Ke ZHANG,Xudong HUANG,Zhifeng XIE,Ming ZHOU

School of Aerospace Engineering,Tsinghua University,Beijing 100084,China

KEYWORDS Aircraft engines;AMESim;Common rail;Fuel injection;Mathematical models;Pressure effects;Structural design

Abstract The heavy fuel compression ignition engines are widely equipped as aircraft piston engines.The fuel injection system is one of the key technologies that determines the performance of engine.One of the main challenges is to precisely control the injected fuel quantity and flow rate in the presence of pressure fluctuation.This challenge is even more serious for heavy fuel.An original design for electrically controlled high pressure fuel injection system called Multi-Pumppressure-reservoirs fuel injection System(MPS)was demonstrated to reduce the pressure fluctuation and help keep injection stable.MPS was compared with an ordinary high pressure Common Rail fuel injection System(CRS).This work established one-dimensional AMESim and mathematical models for both CRS and MPS to study the effect of different structures and geometric parameters on the pressure fluctuations.The calculations show that the average fuel pressure fluctuation of MPS can be reduced by 57%for the crankshaft speed of 1900 r/min,and the pressure fluctuation before injection reduced by 100%.It is concluded that the pressure performance of MPS is less sensitive to pressure reservoir volume than that of CRS,and there is an opportunity for further volume reduction.

1.Introduction

The aircraft piston engine is one of the most widely used aircraft power plant.In the very beginning,diesel was the main fuel for aircraft piston engine.However,the power to weight ratio of diesel engine is too low to support aircraft development.Over the last century,the aircraft piston engine used mainly aviation gasoline as fuel under spark ignition combustion mode.In the recent decades,the heavy fuel compression ignition engine,used as an aircraft piston engine,1–3has gradually become more predominant,as the power to weight ratio increased greatly with the employment of the super-charger and electrical fuel injection system.The heavy fuel compression ignition aircraft piston engine has the advantage of higher compression ratios,which are matched with high pressure fuel injection systems,leading to lower specific fuel consumption and longer cruise duration.Furthermore,heavy fuel has better security and is more suitable for shipboard aircraft.

The fuel injection system is one of the key technologies that determines fuel efficiency and emissions.Typically,a multicylinder diesel compression ignition engine employs high pressure Common Rail fuel injection System(CRS).4One of the main challenges associated with the CRS is to precisely control the injected fuel quantity and flow rate in the presence of pressure fluctuation in the rail and injector.Pressure fluctuation might affect the stability and consistency of fuel injection and further affect the combustion efficiency of the engine.5–7Significant research has been conducted on the influence of different system parameters on pressure fluctuation in CRS.8–10Some studies focused on electrically controlled parameters and operating parameters.11Some research has designed certain types of damping or compensation assemblies for the common rail.10Others have further optimized the structure parameters to reduce pressure fluctuation.12

As the electrical technologies develop,pressure variation caused by fuel quantity variation in the rail can be compensated by advanced electrical control methodology.13One problem is that the sampling frequency of the transducers is not sufficiently high to respond to high frequency pressure fluctuations caused by pressure wave propagation and reflection,consequently limiting the effect of pressure compensation.Structure innovation and parameter optimization remain important for reducing pressure fluctuations.

The challenge of controlling pressure fluctuation is even more serious for heavy fuel as compared with diesel,as heavy fuel is composed of different types of fuel,which have different characteristics.Heavy fuel for aircraft piston engine refers to aviation kerosene or diesel fuel,including JP-8,JP-5 and diesel.When specific fuel type changes,the characteristics such as density and viscosity all change.Hence,the pressure fluctuation features might also change,which could vary the injection pressure and injection amount and consequently form unstable combustion.To solve the problem,we have to reduce the pressure fluctuation of the high pressure fuel injection system to a certain level which does not affect injection obviously,so that the aircraft piston engine can accommodate to different fuel types.However,there is limited research on specially designed high pressure fuel injection systems for heavy fuel compression ignition aircraft piston engine.

This study demonstrates a novel electrically controlled high pressure fuel injection system called Multi-Pump-pressure reservoirs fuel injection System(MPS).The new structure can reduce the influence between cylinders,and thus greatly decrease pressure fluctuation and stabilize injection and combustion with different fuel types.Compared with an ordinary CRS,the fuel pump and common rail of MPS are divided into several parts according to the number of the cylinders.In fact,no longer is there a common rail,which is now replaced by several pressure reservoirs.Each single unit pump and pressure reservoir for one cylinder is integrated into one component as a Pump-pressure-Reservoir(PR)complex.As a result,fuel supply and fuel injection only occur once in the PR during a crankshaft cycle,and the damping time of pressure fluctuation is much longer.14

This work established one-dimensional AMESim and mathematical models for CRS and MPS separately to study the effect of different structure and geometric parameters on the pressure fluctuations.15,16Based on the models,the structure and dimensions of PR of the MPS were optimized to reduce the pressure fluctuations.The calculations show that,compared with CRS,the average fuel pressure fluctuation of MPS induced by periodic fuel pumping and injection can be reduced by 57%for the crankshaft speed of 1900 rpm,and the pressure fluctuation before injection is reduced by 100%.

2.Physical and mathematical model of fuel dynamics in CRS and MPS

2.1.Physical models

To begin with the modelling details of CRS and MPS,we briefly introduce two systems.Fig.1 shows the sketch of CRS,where the main components include a fuel tank,a low pressure supply system,a high pressure inline pump or rotor pump,a delivery valve,a common rail,an electronic control unit,and several electronically controlled fuel injectors.The low pressure supply system supplies assigned amount of low pressure fuel to the pump according to the Electrical Control Unit(ECU).The high pressure pump elevates the fluid pressure to a range of 100–200 MPa,which is stored in the common rail as a pressure accumulator,and injected by the electronically controlled fuel injectors with flexible injection time and stable pressure.

Fig.2 shows the sketch of MPS.MPS has almost the same components as CRS,except for the high pressure inline pump or rotor pump and the common rail,which are replaced by several PRs according to the number of the cylinders in the engine.The PRs can be placed separately besides the cylinders or combined in a pump box,according to the installation space of the piston engine.In this research,we designed an MPS with six PRs and injectors for a six-cylinder heavy fuel aircraft piston engine.

Fig.1 Sketch of CRS for a six-cylinder engine.

Fig.2 Sketch of MPS for a six-cylinder engine.

Fig.3 Sketch of PR of MPS.

The PR is composed of a cam,a unit plunger pump,a pressure reservoir,an input valve,an output valve,and a pressure sensor,as shown in Fig.3.17The plunger chamber and the pressure reservoir chamber are manufactured as a whole to remove unnecessary parts and leakage.The plunger is stubby to shorten supply time and accordingly shorten the fuel leakage.The pressure reservoir is a circular tube with a thick wall to minimize deformation and maintain stable pressure.The cam shape is eccentric circle.The unit plunger pump worked separately with the corresponding pressure reservoir.The electronic control unit received signal from all the pressure sensors on the end of the pressure reservoirs and controlled the low pressure supply system to supply a certain amount of low pressure fuel to the pumps to form the assigned high pressure.

2.2.One-dimensional AMESim models

To study the fluid dynamics in the CRS and MPS,we established physics based models of the two systems in the AMESim environment.Fig.4 shows the layout of the AMESim model of the CRS,based on an actual CRS for a six-cylinder diesel engine cited from research carried out by Tian.18To verify the reliability of the AMESim model,we compared the simulated pressure data of CRS with experimental data from the same reference.

Fig.5 shows the layout of the AMESim model of the MPS.Most parameters are the same with CRS,except for the PRs.The structure parameters and the operating parameters of the CRS and MPS are given in Table 1.

2.3.Mathematical model

To calculate the dynamic fuel pressure fluctuation in the pump and pressure reservoir in detail,we established a mathematical model for the PR of the MPS.The model of the pump and common rail of CRS is the same.The model does not include the injector part,so as to focus on the effect of main structure and geometric parameters of PR on the pressure fluctuations.The assumptions are as follows:

(1)The fuel is considered compressible,and the viscosity and elastic modulus and other physical parameters of fuel are considered to change with pressure and temperature.

(2)The axial flow of fluid and the propagation,reflection and superposition of the pressure wave are considered,while the circular direction and radial flow of the fluid are neglected.

(3)The heat transfer and temperature variation are negligible,and the temperature of the fuel is 80°C.

Fig.4 AMESim model of CRS.

Fig.5 AMESim model of MPS.

Table 1 Structure parameters and operating parameters of CRS and MPS.

(4)Only the elastic deformation of the pressure reservoir is calculated to determine the effect on pressure fluctuation propagation.The deformation of other solid parts under high pressure is neglected.

(5)The mass of moving components in the same movement is considered to be concentrated mass.

(6)The micro radial movement of needle and plunger is not considered.

(7)For small volume fluid chambers,the specific structure shapes are not considered,and the hydraulic properties and parameters are assumed to be the same in the whole chamber.

(8)The friction of the valve in motion is not considered as the motion displacement is very small.The mass continuity equation of fluid transients in the pressure reservoir with appropriate simplification is described as follows19:

State equation of the fuel is given by

so the mass continuity equation reads

where p is the pressure in the pressure reservoir(Pa),ρ the density of the fuel(kg/m3),A the cross-sectional area of the pressure reservoir(m2),u the velocity of the fuel flow in the pressure reservoir(m/s),q the discharge volume per second into the pressure reservoir(m3/s),x the distance from the calculated point to the input point of the pressure reservoir(m),K the bulk modulus of the fuel(Pa),and t the operating time of cam(s).

As the fuel pressure varies tremendously in the CRS and MPS,the pressure reservoir is flexible under the hydraulic pressure,leading to a variable deformation rate.The strain of the pressure reservoir is described by the Lame equation as follows20:

The inner cross-sectional area of the pressure reservoir and the gradient are described as

The expression for the mass continuity equation can be written as

where r is the radial position from the center of the pressure reservoir(m),erthe strain of the pressure reservoir on the radial position of r(m),υ the Poisson’s ratio of the material of the pressure reservoir,E the Young’s modulus of the pressure reservoir(Pa),rithe inner radius of the pressure reservoir(m),rethe external radius of the pressure reservoir(m),pethe external pressure on the pressure reservoir(Pa),krthe coefficient of p in strain,Crthe constant of strain,and kathe coefficient of p in cross-sectional area of the pressure reservoir.

The momentum equation of fluid transients in the pressure reservoir is usually written as19

in which the friction term f(q)can be written with Darcy formula,as the velocity of the fuel in the pressure reservoir is very low and the flow in pressure reservoir is laminar.

where λ is the frictional resistant coefficient,d the inner diameter of the pressure reservoir(m),and ν the kinematic viscosity of the fuel(m2/s).

The fuel flow amount around the output valve orifice is decided by the pressure difference between the pump and the pressure reservoir,while the movement of the valve also brings some fluid flow.The flow rate equations are

where qorificeis the discharge volume per second through the valve orifice into the pressure reservoir(m3/s),qvalvethe discharge volume per second through the movement of the valve ball into the pressure reservoir(m3/s),ppthe pressure of the fuel in the pump(Pa),ρpthe density of the fuel in the pump(kg/m3),Cdthe discharge coefficient of the valve,Avthe flow area of the valve(m2),dvthe seal diameter of the valve(m),and h the lift of the ball valve(m).

Cddepends on the structure of the orifice.Avdepends on the lift and the diameter of the ball valve.The lift of the ball valve is decided by the fluid pressure difference,viscosity resistance,and spring force:

where α is the bevel angle of the slant bore of the valve(°),m the quantity of the ball valve(kg),Cμthe Stokes resistance coefficient,kvthe stiffness of the spring on top of the ball valve(N/m),and h0the compressed distance of the spring on top of the ball valve(m).

The pressure and density in the pump change with the plunger’s movement and the fuel flow through the output valve.The pressure in the pressure reservoir changes with the fuel flow and the deformation of the pressure reservoir:

where Vpis the volume of the pump with the movement of plunge(m3),Vp0the max volume of the pump(m3),Apthe cross-sectional area of the pump(m2),hpthe lift of plunger of the pump(m),V the volume of the pressure reservoir(m3),and L the length of the pressure reservoir(m).

The material parameters of the fuel significantly affect the fluid dynamics.As heavy oil is a group of different types of fuel,we cannot calculate all the fuels in this work,as the fuels’characteristics under 100–200 MPa are not complete.For simplification,we chose the Chinese No-20 diesel oil as an example.The fuel characteristic parameters under high pressure are cited from a specific research on physical properties of Chinese No-20 diesel oil.21

where T is the temperature of the fuel(°C).

Numerical methods for these mathematical models are as follows:One-dimensional fluid dynamics equation is adapted.Lax-Wendroff model22is used to solve the high-pressure fuel pressure fluctuation characteristics.Integrator type is the standard integrator,simulation mode is dynamic,solver type is regular,and error type is mixed.The solution time is 3 s,the steps are 30,000,and the solving step length is equal.The relative error is 1.0×10-7.

3.Results and discussion

3.1.Validation of models

To validate the models,we compare the AMESim simulation data of CRS with experimental data of a six-cylinder diesel engine.

Fig.6 Comparison of common rail pressure of experiment and simulation data of CRS.

Fig.7 Comparison of injector inlet pressure of experiment and simulation data of CRS.

Fig.6 shows the comparison of pressure in the common rail,and Fig.7 shows the comparison of pressure in the injector inlet point.As the experiment was carried out on a sixcylinder diesel engine,both the common rail pressure and injector pressure lines have six low frequency fluctuations during a crankshaft cycle,and one of the fluctuations of the injector pressure has severe oscillation owing to the injection behavior of the tested injector.The experimental pressure in the common rail of the CRS was controlled by Proportion Integration Differentiation(PID)method with certain revision map for air temperature and fuel temperature and injection amount,while the simulation pressure was only controlled by PID method without revision.So the data between experiment and simulation have a certain deviation.However,the two lines were rather consistent in phase angle and fluctuation range.The mean error between the two data lines of pressure in the common rail was within 1 MPa,and that for pressure in the injector was within 2 MPa.Maximum relative errors of the lines in both figures were under 3%,and the curves were identical by 90%.Hence,the AMESim model of CRS was valid and can precisely predict the pressure fluctuation in the rail and injectors.

MPS is a newly designed system,which has not been produced.In this work,we do not have the experimental conditions to perform the same verification for the AMESim model of MPS.As the AMESim model of MPS is established based on the AMESim model of CRS with partial quantitative modification,the following research of model of MPS is carried out based on the valid AMESim model of CRS.

3.2.Comparison of MPS and CRS

Fig.8 shows a comparison of fuel pressure in one of the pressure reservoirs of MPS and the common rail of CRS.As MPS has 6 PRs connecting to 6 injectors separately,the fuel dynamic is quite different from that of CRS.There is only one low frequency pressure wave during a crankshaft cycle in the pressure reservoir of MPS,while there are 6 low frequency pressure waves in the common rail of CRS.The lowest pressure of MPS is lower than that of CRS by about 10 MPa.Under the same injection duration of each injector and almost the same injection amount,the pressure reduction in the pressure reservoir is about 2.6 times that of common rail,for the volume of pressure reservoir is about a half of common rail.However,the overall pressure stability of each cycle is much better for the MPS.The calculation shows that the overall mean fuel pressure fluctuation by time of MPS can be reduced by 57%compared with CRS,and the pressure fluctuation before injection reduced by 100%.It is because fuel supply and fuel injection only happen once separately during a crankshaft cycle,and the damping time of pressure fluctuation is about 10 times longer.

Fig.9 shows the pressure and fuel flow rate in a crankshaft cycle in the pump and injector and pressure reservoir of MPS.

Fig.8 Comparison of fuel pressure in one of PRs of MPS and common rail of CRS.

Fig.9 Pressure and fuel flow rate in a pump and pressure reservoir and injector of MPS.

There is only one injection and one fuel supply in 62 ms.The pressure fluctuation in the pressure reservoir has enough damping time which is about 40 ms to achieve a stable level before the next injection.The ECU can control the pressure much more precisely for the pressure sensor can provide steady signals.

Fig.10 shows the pressure and fuel flow rate in a crankshaft cycle in the pump and injector and a common rail of CRS.Six fuel supplies and injections occur in 62 ms,inducing severe pressure fluctuations and affecting each injection.The damping time of the pressure waves between the last fuel supply and the next fuel injection is about 4 ms,which is not long enough to achieve a stable level.The pressure sensor of the common rail cannot capture every fluctuation for the limited precision,consequently reducing the controlling accuracy of ECU.

Fig.11 shows the comparison of pressure in one of the injectors of MPS and CRS.Although the pressure drop after injection of CRS is bigger than that of MPS,but the pressure drop is stable.Pressure drop is mainly caused by the decrease of amount of fuel in the pressure reservoir,and the drop range remains the same under same injection condition.The pressure fluctuation bringing instability exists before each injection.The pressure at the beginning of each injection in the injector of MPS is almost the same,while that of CRS varies.In CRS,the injection amount of each cylinder differs because of the manufacturing difference and controlling difference inducing different pressure waves in the common rail.The pressure wave cannot damp completely before the next wave,so the waves affect each other,form irregular fluctuations,and further affect the stability of injection amount.In MPS,the injection behavior of each cylinder does not affect each other by physical isolation of the pressure reservoir,leading to a relatively steady injection pressure.Hence,the injection controlling of the MPS has more flexibility and stability.

Fig.10 Pressure and fuel flow rate in a pump and common rail and injector of CRS.

Fig.11 Comparison of pressure in one of injectors of MPS and CRS.

3.3.Optimization of structure parameters of MPS

As the CRS has a three-plunger pump to supply fuel for six injectors,the camshaft speed is the same with crankshaft speed.While the MPS has six unit pumps for six injectors,the camshaft speed is half of the crankshaft.As a result,operating time of one plunge of MPS is twice that of CRS with the same cam profile,which may lead to more fuel leakage in the plunger barrel assembly and a decrease in volume efficiency of the pump.We changed the cam profile of the eccentric arc into single circular arcs.Accordingly,we designed the plunger stubby to shorten fuel supply time.The modified cam profile is shown in Fig.12.

Fig.13 shows the comparison of fuel leakage flow rate of the pump with the single circular arc and eccentric arc cam.The leakage flow is composed of two parts,Poiseuille flow and Couette flow.Poiseuille flow occurred when the pressure in the pump increased during the compressing period.Couette flow occurred with the movement of the plunger.As the acting time of a single circular arc cam is shorter,the velocity of the plunger is higher,so the fuel leakage caused by Couette flow is larger.The pump pressure of a single circular arc cam is almost the same,and the fuel supply time is shorter,so the fuel leakage caused by Poiseuille flow is smaller.In general,the Poiseuille flow is the main part of the fuel leakage.Hence,the fuel leakage of single circular arc cam is obviously reduced.

Fig.12 Optimized cam profile of MPS.

Fig.13 Comparison of fuel leakage rate of pump with single circular arc cam and eccentric arc cam.

For MPS,the pump and pressure reservoir can be designed to connect directly together or by a high pressure pipe as in the case of the CRS.We compared the pressure fluctuation with and without the high pressure pipe as shown in Fig.14.The lack of the high pressure pipe reduces the volume of the pressure reservoir and induces a slightly larger range of pressure reduction of about 2 MPa when injection occurs.However,the pressure returns to the assigned level by fuel supply and the fluctuation quickly attenuates.In the later part of the crankshaft cycle,the pressure of the two PRs are almost the same.Hence,we consider that reducing the high pressure pipe has no negative effect on the system.

The volume of the common rail is a key parameter for the CRS pressure control.It is usually considered that the bigger the volume is,the better the pressure is controlled.But the volume of common rail cannot be too big,which will increase the cold start time of the engine.In MPS,we designed the volume of one pressure reservoir to be about a half of the common rail of the contrastive CRS,and the pressure fluctuation shows good performance.But there are 6 PRs in the MPS,so the total volume of pressure reservoirs is very large.We tried to further find out the possibility of reducing the volume of the pressure reservoir to shorten the cold start time of MPS.This work reduces the volume of the common rail and pressure reservoir by half,and compares the pressure fluctuation in CRS and MPS as shown in Figs.15 and 16.

Fig.14 Comparison of pressure fluctuation in PR with and without high pressure pipe.

Fig.15 Comparison of rail pressure and injector pressure of CRS with normal and smaller common rail.

Fig.16 Comparison of rail pressure and injector pressure of MPS with normal and smaller pressure reservoir.

The pressure drop range of both systems are reasonable.From Fig.15,we can find that the rail pressure drop of a smaller common rail induced by injection increases by about 50%,as compared to a normal common rail.In Fig.16,it is the same situation.Although the volume of common rail and pressure reservoir decreased by a half,the volume of the high pressure pipes did not change,so the total fuel chamber volume only decreased by 1/3.Thus,the injection drop is reasonable.

However,for CRS,the volume reduction induced a significantly greater influence on pressure than for MPS.As shown in the upper half of Fig.15,in a crankshaft cycle the fuel pressure of the smaller pressure reservoir after each fuel supply continuously decreases,and the pressure difference between normal and smaller pressure reservoir varies.As shown in the lower half of Fig.15,the injector pressure difference between normal and smaller pressure reservoir varies tremendously too.

In the upper half of Fig.16,although the pressure drop of smaller pressure reservoir is greater than that of normal pressure reservoir,the pressure recovers to the same level after the fuel supply and remains stable.As shown in the lower half of Fig.16,the injector pressure before each injection of the two situations are almost the same,except that the pressure drops are different.Hence,the injection performance is essentially unaffected by the reduction of pressure reservoir volume.

It is concluded that the performance of MPS is less sensitive to the pressure reservoir volume than that of CRS,and there is a large space for the pressure reservoir whose volume can be further reduced.

4.Conclusion

This work demonstrates a novel structure of a high pressure fuel injection system for a heavy fuel compression ignition aircraft piston engine,named MPS.It has several pump-pressure reservoir complexes according to the number of cylinders of the heavy fuel engine.To verify the improved performance,the MPS was compared with CRS.

This work established the AMESim and mathematic model for CRS.Simulated data were compared with cited experimental data for CRS for a six-cylinder diesel engine,and the curves were identical by 90%.The validity of the models was affirmed.The AMESim model and mathematic model of MPS were established based on that of CRS,and the pressure performance of MPS was proved to be better than that of CRS using Chinese No-20 diesel oil.Compared with CRS,the overall mean fuel pressure fluctuation of MPS decreased by 57%for the crankshaft speed of 1900 rpm,and the pressure fluctuation before injection reduced by 100%.Fuel supply and fuel injection only occur once separately during a crankshaft cycle,and the damping time of pressure fluctuation is much longer.

To further improve the performance of MPS,some structure and parameter optimization were carried out and verified.First,a single circular arc cam is more suitable than an eccentric arc cam for MPS,as the former shortens the supply time and reduces the fuel leakage.Second,a high pressure pipe between the pump and pressure reservoir is unnecessary for MPS and has no obvious negative effect on the pressure fluctuation.Third,the pressure reservoir volume can be significantly reduced,and the pressure fluctuation of MPS is much less sensitive than that of CRS.

Through comparison with CRS,it is proved that the pressure fluctuation of MPS is much less than that of CRS.In fact,the pressure fluctuation in the PR of MPS almost disappeared before injection.Hence,different fuel characteristics rarely affect the pressure fluctuation in the PR.The injection parameters are more stable with different fuel types.The novel MPS is a better fuel injection system for a heavy fuel compression ignition aircraft piston engine.

This study proves that the pressure fluctuations can decrease to such a level with characteristic parameters of Chinese No-20 diesel oil.Diesel is the typical type of heavy fuel,and the characteristics under super high pressure can be acquired reliably.However,the constituent of heavy fuel is too complicated to be all calculated,and accurate characteristics under 100–200 MPa are not measured sufficiently.Therefore,further research on other fuel types should be carried out later to complete the performance of MPS.