，*，，

1.School of Mechanical and Power Engineering，Nanjing Tech University，Nanjing 211816，P.R.China；

2.Department of Light Aviation Power Project，Jincheng Group Co.，Ltd.，Nanjing 210002，P.R.China

Abstract: As a miniaturized direct injection（DI）solution，a self-pressurized injector is of great significance for small aviation piston engines，such as spark-ignited two-stroke heavy-fuel engines. The spray characteristics of DI injectors are an important application prerequisite. In this paper，the computational fluid dynamics（CFD）software AVL Fire is employed to study the spray characteristics. Two types of spray models are established based on the Han Sheet model and the KH-RT model，and simulation works are carried out according to two types of spray tests in the literature. The comparison results show that in the constant volume bomb test，the spray patterns obtained by simulation under the two sets of environmental pressures are similar to those in the experiment，and the simulation spray using the KH-RT model can fit the spray contraction of the near nozzle field and the vortex of the far nozzle field better. In the tube test，the spray patterns obtained by simulation under the five sets of flow velocity are similar to those in the experiment，and the simulation spray using the KH-RT model can fit the spray expansion and the vortex of the far nozzle field better. The RP-3 kerosene spray characteristics of the self-pressurized injector are also experimentally studied，and the results demonstrate that due to the higher viscosity of kerosene，the spray shrinks more easily，resulting in a smaller spray cone angle and larger penetration. Therefore，changes in environmental pressure have greater impact on the kerosene spray pattern.

Key words：direct injection；spray characteristics；piston engine；self-pressurized injector

0 Introduction

In recent years， unmanned aerial vehicles（UAVs）have been widely applied because of their high mobility，safety，and low cost，which can per?form certain difficult or dangerous tasks［1-2］. In the UAV propulsion system，due to the high power and energy densities，the internal combustion engine can provide a longer endurance life than the electric mo?tor［3］. For piston engines，the spark-ignition（SI）engines require lower structural strength，so their weight is light and the power-to-weight ratio is high［4］. The two-stroke engines theoretically have twice the power output，which means a higher pow?er-to-weight ratio［5］.

The two-stroke engines exhibit a simple struc?ture，low weight，and high power-to-weight ratio［6］.However，the unique scavenging process causes a scavenging short circuit-loss［7］. Due to the risk of gasoline fuel in storage，transportation and usage，special applications are more inclined to heavy fuel with a high flash point，low volatility，and high en?ergy density，such as light diesel and aviation kero?sene［8-10］. But this leads to difficulty in cold starting of the engine and a tendency to knock［11］.

The direct injection（DI）technology is widely used to reduce the emissions，improve the power output and reduce the fuel consumption. For twostroke engines，the fuel short-circuit loss can be re?duced by the delayed injection phase，and a well-at?omized spray improves the cold starting perfor?mance and suppresses the knocking tendency［12］.

Numerous studies adopted the gasoline com?mon rail system to investigate the performance and emissions of heavy fuel engines，for the common rail system is mature and the injection pressure reaches 30 MPa or higher［13-15］. But the mechanical system is too complicated to miniaturize，and diffi?cult to apply to small aviation piston engines.

Currently，there are two miniaturized DI solu?tions for two-stroke engines，namely，air-assisted direct injection（AADI）and self-pressurized direct injection［16］，as shown in Fig.1. AADI uses com?pressed air to promote high-quality spray under a rel?atively low injection pressure［17-18］. The atomization of the spray is not sensitive to the type of fuel and is especially suitable for high-viscosity and high-densi?ty heavy fuels［19］. Thus，experimental and numerical studies have been carried out based on the AADI technique［20-24］. However，the injection pressure is just 0.6 MPa，and the atomization is strongly affect?ed by the ambient pressure，making it difficult to achieve a well-atomized stratified mixture［25-26］.

Fig.1 Schematic of two miniaturized DI solutions for twostroke engines

The self-pressurized injector is based on the water hammer effect in which the high-speed flow?ing liquid would generate large pressure due to the sudden drop in flow rate. The ram-tuned injection system developed by Küntscher et al. is the earliest self-pressurized injector［27-28］. Heimberg improved the injector structure with the hydraulic impact method and designed the Ficht injection system［29］.It had been applied on personal watercrafts，and test results showed that hydrocarbon（HC）and nitrogen oxide emissions had been reduced by 75%，and fuel consumption had been reduced by 30%［30］. Strauss et al. of Bombardier updated the Ficht injection sys?tem to a new E-TEC injection system，and com?bined it with an optimized combustion chamber，re?sulting in an overall emissions reduction greater than 50%［31-33］. Team from the University of Idaho de?signed a clean snowmobile for competition using a two-stroke engine equipped with E-TEC system，which had achieved significant improvements in high power，low emissions and long endurance［34-36］.Winkler et al. found that the improvement of the power and emission performance level of E-TEC DI in part-load applications was unattainable by the low-pressure direct injection（LPDI）system，espe?cially under idle and low loads［37］.

In addition to improving power，fuel consump?tion，and emissions，the self-pressurized injection system simplifies the fuel system and can be quickly applied on traditional port fuel injected engines. The high injection pressure allows stratified injection and multiple injection strategies to be used，where strati?fied injection strategy can further improve the fuel consumption and emissions under low engine load and speed［38］，and multiple injection strategy can maximize the charge cooling effect to suppress knock［39］.

1 Simulation Model for Spray

Before studying the application of self-pressur?ized injectors to engines，simulation research is re?quired first，in which the first step is to study the spray model. The CFD software AVL Fire is em?ployed to study the spray characteristics，and to fur?ther study the spray and combustion process in the cylinder.

In order to establish a complete spray model，the parameter acquisition of the injector and the se?lection of the spray sub-model are particularly impor?tant.

1.1 Basic parameters of self?pressurized injec?tor

Before CFD simulation，it is necessary to pro?vide parameters such as the fuel characteristics，the inner and outer diameters of the nozzle hole，the in?ner and outer cone angles of the spray，the fuel in?jection rate，and the injection pressure difference.

Part of the geometric parameters can be ob?tained by measuring the nozzle shaft needle. Fig.2（a）shows the needle at the nozzle exit under the mi?croscope. The measured nozzle cross-sectional view is shown in Fig.2（b）.

Fig.2 Micrograph of injector needle and schematic diagram of nozzle orifice size

The fuel injection rate can be obtained by the flow characteristic test，and Fig.3 shows the flow characteristic curve. The injection dead zone of the injector is 0.7 ms，and the slope of the line connect?ing the points where the fuel pulse width is greater than 0.7 ms is the fuel injection rate.

In order to facilitate the adjustment of fuel in?jection parameters in the simulation process of the whole machine，the following simplified assump?tions are made for the fuel injection dynamic process of the self-boosting injector：the response process of the injector opening and closing phases is not consid?ered；the injection pressure during the fuel injection process is not considered；the fuel injection rate is maintained at a fixed value.

Fig.3 Flow characteristic curve

Table 1 Injector parameters

1.2 Break?up model for self?pressurized injec?tor

The CFD software AVL Fire provides a vari?ety of break-up models. According to the character?istics of the outward-opening swirl nozzle and the hollow cone spray，two suitable break-up models are selected.

1.2.1 Han Sheet model

The sheet model represents a simple，semi-em?pirical primary break-up model used to determine the initial spray conditions such as the sheet thick?ness，velocity，and break-up length. The sheet thicknesshof the liquid sheet at the nozzle orifice is computed as［40］

wherem?lis liquid mass flow，μlliquid dynamic vis?cosity，ρlliquid density，Δpthe pressure difference between liquid and gas，doutouter orifice diameter of the nozzle，andXthe ratio of air core to total area as Eq.（2）.

Velocity coefficientkVis defined as the ratio of the actual discharge velocityvto the theoretical ve?locity corresponding to the total pressure differential across the nozzle，as shown in Eq.（3）.

It has been shown thatkVcan be related to noz?zle dimensions and spray cone angleαoutby Eq.（4）［41］，whereC3is a constant introduced by Lefebvre et al.to fit different injector designs，and the standard set?ting is 1.17 and should be modified according to the actual discharge velocity［40］.

The break-up lengthBLof the liquid sheet is obtained from Clark and Dombrowski by Eq.（5）［42］.

whereσis gas-liquid surface tension，ln(η/η0) ex?perimentally defined parameter，ρggas density，andvrelthe relative velocity between liquid and gas.

The Han Sheet model was originally developed for inwardly opening swirl nozzles. Studies showed that this model is also suitable for outward-opening swirl nozzles，but there are huge differences in pa?rameter settings. The sheet thicknesshof the out?wardly-opening swirl nozzle is limited to the nozzle gap when the injector is fully opened. Regardless of the influence of cavitation，the relationship between the sheet thicknesshand the needle liftHof the shaft needle and the cone angleα1at the outlet is

The relationship between the actual discharge velocityvof the sheet and the liquid mass flowm?land the sheet thicknesshis

Adjust the parameters in the software AVL Fire to make the simulated values of the sheet thick?ness and velocity consistent with the calculated val?ues，thereby completing the setting of the break-up model.

In summary，the Han Sheet model can be used for outward-opening swirl nozzles，but the parame?ter settings are quite different. When the fuel type，fuel injection flow rate，or injection pressure differ?ence change，the sheet thickness calculated by the simulation will also change，but the real sheet thick?ness is basically unchanged. Therefore，the parame?ters need to be re-adjusted every time，making the application of the Han Sheet model more complicat?ed.

1.2.2 KH?RT model

In this model Kelvin-Helmholtz（KH）surface waves and Rayleigh-Taylor （RT） disturbances should be in continuous competition of breaking up the droplets［42-43］. The KH mechanism is favored by high relative velocities and high ambient density.The RT mechanism is driven by rapid deceleration of the droplets causing the growth of surface waves at the droplet stagnation point. The WAVE model equations［44］are as follows

whereRis parent drop diameter，Rachild drop di?ameter，tathe break-up time，Λwavelength，Ωwave growth rate，Weccontinuous phase property andOhddroplet property.

The RT disturbances are described by the fast?est growing frequencyΩand the corresponding wave numberK.

Heregis the deceleration in the direction of travel. If the wave lengthΛis small enough to be growing on the droplet’s surface and the characteris?tic RT break-up time τ has passed，the droplets will be atomized and their new sizes are assumed to be proportional to the RT wave length. The break-up lengthLis calculated as

Droplets within the break-up lengthLare considered to undergo only KH break-up，where?as further downstream both mechanisms are pres?ent. The normal velocity component given to the child parcels is calculated from disturbance wave?length and growth rate modified by model parame?terC8.

The KH-RT model is suitable for break-up with high relative velocity or rapid deceleration of droplets，while the hollow cone spray has a high ve?locity at the nozzle outlet，and has a large decelera?tion after sheet break-up. But the KH-RT model cannot be directly applied to the hollow cone spray，so some adjustments are needed.

Suppose that the outwardly-opening swirl noz?zle is replaced with a large number of orifice noz?zles in the circumferential direction. The cylindri?cal sprays emitted by each orifice nozzle are con?nected to each other to form a hollow cone-shaped liquid sheet with uneven thickness. Under this equivalent condition，the KH-RT model can be used，and the initial droplet diameterD0of each sub orifice nozzle can be calculated according to the method of equal spray cross-sectional area as follows.

In summary，the adjusted KH-RT model is suitable for the spray with an outward-opening swirl nozzle. The initial droplet size is derived from the spray cross-sectional area of the nozzle orifice，and there is no need to modify the nozzle-related parame?ters during the simulation，which makes the applica?tion of the KH-RT model convenient.

2 Spray Simulation Model Verifi?cation

In order to ensure the accuracy of the spray model，it is necessary to carry out the comparison and correction in conjunction with the spray test.

2.1 Variable pressure in constant volume bomb

Constant volume bomb test is a common meth?od to obtain spray characteristics under different en?vironmental pressures.Trejo et al.［45］and Wu et al.［16］have carried out constant volume bomb tests on selfpressurized fuel injectors. Among them，the spray test images obtained by Wu et al. are clearer and serve as a reference for spray simulation in this arti?cle.

The initial and boundary conditions of the simu?lation are shown in Table 2. The simulation results of two spray models and the comparison with the ex?periment are shown in Fig.4 and Fig.5，in which the sizes of all pictures have been adjusted to 50 mm in width and 100 mm in the maximum height.

Table 2 Constant volume bomb simulation parameters

Fig.4 Comparison of spray patterns at pressure of 0.1 MPa

Fig.5 Comparison of spray patterns at pressure of 0.4 MPa

There are some points to explain before analyz?ing and comparing. The width of the spray tip is dif?ferent in the spray images of simulation and experi?ment，in which the size of the simulation is consis?tent with the actual nozzle size，while nozzle occlu?sion affects the extraction of the spray tip in the ex?periment image. The other is that the test spray ex?ceeds the boundary of the window at 1.5 ms with an ambient pressure of 0.1 MPa，making the end of the spray into a circular arc shape.

In the simulation results，when the ambient pressure is 0.1 MPa，the spray patterns obtained by the simulation of the two models are basically con?sistent with the experimental. Because the process of injector opening and the establishment of the spray flow is ignored，the penetration of simulation in the initial stage is larger than the experiment. The Han Sheet model ignores the effect of the liquid sheet with air before it breaks，so the penetration distance is larger than the result of KH-RT model.When the ambient pressure is 0.4 MPa，both mod?els can simulate the coalescence of the far-field spray after breaking up to form a recirculating vor?tex，and the KH-RT model can better simulate the shrinking trend of the spray cone angle no matter in the near field or the far field.

In summary，in the spray simulation of variable ambient pressure in the constant volume bomb，the spray pattern simulated by the KH-RT model is closer to the spray pattern referenced in the experi?ment.

2.2 Variable flow velocity in a wind tube

Strauss et al. found that engines with different in-cylinder air flows can exhibit significantly differ?ent behaviors with similar fuel sprays，and built a test fixture as shown in Fig.6，to evaluate fuel sprays into air counter flows［33］.

The initial and boundary conditions of the simu?lation are shown in Table 3. The simulation results of the two spray models and the comparison with the experiment are shown in Fig.7. Since the spray tip is blocked by the injector bracket，the length is estimated to be 14 mm according to the nozzle size and spray cone angle. Therefore，the simulation re?sult output image size is adjusted to 75 mm×71 mm，where the test image size is 75 mm×56 mm.The images of 1 ms and 2 ms after the penetration reaches 14 mm are selected for comparison.

Fig.6 Experimental setup for wind tube

Table 3 Wind tube simulation parameters

Fig.7 Comparison of spray patterns at variable flow velocities

With the air velocity of 0 m/s，the spray is basi?cally the same as the constant volume bomb test at 1ms，but there is a clear boundary between near-field and far-field spray at 2 ms.This is because in the late stage of injection，the injection pressure drops until the nozzle is closed，which causes the fuel injection rate to drop and the spray cone angle to decrease.However，the simulation process ignores the pres?sure and flow changes at the end of the injection，so the simulation image does not show this phenome?non. Therefore，the comparison between the simula?tion and the test is mainly based on the time of 1 ms.

With the increase of the air velocity，the spray cone angle of the near-field spray gradually increases under the force of the airflow. The cone angle of the far-field spray increases more obviously，and a vor?tex ring is formed after the liquid sheet is broken. In the simulation image，the KH-RT model simulates the change of the spray cone angle better，and there?fore the axial penetration is closer to the test. For the spray penetration，the results of the KH-RT model are closer at low velocity，while the Han Sheet model is closer at the high velocity.

In summary，under the force of the air stream，the spray liquid sheet transitions from a conical shape to a trumpet shape before breaking，and the droplets formed by the breaking of the liquid sheet are more uni?form，resulting in a sharp drop in the penetration.The Han Sheet model fails to simulate the deformation pro?cess of the liquid sheet well，while the KH-RT model performs better.The spray model still needs to be cor?rected by the dynamic data of pressure and flow during the injection process.

Fig.8 Experimental setup

3 Aviation Kerosene Spray Test

Self-pressurized fuel injector is a miniaturized direct injection solution，which is very suitable for light and high-power aviation piston heavy fuel en?gines. The spray tests in the current literatures all use isooctane standard fuel. Therefore it is of in?novative value to study the aviation kerosene spray characteristics of self-pressurized injector.

The experimental setup is shown in Fig.8. The self-pressurized injector is installed on the constant volume bomb and is driven by the self-developed electronic control unit（ECU）together with the fuel pump，and the ECU is controlled by the self-devel?oped interface software on the PC console. The con?stant-volume bomb is filled with argon supplied by an argon cylinder，and pressure regulators at the in?let and outlet control the pressure. The high-speed camera，model Phantom VEO410L，is controlled by the PC through PCC software. When the self-de?veloped ECU drives the injector，another synchro?nous signal is transmitted to the high-speed camera via the BNC cable.

The initial and boundary conditions of the test are shown in Table 4.

Table 4 Aviation kerosene test parameters

The experiment results are shown in Fig.9，in which the sizes of all pictures have been adjusted to 50 mm in width. In order to accurately capture the spray at the nozzle mouth，set the main optical axis of the high-speed camera to be concentric with two pieces of quartz glass. Therefore，when extracting the spray from the background image，the gray scale of the spray near the nozzle is low due to the influence of the bottom surface of the injector brack?et，but this does not affect the obtained spray pat?tern.

Fig.9 Aviation kerosene spray at variable pressures

When the ambient pressure is 0.1 MPa，the near-field spray is conical. At 0.6 ms，the boundary of far and near field sprays can be clearly observed，where the liquid sheet is broken and discrete jet string and detached droplets formed. After 1 ms，the gray scale of the near-field spray drops signifi?cantly，because the fuel flow rate drops due to the decrease in the injection pressure at the late stage of the injection. The spray pattern of kerosene fuel is significantly different from that of isooctane fuel.

When the ambient pressure increases，the pen?etration at the early stage of the spray basically de?creases proportionally. The spray is difficult to main?tain a conical shape and it quickly transitions to a cy?lindrical shape，and even shrinks further before breaking. The position where sheet break is no lon?ger fixed，which gradually moves downward as the spray develops，and the spray breaking position is basically the same under the pressures of 0.2 MPa and 0.4 MPa. After the spray is broken，there are no more discrete jet strings but only droplets. The shape of the vortex ring formed by the droplets is al?so different，which is closer to a circle at an ambient pressure of 0.2 MPa，and closer to a heart shape at 0.4 MPa. The greater ambient pressure，the faster the droplet kinetic energy decreases，which leads to the drop of spray penetration and the change of the vortex ring shape.

In general，the difference in physical and chem?ical properties of aviation kerosene and isooctane leads to obvious differences in sprays. The spray of aviation kerosene has a smaller cone angle，larger penetration and faster breaking，easier to produce vortex ring.

4 Conclusions

This paper reviews the recent development of the UAV power unit and the application of direct in?jection technology，with an emphasis on two minia?turized direct injection technologies：AADI and selfpressurized injection. The AADI technology has been proved to provide excellent spray characteris?tics with particle size about 7 μm. The self-pressur?ized injection technology can provide an injection pressure of 5 MPa，and there is still considerable room for improvement. This paper has carried out simulation and experimental research on self-pres?surized injectors，and the conclusions obtained are as follows.

（1） There are two break-up models in the AVL Fire software suitable for the hollow cone spray of self-pressurized fuel injector. When apply?ing the Han Sheet model，the thickness of the liquid sheet needs to be adjusted according to the gap of the open nozzle，which makes the parameter setting inconvenient. When applying the KH-RT model，an equivalent assumption needs to be made，and the application of the model is convenient.

（2） The spray simulated by the Han Sheet model and KH-RT model can basically simulate the spray development process under the two pressures of the constant volume bomb environment，and the KH-RT model fits the spray cone angle better. The process of fuel pressure establishment and nozzle opening has a significant effect on the initial penetra?tion distance of the spray，which affects the accura?cy of the initial spray simulation.

（3）The air counter flow has a huge impact on the hollow cone spray morphology，especially the liquid sheet part before spray break-up. The Han Sheet model fails to simulate this phenomenon，re?sulting in a smaller axial penetration. The process of fuel pressure drop and nozzle closing has a signifi?cant effect on the initial spray velocity and broken length，which affects the accuracy of the final spray simulation.

（4）The aviation kerosene spray test shows that the different physical and chemical properties of kerosene and gasoline lead to differences in spray patterns. This difference is more pronounced on swirl nozzle than on traditional orifice nozzle. Under normal pressure conditions，it is already difficult for kerosene spray to maintain the initial spray cone an?gle. When the background pressure increases by 0.1 MPa，the kerosene spray becomes cylindrical，which has a serious negative impact on the atomiza?tion process and particle size of the spray.

AcknowledgementsThis work was supported by the Na?tional Natural Science Foundation of China（No.51865031），the State Key Laboratory of Engines of Tianjin University（No.K2020-05），and the Natural Science Foundation of the Jiangsu Higher Education Institutions of China （No.20KJB470014）.

AuthorsDr. JI Haocheng received the B.S. and Ph.D. de?grees in vehicle engineering and power engineering from Nanjing University of Aeronautics and Astronautics in 2012 and 2020，respectively. He is currently affiliated with the School of Mechanical and Power Engineering，Nanjing Tech University. His current research interests include electronic control technology for two-stroke engines.

Dr. LIU Rui received the B.S. and Ph.D. degrees in vehicle engineering from Nanjing University of Aeronautics and As?tronautics in 2011 and 2017, respectively. He is currently af?filiated with School of Mechanical and Power Engineering,Nanjing Tech University. His current research interests in?clude the control and numerical simulation of direct injection internal combustion engines.

Author contributionsDr. JI Haocheng designed the study， complied the models， conducted the analysis，interpreted the results and wrote the manuscript. Dr. LIU Rui designed the spray experiment and contributed data for the analysis. Dr. LI Jing contributed to the discussion and background of the study. Dr. ZHAI Buyun contributed to the spray experiment. All authors commented on the manuscript draft and approved the submission.

Competing interestsThe authors declare no competing interests.