pressure is established. The requirements for simulating the pressure are put forward before we design an automatic regulating facility. Finally, experiments are conducted to verify the performance of the facility and its application in the HIL simulation. Results show that throughout this simulation, the settling time of FCU back pressure controlled by the automatic regulating facility for a large step change is no more than 1 s and its steady error is within 2%, which proves its application in the HIL simulation and increases confidence thereof.

Footnotes

Funding

The authors disclosed receipt of the following financial support for the research, authorship, and/or publication of this article: This work was supported by Postgraduate Research & Practice Innovation Program of Jiangsu Province (KYCX19_0186).ss

ORCID iD

Yuan Yuan_

Author biographies

Mr Yuan Yuan is a PhD candidate at College of Energy and Power Engineering, Nanjing University of Aeronautics And Astronautics. His doctoral research focuses on the fault tolerant control, optimal control and hardware-in-the-loop simulation for propulsion systems.

Mr Zhiwen Zhao is a PhD student in the Centre for Propulsion and Engineering at Cranfield University. He revceived his MSc in Aerospace Propulsion from Cranfield University. His primary research interests include the gas turbine performance simulation and turbine blade lifing techniques.

Dr Tianhong Zhang is a Professor of Aircraft Engine Control Technology at Nanjing University of Aeronautics And Astronautics, where he received his MAS and PhD. His primary research interests include modelling, simulation, and testing for engine control system.

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