A novel approach for predicting inlet pressure of aircraft hydraulic pumps under transient conditions

Yan WANG, Hongkang DONG, Yongling HE

School of Transportation Science and Engineering, Beihang University, Beijing 100083, China

KEYWORDS

Abstract Cavitation caused by insufficient suction is a major factor that influences the life of aircraft pumps. Currently, pressurizing the tank can solve the cavitation problem under steady largeflow conditions.However,this method is not always effective under transient conditions(from zero flow to full flow in a very short time). Moreover, to apply and design other measures, such as a boost impeller,the suction dynamics during the transient period must be investigated.In this paper,a novel approach based on the pressure wave propagation theory is proposed for predicting the inlet pressure of an aircraft pump under transient conditions.First,a dynamic model of a typical aircraft pump is established in the form of differential equations.Then,the transient flow model of the inlet line is described using momentum and continuity equations, and the governing equations are discretized by the method of characteristics and the finite difference method. The simulated results are in good agreement with the results from verification tests.Further simulation analysis indicates that the wave velocity and transient time may influence the inlet and reservoir pressure as well as the size of the inlet line. Finally, solutions for upgrading the inlet pressure are discussed. These solutions provide guidelines for designing inlet installations.

1. Introduction

When a positive displacement pump is driven at high speed with insufficient pressure,cavitation may occur due to the vacuum created during the intake stroke. Moreover, when flow demand is suddenly increased, the inertia of the fluid in the inlet line can reduce the pressure at the pump inlet below the critical value and produce cavitation. Cavitation in the pump is a severe problem that often causes low efficiency, vibration,and erosion,eventually leading to poor reliability.Pumps used in aircrafts, such as engine-driven pumps, are more likely to experience cavitation than that other engineering applications because they work at extremely high speeds.1-7Furthermore,the size and weight requirements for airborne components considerably limit the diameter of the inlet line. The separation between the tank and pump necessitates an elongated pipe.Therefore,the inlet supply system must be pressurized to avoid pump cavitation at all times,including during transient conditions (from zero flow to full flow in a very short time).

In practice, there exist some solutions for addressing the problem of cavitation, such as pressurizing the tank8,9and incorporating an integral boost impeller10,11(Fig.1). Currently, bootstrap- and pressurized-gas-type reservoirs are widely used in civil and military aircrafts.However,the cavitation phenomenon still occurs if tank pressurization is the only solution applied because the pressure loss in the suction line significantly limits the pressurization effect, especially during transient periods. The integral boost mechanism in the pump is very effective for preventing cavitation. It can also dissolve some of the entrained air.When the boost configuration is well designed, the critical inlet pressure of the pump combination can be reduced to 34.5-69 kPa(absolute pressure)12.However,the suction dynamic under transient conditions must be analyzed when adopting such a boost configuration.

Fig.1 Cross-section view of a typical civil aircraft pump.

Although few studies have examined the suction performance of an axial piston pump in transient conditions, many studies have examined transient flow in other engineering applications, such as long oil pipelines and nuclear reactor coolant systems. Chaudhry21introduced hydraulic transients in their monograph in a comprehensive and systematic manner and demonstrated several available numerical solutions for different engineering fields. Among the numerical solutions, the method of characteristics (MOC) has become popular and is superior than other methods for solving one-dimensional hydraulic transient problems. Elaoud et al.22established a numerical model by using the MOC to determine the pipe transient flow caused by the start-up of a centrifugal pump. They demonstrated that the evolution of the hydraulic variables was influenced by the pump starting time. Rezghi and Riasi23investigated the sensitivity of the hydraulic transient for two parallel pump-turbine units in hydroelectric power plants.

As per our knowledge, no studies have yet investigated the suction dynamics of the aircraft piston pump during the transient period. Therefore, we present an approach based on the pump dynamic model and inlet transient flow model for predicting the inlet pressure.The theoretical results were validated through experiments. A series of simulations were performed to determine the nature of the pressure wave propagating in the inlet line and provide guidance for the design of inlet installations, such as pressurized reservoirs, inlet lines, and boost impellers.

2. Mathematical model

The proposed mathematical model mainly comprises two parts, namely the pump dynamic model and transient flow model of the inlet line. The pump dynamic model provides a superior understanding of the transient response of the pump.It also indicates the discharge flow, which is the input parameter for the transient flow model. The inlet flow rate of the pump is assumed to be approximately equal to its discharge flow due to negligible leakage.The transient model can be used to calculate the inlet pressure of the aircraft pump under the transient condition as well as the distribution of the pressure and flow rate along the inlet line.

2.1. Dynamic model of the pressure-controlled pump

As evident from Fig.1, the pressure compensated pump can fulfill its function via the compensator valve, an actuator piston, and a rotatable yoke. The objective of the compensator valve is to command the control pressure such that the outlet pressure of the pump is maintained at a constant and predetermined value.The input signal into the compensator is the outlet pressure, which acts against the top surface of the spool.When a sudden load change causes the outlet pressure to exceed the upper threshold of the pressure regulation range,the spool moves downward to open the load port on the outlet pressure side itself. As a result, high-pressure fluid flow occurs into the control actuator, which reduces the pump displacement.The decrease in the displacement reduces the outlet pressure of the pump, which causes the spool to return to its neutral position. Conversely, if the outlet pressure suddenly drops below the lower threshold of the pressure regulation range, the pump increases its displacement to cause the pressure to rise. Thus, when a sudden load change occurs on the pump, the system change is first encountered by the compensator valve, and the dynamic model of the pump begins with the analysis of the compensator valve.

2.1.1. Motion equation of the compensator valve spool

The following equation describes the motion of the spool under the action of pressure, inertia, viscous friction, and spring forces:

where Asis the action area of the compensator valve spool,poutis the outlet pressure,msis the mass of the spool,xsis the spool displacement, Cdsis the damping coefficient of the spool, ksis the stiffness of the compensator spring,and xs,0is the precompression of the spring.

For steady-state conditions, the following equation is obtained:

where pout,0is the steady-state discharge pressure of the pump.

By substituting Eq.(2)into Eq.(1),the spool motion equation can be rewritten as follows:

2.1.2. Compensator valve flow

Fig.2 displays the compensator valve used to provide volumetric flow into the left chamber of the actuator piston. The supply pressure to the valve is the outlet pressure of the pump,and the return line is generally connected to the pump case.Mathematically, the volumetric flow rate into the pump actuator can be obtained by calculating the difference between the volumetric flow rates in and out of the valve.

where Qcis the flow into the control actuator, Q1is the flow into the compensator valve, and Q2is the flow return to the pump case.

According to the classical orifice equation, Q1and Q2can be expressed as follows:

Fig.2 Fluid flow of the compensated valve.

where Cqis the flow coefficient,dsis the diameter of the spool,xlap,0is the opening when the spool is in the neutral position,pcis the pressure in the left chamber of the actuator piston, ρ is the fluid density, and pcaseis the case pressure. By neglecting the variations in poutand pcase, Eqs. (5) and (6) can be linearized as follows:24

where Q0is the nominal flow rate across each passage. The coefficients Kq1and Kq2are commonly called the flow gains,whereas Kp1and Kp2are commonly called the pressure flow coefficients. The coefficients Kq1, Kq2, Kp1, and Kp2are given as follows, respectively:

The subscript 0 indicates the steady state when the spool is in the neutral position. By substituting Eqs. (7) and (8) into Eq. (4), the flow rate into the actuator can be simplified and represented as follows:

where Kq=Kq1+Kq2and Kp=Kp1+Kp2.

2.1.3. Motion of the rotating assembly

Fluid flow into the control actuator forces the piston to move to the right side (Fig.2). Thus, the flow continuity equation applied on the actuator can be expressed as follows:

where Apis the cross-sectional area of the actuator piston,xpis the displacement of the piston, β is the bulk modulus of the fluid,and Vpis the volume of the left chamber of the actuator,which is assumed to be constant in this study.

As evident from Fig.3,the motion of the rotating yoke and attached control piston is governed by the following equation:

where L is the distance between the rotation axis of the yoke and the axis of actuator piston, J is the moment inertia of the rotation assembly, θ is the Cvfis the viscous friction coefficient of the assembly, and kyis the stiffness of the yoke spring. Because xp≈θL, Eq. (12) can be modified as follows:

Fig.3 A free-body diagram of the rotating yoke.

where ma=J/L2and Cda=Cvf/L, which can be approximately assumed to be the damping coefficient of the actuator piston.

2.1.4. Pump displacement

The theoretical discharge flow of the pump can be expressed as follows:

where Qtheois the theoretical discharge flow rate, dpis the diameter of a single piston in the pump, Dpis the piston pitch diameter of the cylinder block,n is the number of pistons in the pump,ω is the angular velocity of the driving shaft,and Kpumpis the pump flow gain. The negative sign in Eq. (14) indicates that the positive motion of the actuator piston reduces the displacement.

2.1.5. Pump outlet pressure

The pump outlet pressure is modeled using a common control volume (Fig.4) approach that assumes that the fluid pressure within the outlet chamber is homogeneous. The fluid inertia and viscous effect are negligible compared with the hydrostatic pressure effects of the fluid. According to the aforementioned assumptions, the mass conservation equation for the outlet pressure can be written as follows:

where Qoutis the required flow rate of the load,Cpis the leakage coefficient of the pump,and Voutis the equivalent volume of the outlet port.

Fig.4 Outlet control volume.

2.1.6. Summary

In summary, the dynamic model of the pressure-controlled pump can be described using Eqs. (3), (10), (11), and (13)-(15).Fig.5 displays the block diagram of the dynamic system;the reference input on the left is the desired outlet pressure(pout,0) and the output on the right is the instantaneous outlet pressure(pout).The flow demand from the load circuit(Qout)is defined as a disturbance to the dynamic system, which immediately changes the outlet pressure. In this study, the transient condition occurs because of flow disturbance, which can be created by opening a flow control valve suddenly. This dynamic model of the pump is implemented in MATLAB/Simulink and solved using the fourth-order Runge-Kutta method. By simulating the dynamic model, the change in the pump flow can be obtained during the transient period caused by flow disturbance.Furthermore,the calculated pump flow is the input of the transient flow model, which is introduced in the following section.

2.2.Transient flow model of inlet line and characteristics method

At the reservoir end, sufficient pressure should be available to push the fluid through the inlet line such that,at the pump inlet port, the fluid pressure is still above the critical inlet pressure.However,when flow demand is suddenly increased,the instantaneous vacuum in the suction chamber may produce cavitation due to the long inlet line between the pump and the reservoir.Therefore,it is necessary to consider the wave propagation effect for the analysis of transients in the long pipe.In this section, the governing equations of the transient flow in the inlet line is presented based on wave propagation theory,and the method of characteristics is derived for solving the equations.

2.2.1. Governing equations

The governing equations for the inlet line flow are a set of two coupled hyperbolic partial differential equations. These equations are originally derived from Newton’s second law and the mass conservation law21(Eq. (16)).

where Q is the flow rate,p is the pressure,ρ is the fluid density,f is the Darcy-Weisbach friction coefficient, A is the crosssection area of the inlet line,D is the diameter of the inlet line,and a is the wave speed, which can be expressed as follows:

where E is the elastic modulus of the inlet line wall and ψ is a nondimensional parameter that depends on the elastic performance of the pipe. For a thick-walled elastic pipe, ψ can be obtained as follows:

where ε is the Poisson ratio of the pipe wall and Roand Riare the external and internal radius of the pipe, respectively.

Fig.5 Block diagram of the pressure-controlled pump.

2.2.2. Method of characteristics

The equations of motion and continuity can be represented by L1and L2, respectively. The two equations can be combined linearly with an unknown multiplier λ.

After rearranging Eq. (19) the following equation is obtained:

The dependent variables p and Q are the functions of the independent variables x and t. The total derivatives can be expressed as follows:

The unknown multiplier λ is assumed to satisfy the following reaction:

The solution of Eq. (22) yields two specific values of λ.

By substituting the values of λ, Eq. (20) can be written as follows:

and

if

Thus,the two values of λ are used to transform the original partial difference equations into new ordinary difference equations.Eqs.(24)and(26)are valid only when Eqs.(25)and(27)are satisfied. Because there exist no mathematical approximations for the transformation,the solution of Eqs.(24)and(26)is the solution of the original equations.

Consider that the inlet line is divided into N equal reaches and each reach has a length of Δx(Fig.6).To satisfy Eqs.(24)and(26),the time interval is defined as Δt=Δx/a.If each term in Eqs.(24)and(26)is multiplied with dt,the integration along the C+and C-characteristics provides the following equations:

Eqs. (28) and (29) are two compatibility equations that describe the basic algebraic relations between the pressure and flow in the pipe during transient propagation.By eliminating QP,j, the pressure pP,jin the x-t plane can be calculated as follows:

In the same manner, we can determine QP,jas follows:

First, the steady conditions are calculated for the bottom grid points at t=t0(Fig.6).Then,to determine the conditions at t=t0+Δt, Eqs. (30) and (31) are used for the interior nodes. For the end nodes at the left and right sides, special boundary conditions are required,which are discussed in detail in the following section. Thus, the elevated time levels are computed step-by-step until transient conditions are reached for the determined time.

Fig.6 Characteristic lines in x-t plane.

2.2.3. Boundary conditions

In this study, two boundary conditions are considered. At the upstream,the pipe is connected to a pressurized reservoir,and at the downstream,the pipe is connected to the inlet port of the piston pump (Fig.7). At each end of the pipe, only one of the compatibility equations is valid along a certain characteristic.For the upstream end,Eq.(28)is valid along the C-characteristic, and for the downstream end, Eq. (29) is valid along the C+characteristic. Thus, two auxiliary constraint conditions are required to specify the pressure and flow in each boundary.

In aircraft hydraulic systems, bootstrap- and pressurizedgas-type reservoirs are used to maintain pressure. Furthermore, the pressure in the reservoir is assumed to remain constant during the transient period. Therefore, the first auxiliary constraint condition for the upstream boundary can be represented as follows:

where presvis the pressure in the reservoir.

For the downstream end, the inlet port of the piston pump can be considered as a capacitive chamber (Fig.7). According to the mass conservation law, the relationship between the pressure and flow in the control volume can be expressed as follows:

Fig.7 Boundaries of the inlet line.

Fig.8 Schematic (left) and overview (right) of the test rig.

where Qsucis the suction flow from the inlet line;Qinis the flow rate into the pump, which can be obtained from the dynamic model of the pressure-controlled pump in real time; Vinis the equivalent volume of the inlet chamber; and pinrepresents the pressure in the inlet port of the pump. To make Eq. (33)suitable for numerical computation,it can be transformed into a difference equation as follows:

3. Test rig and model validation

3.1. Test rig setup

A test rig is used to verify whether the established model can characterize the real dynamic behavior of the pump suction(Fig.8). The suction dynamic test circuit mainly consists of the reservoir, tested pump, throttling load component, and connected pipes. The pressure in the reservoir is maintained using a charge pump and relief valve 7.1.The load component is divided into two oil-ways to determine the flow transient.The main parameters of the test rig and sensors characteristics are presented in Table 1 and Table 2 respectively.

Table 1 Main parameters of test rig.

Table 2 Sensors characteristics.

The test rig used in this study allows the response time of the tested pump to be investigated. Moreover, the suction dynamics during the transient period can be determined by monitoring the inlet pressure.Before starting data acquisition,both the throttle valves should be individually regulated to allow the entire flow to pass through them. Then, the bypassed oil way is cut off by closing the switch valve and throttle valve 13.1 is slowly closed to decrease the pump flow to zero. Data is acquired when the parameters are stable. After a few seconds, the switch valve is reactivated to increase the pump flow rapidly. Finally, the various parameters during the flow transient can be obtained.

Table 3 Main parameters and coefficients for the simulation.

3.2. Experimental results and model validation

As indicated in Table 1, a dual-pressure pump is used in the test rig. Verification tests were performed at two pressure levels. The simulation results obtained from the mathematical model were implemented in MATLAB. The main parameters and coefficients involved in the tests are presented in Table 3.25,26

The graphs in the left panel of Figs. 9 and 10 present the measured and simulated outlet pressures as obtained from the pump dynamic model. Both the measured and simulated outlet pressure steeply declined, and the discharge flow increased from zero to full flow. The elapsed time for the two flow acceleration processes was approximately 20 ms(21 ms for the 21 MPa test and 19 ms for the 28 MPa test).The elapsed time was determined from the natural characteristics of the test pump. When the flow reached the maximum value, the simulated inlet pressures began diverging from the measured inlet pressure. This disagreement may be caused by the loading component, which is difficult to incorporate in the simulation. However, this disagreement does not affect the validation because we mainly concentrate on the acceleration process of the discharge flow for the pump dynamic model.

The graphs in the right panel of Figs. 9 and 10 present the measured and simulated inlet pressures as obtained from the inlet transient flow model.As it can be seen in the two graphs,both the measured and the simulated inlet pressures experience a significant undershoot, and then gradually stabilized after several periods of oscillations. Although the simulated inlet pressure curves are not fully consistent with the measured data during the entire measurement period, the curves are in good agreement during the transient period. Therefore, the mathematical model proposed in this study can reflect the dynamic characteristics of the inlet pressure under transient conditions.

Fig.9 Experimental and simulated results at a setting pressure of 21 MPa.

Fig.10 Experimental and simulated results at a setting pressure of 28 MPa.

The critical inlet pressure(pcrit)for the test pump should be higher than 0.28 MPa to prevent cavitation.12Both the measured and simulated inlet pressures are larger than 0.4 MPa when the flow is stable at full flow, which indicates that the inlet pressures are adequate in such a condition.However,cavitation is still likely to occur during the transient period because the inlet pressure can fall below 0.2 MPa for a considerable period.

4. Simulation results and analysis

In this section,the pressure and flow rate curves are presented.Moreover,the trend of the inlet pressure is explained considering the propagation of the pressure wave. Furthermore, the effect of wave velocity and transient time are analyzed by comparing different sets of simulations. Finally, measures for increasing the inlet pressure to prevent cavitation are discussed.

4.1. Inlet suction dynamics

In Fig.11, the inlet pressure (pin), flow rate into the pump(Qin), and difference between Qinand Qsucare distinguished using different vertical axes. As evident from the left panel of Fig.11,the inlet pressure drops rapidly at 0.1 s and exhibits oscillatory changes till the pressure is stabilized to approximately 0.5 MPa at 1 s. Therefore, the pressure drop between the reservoir and pump is approximately 0.1 MPa when the flow rate is 200 L/min in the steady condition.Such a pressure drop is acceptable for pump suction with sufficient hydraulic fluid. However, during the transient period, the inlet pressure drops below 0.1 MPa for 60 ms, which can easily lead to cavitation in the pump.To illustrate the variation in the inlet pressure characteristic with the rapidly rising inlet flow, a magnification of the transient period measurements is evident from the right panel of Fig.11.In the steady-state condition in region I, the inlet pressure is equal to the reservoir pressure because the flow rate is zero. In region II, the flow into the pump begins to increase and full flow is achieved in 15 ms.The flow difference between Qinand Qsucis positive, which causes the inlet pressure to decrease according to Eq. (33). In region II, the flow rate from the inlet line (Qsuc) is a follower after Qin. In region III, the flow into the pump does not continue to increase and the driving effect of Qindisappears.Thus,the flow difference is very close to zero.Consequently,the inlet pressure is almost constant at a low pressure level.

Fig.11 Simulated inlet pressure and flow rate in time domain.

Fig.12 Distribution of the pressure and flow rate in the time domain and along the pipe length.

To illustrate pressure wave propagation along the inlet line,the distribution of the pressure and flow rate along the time and length domains is evident from Fig.12. When the flow demand of the pump increases suddenly, the inlet chamber is the first component to be affected by the pressure change.Consequently,a pressure difference is formed because the pressure of the upstream node is still equal to the pressure of the reservoir.The pressure difference may result in hydraulic fluid flow into the inlet chamber. The pressure of the nodes along the inlet line decreases one-by-one with pressure wave propagation(left arrow in Fig.12).However,due to the large volume of the reservoir,the pressure may remain constant when the pressure wave reaches the reservoir.Moreover,the flow from the reservoir into the inlet line encounters an impulse due to fluid inertia and the pressure of the node near the reservoir increases.Thus, the pressure wave propagates again from the reservoir back to the pump (right arrow in Fig.12). In this simulation,the length of the inlet line is 3 m and the wave velocity is set to 80 m/s. The time taken by the pressure wave to complete a round trip is calculated to be only 75 ms,which is in agreement with the simulation results (Figs. 11 and 12).

Fig.13 Comparison of the inlet pressures at different wave velocities.

Fig.14 Inlet pressures at different transient times.

4.2. Effect of the wave velocity and transient time

Fig.13 depicts a comparison of the inlet pressures for different wave velocities. According to Eqs. (17) and (18), the wave velocity can be modified by changing the elastic modulus of the wall of the inlet line. However, the size of the inlet line and the ramp time of the inlet flow remain the same in the simulations.In the simulation,the pump demand flow rate(Qin)is set to increase from 0 to 200 L/min in 15 ms. The first feature observed from the curves is that the duration of low inlet pressure decreases with increasing wave velocity.This trend can be easily explained through pressure wave propagation, as discussed in Section 4.1. An increase in the wave velocity increases the undershoot of the inlet pressure, which increases the likelihood of cavitation. The inlet pressure decreases by 0.06 MPa for every 10 m/s increase in the wave velocity, as shown in the magnification of the transient region.

Fig.15 Undershoot of the inlet pressure versus the internal diameter of the inlet line with different reservoir pressures.

To study the influence of the transient time Δt2on the inlet pressure, six sets of simulations are performed by modifying the damping coefficient of the swash plate assembly. Fig.14 illustrates a comparison of the inlet pressures for the six sets of transient times. The length of the inlet line is 3 m, and the wave velocity is 80 m/s. Thus, the pressure wave requires 75 ms to complete a round trip from the pump to the reservoir.As evident from Fig.14, the minimum inlet pressure is almost unchanged when the transient time is less than 75 ms. However, the duration of the undershoot decreases with increasing transient time. Moreover, the pressure wave is shaped as an inverted triangle when the transient time is 75 ms. If the transient time continues to increase, the undershoot of the inlet pressure decreases and the wave continues to have an inverted-triangle shape.

4.3. Increasing the inlet pressure

In addition to the factors discussed in Section 4.2, the inlet pressure can also be increased by increasing the reservoir pressure and internal diameter of the inlet line. However, pressurizing the reservoir causes noneffective power increase and enlarging the inlet line leads to considerable weight increase.Thus,the aforementioned two parameters cannot be increased without limits.Fig.15 illustrates the variation in the inlet pressure undershoot with the internal diameter of the inlet line under different reservoir pressures. The horizontal dashed line indicates the critical inlet pressure required to prevent cavitation in the pump used. Thus, the inlet pressure should be increased when it falls below the critical value.

As evident from Fig.15, when the reservoir pressure is relatively high (e.g., 0.8 or 1 MPa), a very thin inlet line can be designed. However, reaching the critical inlet pressure by enlarging the inlet line is extremely difficult when the reservoir pressure is low(e.g.,0.2 MPa).The size of the inlet line can be significantly decreased by increasing the inlet pressure through other methods,such as integrating a boost impeller.For example, if the reservoir pressure is 0.4 MPa, the internal diameter of the inlet line can be reduced from 37 to 31 mm when a booster with a pressurizing capacity of 0.1 MPa is adopted.

In practical applications, both the reservoir pressure (presv)and diameter of the inlet line (D) have upper limits. Assume that the upper limits of presvand D are presvupand Dup,respectively,for a specific hydraulic system.The applicable region for the boost impeller is represented by the green shadow area evident from Fig.15.Therefore,we can obtain the corresponding expected value for the boost capacity of the impeller from this method.

5. Conclusions

A dynamic model for predicting the inlet pressure under transient conditions is proposed for the first time.This model comprises the pump dynamic model and inlet transient flow model,which are based on the working principles of the pump and pressure wave propagation theory, respectively. The verification test indicates that the simulated inlet pressure is in agreement with the experimental result during the transient period.The conclusions obtained from further investigations can be summarized as follows:

(1) The experimental and simulated results indicate that even when the inlet pressure is considerably higher than the critical inlet pressure requirement under steady-state full-flow conditions, cavitation is still likely during the transient period.

(2) The simulations indicate that the wave speed and transient time significantly affect the inlet pressure undershoot.

i. The amplitude of the undershoot increases, whereas the duration of the undershoot decreases when the wave velocity increases. And, the inlet pressure decreases by 0.06 MPa for every 10 m/s increase in the wave velocity.

ii. The amplitude of the undershoot changes considerably when the transient time is higher than the propagating time of the pressure wave. It means increasing the response time of the pump could improve the anticavitation performance.

(3) When the pressure in the reservoir comprises only the atmospheric pressure or the pressure is relatively low,meeting the critical inlet pressure requirement by enlarging the inlet line is difficult. In this case, the inlet pressure must be increased using other methods, such as integrating a boost impeller.

This paper comprehensively describes the suction dynamics of aircraft hydraulic pumps under transient conditions. The conclusions from this study may be used as guidelines for engineering applications.

Acknowledgment

This study was financially supported by the National Natural Science Foundation of China (No. 51775013).