Research on fuel injection characteristics of common rail system based on high pressure pipeline integration and matching

The modular prediction model of high pressure common rail system was established to study the influence of high‐pressure pipeline integration matching on the fuel injection characteristics of common rail system. The influence of common rail volume on pressure building and pressure fluctuation in common rail tubes was analyzed. The influence of common rail volume on the matching of fuel injection frequency (number of fuel injectors) and fuel supply frequency (number of plunger pumps) was studied by using the control variable method, and the basic optimal solution of the system was obtained. The influence of the common rail structure on the fuel flow characteristics of the system was also studied. The matching relationship between high pressure tubing and common rail system is studied by introducing dimensionless numbers such as length‐diameter ratio of pipeline. The results demonstrate that the increase of the storage space of the accumulator can effectively reduce the fluctuation in the system, so that the injection volume increases slowly and then decreases rapidly, with a slope of −5.70 × 10−3 mm3. The increase of the diameter of the common rail makes the fuel flow characteristics become good first and then bad, and the increase of the length of the common rail can soothe the pressure fluctuations. The increase of the diameter of the link tube (LT) makes the fuel injection volume of the injector increase first and then decrease. The optimal VR solution for the LT is 0.0249 and the optimal ratio of the length to diameter of a pipeline solution is 55.10. The structure of the distribution tube and its matching to the common rail have little effect on the fuel flow characteristics. When the diameter and length of the injection tube are too large, the influence on the injection pressure of the injector is negatively correlated.


| INTRODUCTION
6][7] The fuel flow characteristics of injectors measure the performance of HPCRS.[10][11] HPCRS are studied in the order from fuel supply module to accumulator module and then to fuel injection module based on the fuel running route.Su et al. 12 carried out a three-dimensional hydrodynamics simulation calculation on the oil supply pipeline of HPRCS, and studied the relationship between the pressure fluctuation in the pipeline and the flow rate fluctuation.To keep a constant pressure in oil pipe when high pressure oil pump is at a high-speed Wu et al. 13 put forward a conjecture between the cam speed and the injector configuration, and carry out simulation verification.After the low-pressure fuel is pumped out by the oil supply module, it becomes unstable high-pressure fuel which enters the accumulator module and finally enters the fuel injection module.Wei et al. 14 established a prediction model of the HPCRS and analyzed the influence of different hydraulic components such as pumps, rails, and injectors on pressure fluctuations by employing hydraulic decoupling method.The pressure fluctuations are mainly induced by the coupling of high and low frequency pressure waves.Low-frequency fluctuations everywhere are highly consistent, whereas high-frequency fluctuations are affected significantly by the working properties of hydraulic components.The volume of common rail pipes has an effect on the fluctuation degree and filtering capability.Gao et al. 15 studied pressure fluctuation in HPCRS by simulation, found that the fluctuation can be caused by hydraulic structures and control factors and defined a dimensionless parameter to quantitatively describe the effects of control factors and hydraulic structures on pressure fluctuation.They found that the increase in volume by increasing the diameter was found to decrease the pressure fluctuations more effectively compared to the impact of the length, but there is a marginal diminishing effect.Although they studied the influence law of common rail structure from the angle of pressure fluctuation in the tube, they did not study from the angle of other fuel flow characteristics of common rail system.In this study, the pressure in the common rail tube and the consistency of fuel injection of are continued to be studied, which has a certain complement to the previous work.Petrea et al. 16 improved the key structure of common-rail pump and compared two ball check valves with conical and spherical seat designs.The spherical seat makes the common rail tube show better flow dynamics characteristics, and the fluid pressure distribution in the valve is more uniform.Hu et al. 17 concentrated on the optimization in the hydraulic layouts and the structure parameters to manage the energy stored in the pressure waves and found a longer length and larger diameter of the rail-to-injector pipe could reduce the standard deviation of the injection volume and the rail pressure fluctuation rate simultaneously.Wei et al. 18 studied the injection consistency and pressure fluctuation stability of HPRCS of Marine high speed diesel engines and found that the injection consistency is related to the effective pressure storage capacity of the system.Ferrari et al. 19 realized lumped parameter numerical model of the high-pressure hydraulic pipeline and validated the model outcomes through a comparison with frequency values that were obtained by applying the peak-picking technique to the experimental pressure time histories acquired from the pipe that connects the injector to the rail.Some geometric features of the injection apparatus can have a significant effect on the system dynamic.Li et al. 20 used the oil pump test bench to analyze the rail pressure change process caused by the injector injection of HPRCS, and found that the injector injection would cause the rail pressure drop.So as to improve the fuel flow dynamics and pressure stability, predecessors have carried out a lot of research on improving the key structure and characteristics of the common-rail pump and its components in the common rail system.However, there is a lack of research on the matching relationship between the fuel injection frequency and the fuel supply frequency of the common rail system, so the paper has done some research on this aspect.Inspired by Wang,4 this article aims to use a modular modeling approach to establish a simulation model with interconnected sub-modules.The submodules are the fuel supply module to provide high pressure fuel, the storage module to store high pressure fuel, and the fuel injection module to release fuel.
After testing and verifying the submodel, the three submodels are integrated together to form a complete common rail system model.From the perspective of the matching of high-pressure pipelines, this article includes the matching relationship between the supply frequency and the injection frequency, as well as the matching relationship between the high-pressure oil circuit and the common rail.The main factor affecting the frequency of oil supply is the number of plunger pumps.Injectors spray oil in sequence, and the number of injectors is the main factor affecting the injection frequency.Several nondimensional parameters are introduced to describe the matching relationship between the high-pressure oil circuit and the common rail, providing a new method for the design and optimization of the high-pressure common rail.These dimensionless numbers include the structure parameter of various fuel channels in the common rail system, and also include evaluation indicators, such as the ratio of fuel injection volumes of different injectors, and other dimensionless numbers for the flow characteristics of high-pressure fuel.
Finally, the optimal solution for each parameter is obtained, which can effectively improve the fuel flow characteristics of the system.The injection volume has been slightly increased, and the injection consistency has become better.First, the physical model was established.And then the mathematical model was set up on the basis.Whereafter, the one-dimensional unsteady flow simulation model of HPCRS was built using AMESim.Based on the simulation model, the matching design of HPCRS fuel supply frequency and injection frequency was studied.The influence law of common rail volume on fuel flow characteristics was explored and the optimal solution of the system was obtained.The matching relationship between the highpressure oil circuit and the common rail pipe in the common rail system was deeply explored, and the two were integrated, and the influence of the high-pressure oil circuit structure on the fuel flow characteristics was emphatically studied, and the excellent solution of each pipeline structure was obtained.

| EXPERIMENTAL SETUP AND SIMULATION MODEL
To research the integration and matching of highpressure pipelines for high-speed diesel engines for automobile and ship, a test bench as shown in Figures 1 and 2 was established.The test bench adopts the Bosch CP4.2 high-pressure common rail system.The test fuel is first pumped out from the fuel tank by a lowpressure oil pump, enters the low-pressure oil circuit built by the experimental team, and then goes into the six-plunger high-pressure oil pump composed of Bosch CP4.2, where it is transformed into high-pressure fuel.The high-pressure fuel then enters the Bosch CRIN 4.2 common rail pipe and is finally sprayed out by a Bosch-CRIN2 injector, controlled throughout the process by a Bosch EDC17 controller.The process of accumulating fuel pressure in the high pressure common rail system and the process of injection of high pressure fuel by the injector are completely independent.The common rail tube is equipped with a limited pressure valve and pressure sensor.The pressure sensor provides a rail pressure signal to the ECU.The pressure limiting valve ensures that the high pressure fuel in the common rail can be released quickly when the fuel pressure rises abnormally.This allowed the oil pressure in the common rail tube to be precisely controlled, so the oil pressure in the high-pressure tube was independent of the engine speed.According to the control signal issued by the ECU, the injector sprays high pressure fuel in the common rail into the combustion chamber of the diesel engine by controlling the opening and closing of the solenoid valve.The solenoid valve of the ECU control injector is opened for 0.509 ms.The HPCRS used the axial inline double plungers cam with double peach tip to drive a highpressure oil pump.The fuel was alternately compressed and pumped by six plungers, which reduces fluctuations in fuel pressure and drive torque caused by pumping fuel.
Fuel supply frequency, fuel injection frequency and pressure storage module three modules are included in the system by using the modular modeling idea.The typical Bosch HPCRS model was used as the reference model, which has universality.The AMESim software was used for simulation calculation.The system consisted of a six-plunger inline pump, a distribution valve, two common rail pipes, twelve injectors and high pressure oil pipes, which is shown in Figure 3.According to the constraint indexes and structural parameters shown in Table 1, three subsystems of high-pressure rotor pump, common rail and fuel injector were first established.Then, each subsystem was connected and coupled, and the established model was checked.The actual operating speed of the diesel engine determines that the high-pressure rotor pump in the common rail system rotates at 2600 rpm.The common rail pressure of 180 MPa can effectively improve the fuel atomization effect.To meet the fuel injection demand under actual working conditions, the injection duration is set to 2.2 ms.This study utilized 0 # diesel as the experimental fuel, with its properties presented in Table 2.In the simulation, Robert Bosch adiabatic diesel built in AMESim is used as the fuel model, and the influence of fuel pressure on the bulk modulus is mainly considered.
The evaluation indexes determined in the paper are continuous injection volume, injection duration, injection pressure and injection rate, and common rail pressure.The continuous injection volume reflects the maximum energy provided by the injection system.The coupling effects of injection duration, injection pressure and injection rate affect the injection quality which directly determines the spray effect.The common rail pressure reflects the storage capacity of the system.The sample data from this experiment follows a normal distribution.Therefore, the "t-distribution confidence interval method" is used as a robust optimization solution.The confidence interval was obtained using the sample data of the fuel injection rate from 10 pre-experiments, and for each group, the sample data was acquired by conducting three experiments and taking their average value as the experimental data for that group.These experimental data serve as calibration for simulation data, ensuring the accuracy of the simulation model.The comparison between the experimental value and the simulated value of fuel injection rate and common rail fuel pressure is shown in Figure 4.The numerical values from simulation and the measured values from experiments are in good agreement.The relative error of the average value of CRP pressure simulation calculation is 4.59%, and the relative error of fuel injection quantity simulation calculation is 0.46%.

| Common rail volume
The establishment of pressure in the CRP has two main processes: pressure building and pressure stabilizing.The pressure building process can be divided into an intense growth zone and a slow increase zone.During the intense growth zone, the pressure rises linearly from 0 bar until the liquid fills the storage space.Then, continued fuel feeding compresses the fuel in the pipe and increases the fuel pressure.At this time, the pressure rise fluctuates irregularly and smaller than before until it reaches the rated pressure, entering the pressure stabilization process.Pressure fluctuation is mainly caused by pulsating oil supply and sequential injection.The fluctuation amplitude decreases with each cycle, and with a longer time, the fluctuation becomes smaller.The pressure fluctuation decreases with an increase in the common rail volume.The high-pressure fuel pump pushes high-pressure fuel into the common rail through the plunger in a periodic manner.The electromagnetic valve controls the opening and closing of the fuel injector valve to release high-pressure fuel.These two factors together cause the high-pressure fuel to exhibit fluctuating flow characteristics in the common rail.When fuel flows in the common rail, it generates a certain inertia force and damping force.As the volume of the common rail increases, the inertia force and damping force of the flowing fuel also increase, thereby reducing the fluctuation flow characteristics of the fuel and subsequently reducing the fluctuation of the rail pressure.The matching design scheme is aimed at matching parameters which mainly includes fuel supply frequency, fuel injection frequency and the pressure storage module.First, the matching relationship between the fuel supply frequency and the pressure storage module was studied.As shown in Figure 5A, the fuel injection quantity of the fuel injector increases with the increase in the volume of the common rail.This is because when the volume of the common rail is small, there is a larger fuel pressure fluctuation.The significant fuel pressure fluctuation poses challenges for fuel injection control in the fuel system, resulting in unstable fuel injection quantity and smaller fuel injection quantity from the injector.When the volume of the common rail is small, the fuel pressure recovery more quickly, allowing the fuel injector to provide a larger fuel injection quantity.However, when the volume of the common rail increases to a certain extent, the rate of fuel pressure upswing slows down, causing the fuel injector to be unable to provide a larger fuel injection quantity.Therefore, as we continue to increase the volume of the common rail, the fuel injection quantity will rapidly decrease after crossing a turning point.The turning point is called the the optimal point of matching volume (OMVP).This means that the best common rail volume to achieve fuel flow characteristics is OMVP.At this time, it can ensure that the common rail tube can accommodate more pressure fluctuations.When the OMVP is exceeded, the fuel supply frequency is too small to match the storage space.The pressure in the common rail tube cannot be effectively enhanced, resulting in the deterioration of the fuel flow characteristics in the system.Different fuel supply frequencies have different OMVPs.When the number of injectors was fixed at 8, and the number of plunger pumps was 4, 5, and 6, the optimal volume values were 87.9, 113.3, and 143.8 mL, respectively.For different injection frequencies, the optimal volume increases nonlinearly with the increase of the number of piston pumps.While the volume increases beyond the OMVP, the fuel injection quantity will decrease linearly.
For different fuel supply frequencies under the condition of fixed fuel injection frequency, the slope of linear reduction of fuel flow characteristics is very similar, which is close to −5.70 × 10 −3 .The slope is very approximate even when the injection frequency is not fixed.As shown in Figure 5B, when the number of plunger pumps is fixed at 5 and the number of injectors is 8, 10 and 12, the optimal volume values are 113.3,114.1, and 138.7 mL, respectively.The optimal volume value increased nonlinearly with the increase in the number of injectors.Similarly, for different numbers of injectors, the injection rate would increase slowly as the volume of the common rail increases, and would decrease linearly as the volume increases beyond the OMVP.Therefore, a relatively universal rule could be obtained: In the matching design of fuel supply frequency, fuel injection frequency and pressure storage module, there is an OMVP for the storage space of the pressure storage module.When the storage space exceeds the OMVP, the variation of fuel flow characteristics has a linear relationship with the increase of storage space.

| Common rail structure
The dimensionless ratio of the length to diameter of a pipeline (LDR) is used to describe the structural characteristics of the pipeline.As shown in Figure 6A, keeping the length-diameter ratio unchanged, with the The reduction of oil pressure will affect the working state of the injector, resulting in a reduction in the amount of fuel injection because the injector needs a certain high pressure to overcome the resistance of the nozzle needle valve, so as to achieve fuel injection.When the oil pressure is reduced, it cannot provide enough pressure to overcome the resistance, resulting in a reduction in the amount of fuel injected, and even causing the injector to fail to open.In addition, when the injector opens the oil injection, the sudden drop in pressure at the control chamber and injector hole will produce an expansion wave, which will be transmitted along the high-pressure oil pipe to the common rail pipe.Since the common rail pipe is a long straight pipe, it is specified that the direction from the high pressure oil pump to the end of the common rail pipe is positive.The pressure fluctuation starts from the position of the injector, propagates along the positive direction, reaches the end and reflects, gradually attenuates in the propagation process.The longer the propagation distance, the greater the degree of attenuation, so the closer the injector to the end of the high-pressure oil pump, the smaller the pressure fluctuation, the greater the injection pressure, the greater the injection volume, the better the fuel flow characteristics.When the injector is closed, the pressure surge at the injector hole will produce a compression wave, which will be transmitted along the high-pressure oil pipe to the common rail pipe.When the compression wave reaches the IFP, due to the large fuel volume here, the pressure increase is small; when the compression wave reaches the ICP through the common rail pipe, due to the small volume of the surrounding fuel, the pressure increase is obvious.Therefore, the fuel injection volume of the injectors distributed in different positions of the common rail tube is different.In one working cycle of the engine, the injectors inject oil in order of distance from the pump.By comparing the injection volume and pressure of the injector in different positions, it is found that the closer the injector is to the pump, the better the fuel flow characteristics.The location of the injector significantly affects the fuel injection consistency.Injection consistency is critical in multicylinder engines, ensuring uniformity in the quantity and quality of fuel injection, resulting in improved combustion efficiency, power performance, reduced vibration noise, and enhanced fuel economy.Therefore, two dimensionless numbers, the ratio of injection volume (FIR) and the ratio of injection pressure (PR), are introduced to evaluate the index.FIR represents the fuel injection quantity ratio of the farthest injector from the pump to the nearest injector, while PR represents the ratio of pressure.The closer these two values are to 1, the better the consistency.Observing the ratio diagram of the injection pressure and the injection amount, the optimal solution of the diameter of the common rail tube is 19.1 mm.According to the functional and structural characteristics of the CRP, it can be divided into three types of pipelines: First of all, there is the part of the common rail between the fuel distributor and the first injector named the GP (pipeline acting as a guide); The fuel is distributed by the CRP and enters the injectors and the injectors are evenly distributed.Therefore, the length of the common rail pipes between the injectors is the same named SP (pipeline acting as a spacing); The end of the common rail is connected to the pressure relief valve, and the CRP between the terminal injector and the pressure relief valve is called the AP (pipeline acting as accommodating).Observing Figure 7A, when the current LDR of the catheter is less than 5 the FIR fluctuates.After the fluctuation ends, the consistency of the fuel injection volume of the multicylinder injector gradually tends to be excellent.When LDR is very small, ICP is greatly affected by the fluctuation of fuel supply pressure, and fuel flow characteristics will fluctuate greatly.With the increase of LDR, the ability of common rail to accommodate the fluctuation of pressure is enhanced, and the consistency of fuel flow characteristics of ICP and IFP is enhanced.However, engineering application and engine layout should be fully considered in the design, so the LDR should not be too large, and the minimum FIR point should be found in the fluctuation section.Therefore, 2.20 can be selected as the engineering reference for LDR.By observing Figure 7B, the structure of SP has a similar influence trend on FIR as that of GP, but the location of fluctuations is different.When LDR of SP is less than 10, FIR fluctuation occurs.When the fluctuation ends, the fuel flow consistency tends to be excellent.The reason for the fluctuation is that the pressure in the tube fluctuates greatly due to the structure of the SP, so that the consistency is poor.To sum up the above reasons, LDR of SP was selected to be 6.90.When we turn to AP, the situation is slightly different.The initial fluctuation caused by the increase of AP LDR is special.Observing Figure 7C, although there is fluctuation, the general trend of fluctuation is rising, which is caused by the particularity of the position of pressure relief valve.Therefore, the optimal LDR of AP is 1.23.module of the high-pressure oil pump, and then becomes high-pressure fuel through the compression of the highpressure oil pump.The high-pressure fuel flows out of the high-pressure oil pump module into the distribution valve.The high-pressure oil pipe between the distribution valve and the high-pressure oil pump is called a link tube (LT).The distribution valve plays a role in the assembly and distribution of fuel.It contains a highpressure tubing, which is called a collection tube (CT).After the high-pressure fuel flows out of the distribution valve, it will enter the common rail pipe through the high-pressure pipeline which is called the distribution tube (DT).Because it uses the common rail system model of the 12 injectors, the fuel flowing out of the assembly pipe needs to enter two common rail pipes with the same parameters and the same arrangement position evenly.Therefore, there are two distribution pipes, and the relative position and parameters are exactly the same, and their impact on the fuel flow characteristics is also consistent.After the fuel flows out of the common rail pipe, it will flow into the injector through the highpressure tubing which is called the injection pipe (IT).
According to the previous research, we have obtained the optimal solution of the diameter and structural shape of the CRP, so that we can continue to study the matching scheme of the high-pressure tubing to the CRP and its own structural shape.The following research will focus on these two points.To obtain the matching relationship between high-pressure tubing and CRP, our research team introduced a dimensionless number: the volume ratio of high-pressure tubing to the CRP, and named it VR, so as to study the impact of the matching relationship between high-pressure tubing and common rail pipes on fuel flow characteristics.After obtaining the best scheme of matching relationship, to get the best state of the structural shape of the high-pressure tubing, we studied the influence of its structure on the fuel circulation characteristics by using the LDR of the highpressure tubing.

| Link tube
For ICP, when LT's VR rises, FIQ rises first.When VR = 0.0466, it reaches the maximum value, then declines slightly, with a decrease of 0.5 mm 3 , and then it rises, but the rising slope is much lower than the slope of VR between 0 and 0.0466.When the volume of LT is very small, compared with the system, the diameter of LT is very small, which will have a throttling effect.The pressure in the system is unstable, which will cause the FIQ to not be high.With the increase of volume, the ability to accommodate pressure fluctuations, which makes the pressure fluctuations decrease.However, when the node is exceeded, this enhancement capacity gradually weakens.Because the proximity between the ICP and the pump, the length of the CRP pipeline between them is short and the volume is small, so the ability to accommodate pressure fluctuations is weak, so that the slope goes down.
There is a long CRP between LT and IFP, which can accommodate most of the pressure fluctuations, but when the pipeline is so long that there is delay loss and local loss, which leads to the loss of the enhancement capacity mentioned above.Therefore, for IFP, when the VR of LT rises, the FIQ drops first, and when VR = 0.0589, it increases after reaching the minimum value of 606.13 mm 3 .For ICP, the IP rises first, after reaching the VR node 0.0590, the injection pressure decreases.For IFP, IP drops first after reaching the VR node 0.0615, IP rises.For ICP, the distance to the distribution valve is very close, the CRP between the ICP and the distribution valve is shorter, and the ability to accommodate pressure fluctuations is weak.For IFP, the CRP between the IFP and the distribution valve is longer, and the ability to accommodate pressure fluctuations is relatively improved, but at the same time, the pressure loss will also increase.
Looking at Figure 9A, the FIR increases first and then decreases.When VR = 0.0567, the extreme value is obtained.At this time, the FIR = 1.077.When FIR < 1.1, it can be considered that the consistency of fuel injection volume is excellent.When the VR between LT and CRP becomes so large that it approaches 1, LT is similar to CRP at this time, but it is not applicable from the perspective of engineering application.The fuel injection pressure also has a similar law, so combined with Figure 9B, taking into account the fuel flow characteristics of a single injector and the consistency of the system, an optimal solution is VR = 0.0249.
Then our team studied the influence of the structural characteristics of LT on the fuel circulation characteristics from LT's LDR.First of all, for the FIQ and IP of ICP, with the growth of LT's LDR the FIQ and injection pressure continues to decline, but the decline is very small: when the LDR increases from 0.1 to 500, the change range of FIQ does not exceed 5 mm 3 , and the year-on-year injection pressure is −0.011 bar.With the significant growth of LT's LDR, the impact on the fuel flow characteristics of ICP is very small.For IFP, with the growth of LT's LDR, FIQ and injection pressures continue to rise.The rise slope of FIQ is 0.0033 mm 3 , and the rise slope of fuel injection pressure is 0.025 bar.It can be seen that the increase in the fuel flow characteristics of IFP is slightly greater than that of ICP.Looking at Figure 9C,D, it can also be found that with the growth of LT's LDR, PR, and FIR are approaching 1, which can effectively enhance system consistency, but it is not suitable in the compact engine layout, and it costs too much compared with gain effect, so such a DT size design is unreasonable.Looking at Figure 9C,D, it can also be found that with the growth of LT's LDR, PR, and FIR are approaching 1, which can effectively enhance system consistency.This is because the compression wave generated by the oil supply module travels back through the system.The farther the distance is, the faster the compression wave attenuates.At the end of CRP, it collides with the wave bounced off the wall and is eliminated, where the volume is smaller and more fuel injectors have been experienced and more expansion waves have been experienced.The fuel flow characteristics gap between IFP and ICP is narrowed by this effect.However, the elongated high-pressure tubing structure is not suitable for the compact engine layout, and the cost is too high compared to the gain effect, so the DT size design is not reasonable.According to the previous research, we have obtained the optimal solution of the diameter and structural shape of the CRP, so that we can continue to study the matching scheme of the highpressure tubing to the CRP and its own structural shape.
The following research will focus on these two points.To obtain the matching relationship between high-pressure tubing and CRP, our research team introduced a dimensionless number: the volume ratio of highpressure tubing to the CRP, and named it VR, so as to study the impact of the matching relationship between high-pressure tubing and common rail pipes on fuel flow characteristics.After obtaining the best scheme of matching relationship, to get the best state of the structural shape of the high-pressure tubing, we studied the influence of its structure on the fuel circulation characteristics by using the LDR of the high-pressure tubing.The distribution valve contains a short high-pressure tubing, which is mainly coupled with DT to form a onein-two-out three-way pipeline.For IP and FIQ of ICP, when LT's VR rises, the FIQ drops to the lowest point, and then rises.The rising slope is consistent with the absolute value of the decline slope, but rising to 652.45 mm 3 , it maintains a slight decline; for IFP, it is the opposite.These affect the consistency of the fuel flow characteristics of the system.Looking at Figure 10A,B, it can be found that when VR = 0.00126, the fuel flow characteristics are the best.Observing Figure 10C,D, first of all, the fluctuation of PR of the system is not large, and the peak amplitude is 0.085.When LDR = 58.50, the pressure consistency is better.Therefore, to obtain better spray effect, the optimal value point can be defined as this value.
High-pressure fuel flows out of the distribution valve into the CRP.Between the two components, there is a high-pressure tubing DT.Keeping the length of the DT pipeline unchanged, controlled the volume change of DT by changing its diameter.For ICP, with the increase of VR, FIQ first rises.After reaching the upper extreme point, the increase in the amount of fuel injection at this time is very small, only 3.01 mm 3 , and then the amount of fuel injection decreases, and the decrease is not large, only 4.05 mm 3 .After reaching the lower extreme point, the amount of fuel injection increases, and the slope k in the rising stage is 9.81 mm 3 .For IFP, with the increase of VR, FIQ drops first, with a large decline.When VR = 0.2212, it drops to the extreme point.At this time, the decline is 28.88 mm 3 , and then FIQ rises, with an increase slope of 14.71 mm 3 .
Compared with the system, when the volume of DT increases, the ability to transport fuel increases, and the ability to accommodate pressure fluctuations is also enhanced.When VR = 1, DT actually becomes a CRP.For the ICP, because it is relatively close to the inlet end of the CRP, it is more sensitive to the pressure fluctuation of the outlet of the DT tube.Therefore, when the diameter of DT is small, the throttle effect will make the pressure in the CRP low, so that the FIQ is not high.With the improvement of VR, the throttle effect gradually weakens.At this time, IP increases, and FIQ also increases.When the impact of the throttling effect is completely eliminated, at this time, with the increase of DT volume, the fuel volume that DT can hold is also increasing, which will lead to a slight decrease in the fuel pressure in the tube when the fuel supply frequency remains unchanged.At the same time, DT's ability to accommodate pressure fluctuations is also increasing.When FIQ reaches the lower extreme point, with the volume growth of high-pressure tubing, the highpressure tubing assumes part of the CRP function to accommodate more fuel pressure fluctuations.At this time, FIQ increases with the rise of VR.For IFP, due to the long distance between it and CRP, the volume of the CRP contained between it is larger, and the throttling effect caused by the small diameter of the tubing has less impact on it, but the impact of the reduction of fuel pressure caused by the increase of DT volume is inevitable.Therefore, when VR increases, IP and FIQ of IFP declines.Only when they reach the lower pole, when VR increases again can FIQ gradually recover when DT assumes part of the common orbital tube function.
Through observation of Figure 11A, it can be found that with the increase of VR, it can be found that the FIR is growing.When the VR is equal to 0.0716, the FIR reaches the maximum value of 1.307.At this time, the consistency of fuel circulation performance is worse, but when the VR is greater than 0.0716, if the VR is increased, the FIR is gradually decreasing.The gap between the maximum and minimum values of FIR is 0.063.When the FIR is less than 1.100, the consistency of fuel circulation performance can be considered to be relatively good, so we can choose the best value point in the small stage of VR.After comprehensive consideration, we chose the optimal value of VR as 0.0249.
First of all, a study of the ICP can be found that with the growth of DT's LDR, IP and FIQ decrease first.After reaching the lowest point of the pressure, it then rises.When LDR = 155.75,FIQ reaches the lowest value, but the decrease is less than 5.64 mm 3 .The absolute value of the slope of the rising stage is similar to that of the slope of the falling stage, and the rising slope is 0.0376 mm 3 .For IFP, with the increase of LDR, IP and FIQ have been growing, but they are divided into two stages.The rising slope of the first stage is higher than that of the second stage.When the LDR is less than 31.09, it is in the first stage.At this time, the rising slope is relatively large, and the rising slope k is 0.34 mm 3 .When the LDR is greater than 31.09, it is in the second stage, the rising slope is 0.11 mm 3 .Moreover, IFP changes more than ICP, so the main factors affecting the consistency of fuel flow characteristics are IP and FIQ of IFP.This is mainly because, first of all, with the increase of DT's LDR, the length of DT increases, and the pressure loss along the process also increases.ICP is closer to the entrance of CRP, and it is more sensitive to pressure fluctuations, so FIQ decreases in the early stage of LDR enlargement; for IFP, it is far from the entrance of CRP, and the pressure fluctuation has little impact on it.When the LDR increases, the volume of DT increases, and the ability to accommodate pressure fluctuations is enhanced, so the FIQ of IFP increases.When the LDR increases to the certain node, the FIQ of IFP and ICP increases, because at this time, the increase of DT volume to slow down pressure fluctuations is greater than that of pressure loss along the way.At this time, whether IFP or ICP, their FIQ will increase, but the growth rate of IFP is not as good as before, which is because the pressure loss along the process should be considered.
Looking at Figure 11B, it can be found that due to the large impact of the fuel flow characteristics of IFP, the FIQ has been declining with the increase of LDR, indicating that the FIQ of IFP is gradually approaching the FIQ of ICP.The FIR of the system can be divided into two stages with the decline of LDR growth.The node of the stage is that the LDR is equal to 32.21.When the LDR is less than 32.21, the decline slope at this time is larger, and the decline slope of this stage is 8.0 × 10 −4 ; When the LDR is greater than 32.21, the decline slope at this stage is slower, and the decline slope k at this stage is 1.6 × 10 −4 .Therefore, the optimal solution of LDR can be obtained, that is, LDR = 32.21,because after breaking through this point, the decline slope slows down, and the optimal solution that continues to pursue consistency is not worth the loss.

| Injection tube
When the high-pressure fuel flows out, to reach the final injection module, you also need to go through the highpressure tubing IT.One end of IT is connected to CRP and the other end is connected to the injector.Whether it is IFP or ICP, with the growth of VR, IP increases first.
When VR increases to 0.0172, IP increases by 726.15 bar, and then increases VR until VR is 1, and IP increases by 215.37 bar.With the growth of VR, whether it is IFP or ICP, FIQ grows rapidly first, and the growth rate is very large.When VR grows to 0.0546, the change range of FIQ is 376.6 mm 3 .When VR is greater than 0.0546, it grows, and FIQ grows slowly.At this time, the growth rate of FIQ is not large.This is because when the diameter of the IT tube is very small, IT will have a throttling effect, and the IT filtration ability for fluctuation will also be weakened.When the high-pressure fuel enters the thinner pipeline from the thicker pipeline, the larger the diameter difference between the two, the greater the local pressure loss.This will lead to the VR being smaller and the fuel circulation characteristics are not good.With the increase of VR, this negative effect will weaken.After exceeding the growth node, the negative effect will be completely eliminated.At this time, further growth VR can enable it to accommodate more pressure fluctuations, but the growth effect is not obvious.Therefore, after exceeding the node, the fuel circulation characteristic ability is slowly enhanced.
Looking at Figure 12A, with the growth of VR, FIR is also growing, that is, as IT increases relative to CRP VR, the consistency of the system is deterrer.When VR = 0.0436, the FIR reaches a maximum value of 1.165, and then gradually decreases.First of all, in the process of rapid improvement of fuel circulation characteristics, although the FIQ change trend of ICP and IFP is similar, their range of change is still different.First of all, there will be delayed pressure loss when the high-pressure fuel is transmitted forward along the length direction of CRP.Second, there are pressure fluctuations in the CRP.The pressure fluctuation inlet section of CRP is relatively stable.High-pressure fuel will experience multiple injectors with the propulsion of the length of CRP, which will not only increase the pressure fluctuation but also increase local losses.Therefore, the FIQ change range of IFP will be smaller than that of ICP.Finally, when VR is very large, IT assumes the function of CRP at this time, but system consistency is not completely unified, which shows that the existence of IT is necessary.As long as the FIR is less than 1.1, consistency can be considered to be excellent.With FIQ as the main consideration, the VR optimal solution of IT can be 0.0052, and the optimal solution can be expanded according to the needs of FIQ in actual production and Looking at Figure 12B, it can be found that the PR of IT rises rapidly with the growth of VR.After reaching the maximum point, it will fluctuate in the process of decline, but the fluctuation trend is not large, and the overall trend tends to stabilize.
With the growth of IT LDR, whether it is IFP or ICP, IP and FIQ fall rapidly first.After breaking through the inflection point, the downward trend of pressure slows down.However, the IP is not exactly the same as the inflection point of FIQ.The inflection point of FIQ's LDR is LDR = 79.11.When the LDR is less than 79.11, the decline slope is 2.74 mm 3 , and the slope after breaking through the inflection point, the slope is 0.31 mm 3 .In the early stage of IT growth, the delay pressure loss is relatively large.At this time, the volume of IT tubes is small, and the pressure fluctuation that can be accommodated is smaller, so the FIQ and IP drop rapidly.When the inflection point is exceeded, the volume increase of IT gradually enhances the ability to hold pressure fluctuations.At this time, the fuel circulation characteristics become better, so the FIQ and IP slowly decrease.Looking at Figure 12C, it can be found that with the growth of IT LDR, FIR fluctuates up and down, and fluctuates greatly, which shows that although the change trend of fuel flow characteristics of IFP and ICP is consistent, the range of change between the two is different.This is because the regional pressure fluctuations near the CRP entrance are small, while the pressure fluctuation of the area far away from the CRP entrance is greater.When the consistency of fuel injection quantity is high, the optimal value solution of LDR can be selected as 1.105.For the consistency of IP, observing Figure 12D, with the growth of IT LDR, PR fluctuates up and down, especially in the second half, which shows that there is a certain correlation between FIQ and PR in the overall trend, but the range of change between the two is not the same.If the consistency of fuel injection pressure is high, the optimal solution of LDR can be 1.054.

| CONCLUSION
A modular HPCRS prediction model for fuel circulation characteristics is established, and the pressure fluctuation mechanism based on CRP structure and pressure storage space is studied, and the influence of CRP on fuel flow characteristics is revealed.Using the method of integrated matching between pipelines, the matching scheme between different pipelines and the core CRP is obtained, and the integration scheme of each pipeline is obtained, which provides a theoretical basis and guidance scheme for improving fuel circulation characteristics and system consistency.The specific conclusions are as follows: (1) The results show that the increase of storage space of the pressure storage module can effectively reduce the fluctuation in the system, but it does not significantly help to establish the time change of the pressure process.For different oil supply frequencies under fixed fuel injection frequency and different injection frequencies under fixed fuel supply frequency, increasing the volume of CRP matching them can be found that the fuel flow characteristics are slowly enhanced first and then rapidly reduced.When comparing the two schemes themselves, their decline slope is similar, but if the curve inflection point is different, the curve inflection point can be regarded as the best value point to match the space size.(2) By modifying the LDR of CRP, the CRP of different structures is obtained, and the influence of the structure of CRP on fuel flow characteristics and system consistency is obtained.With the increase of CRP diameter, the fuel circulation characteristics become excellent first.After breaking through the inflection point, the fuel circulation characteristics become worse.However, for ICP and IFP, the inflection point obtains different positions.Taking system consistency as the main measure, the optimal solution of CRP diameter is limited to 19.1 mm.According to different positions, CRP is divided into three pipes.Using system consistency, the optimal LDR solution for each pipeline is obtained.Generally speaking, the increase in the length of any pipe can soothe pressure fluctuation.(3) The growth of LT diameter will make the fuel circulation characteristics of ICP better first and then worse.First, it will negatively affect the fuel circulation characteristics of IFP, and then promote it.According to system consistency as a measure, the VR optimization solution of LT is 0.0249.The length growth of LT has little impact on fuel flow characteristics.Similarly, the LDR optimal solution of LT can be 55.10.(4) According to the measurement, the optimal value of VR selected CT is 0.00126, and the optimal value of DT's LDR is 58.50.The structure of DT has little impact on the fuel flow characteristics of ICP, and with the increase of VR between DT and CRP, the changes of FIQ and fuel injection pressure are volatile.The structure of DT mainly affects the fuel flow characteristics of IFP.It is negatively correlated with DT's VR and positive correlation with DT's LDR.Therefore, the optimal solution of VR is 0.0249 and the optimal solution of LDR is 32.21.(5) The growth of IT VR promotes fuel circulation characteristics and greatly improves fuel circulation characteristics.However, after exceeding a certain node, this growth effect weakens, but the growth of VR has a weakening effect on system consistency.For different requirements, the optimal value points selected are also different.The growth IT's LDR is negatively correlated with the fuel flow characteristics, which will also cause system consistency to fluctuate.(6) This study established a modular HPCRS prediction model for fuel circulation characteristics and investigated the pressure fluctuation mechanism based on the CRP structure and pressure storage space.Dimensionless numbers were introduced to evaluate the system, providing a theoretical basis and guidance scheme for improving fuel circulation characteristics and system consistency, which is beneficial for advancing the research on Common Rail systems.The study revealed optimal solutions for each pipeline and their impact on fuel flow characteristics and system consistency, demonstrating the validity of the applied method.Future research can further explore the impact of other factors on fuel circulation characteristics and search for more optimization solutions for Common Rail systems.

F I G U R E 2
High pressure common rail system test bench.(A) Experiment bench, (B) injector, and (C) control and data acquisition system.F I G U R E 3 Simulation model of HPCRS.

F I G U R E 4
Simulation calculation data and experimental data comparison.(A) Fuel injection quantity comparison and (B) common rail pressure comparison.F I G U R E 5 The matching design of fuel supply frequency, injection frequency and pressure storage module.(A) Matching design of plunger pump and common rail tube volume.(B) Matching design of fuel injector and common rail tube volume.increase of the diameter of the common rail tube, the injection pressure of fuel injector near the inlet segment of the common rail pipe (ICP) and fuel injector near the end of the common rail pipe (IFP) increases first, and then decreases.Observing Figure6B, the same pattern applies to FIQ.The fuel injection pressure (IP) of ICP reached the maximum 1889.36 bar at the CRP diameter of 16.9 mm.The IP of IFP reaches a maximum of 1929.88 bar at CRP diameter of 14.8 mm.The FIQ of ICP reached a maximum of 657.45 mm 3 when CRP diameter was equal to 18.5 mm.When the CRP diameter was 14.8 mm, the FIQ of ICP reached a maximum of 679.88 mm 3 .The high pressure pump pressurizes the fuel into the common rail pipe.The increase of the length of the pipe leads to the increase of the resistance of the oil flow, which reduces the oil pressure at the IFP.

F I G U R E 6
The influence of common rail diameter on fuel flow characteristics.(A) Comparison of fuel injection volume.(B) Comparison of injection pressure.

3. 2 |
The influence of high-pressure tube HPCRS modules are mainly connected by high-pressure tubing.The connection of various pipelines is shown in Figure 8. Low-pressure fuel first enters the integrated F I G U R E 7 The influence of structural parameters of common rail on fuel flow characteristics.(A) The influence of GP's LDR on fuel injection volume.(B) The influence of SP's LDR on fuel injection volume.(C) The influence of AP's LDR on fuel injection volume.AP, pipeline acting as accommodating; GP, pipeline acting as a guide; LDR, ratio of the length to diameter of a pipeline; SP, pipeline acting as a spacing.

F I G U R E 8
Distribution map of various tubes.

F I G U R E 9
The influence of structural parameters of link tube on fuel flow characteristics.(A) The influence of VR of LT and CRP on fuel injection volume.(B) The influence of VR of LT and CRP on fuel injection pressure.(C) The influence of LT's LDR on fuel injection volume.(D) The influence of LT's LDR on fuel injection pressure.

10
The influence of structural parameters of collecting tube on fuel flow characteristics.(A) The influence of VR of CT and CRP on fuel injection volume.(B) The influence of VR of CT and CRP on fuel injection pressure.(C) The influence of CT's LDR on fuel injection volume.(D) The influence of CT's LDR on fuel injection pressure.

11
The influence of structural parameters of distribution tube on fuel flow characteristics.(A) The influence of VR of DT and CRP on fuel injection volume.(B) The influence of DT's LDR on fuel injection volume.

F
I G U R E 12 The influence of structural parameters of injection tubes on fuel flow characteristics.(A) The influence of VR of IT and CRP on fuel injection volume.(B) The influence of VR of IT and CRP on fuel injection pressure.(C) The influence of IT's LDR on fuel injection volume.(D) The influence of IT's LDR on fuel injection pressure.
Simulation calculation parameters of HPCRS.
T A B L E 1 T A B L E 2 Physical properties of test fuel.