The injection rate shape is an important factor that affects the spray formation. After leaving the injector, the fuel spray atomizes into droplets, vaporizes, and mixes with the air. In this work, models with different injection rate shapes are analyzed for their spray and fuel mixing behavior using the basic conditions from the previous work on ECN case No. 2, as shown in
Table 2. The four injection rate shapes shown in
Figure 12 were selected for this study. The rectangular injection rate (RECT) shape is the constant injection rate and is a commonly used injection rate shape. The other three shapes consist of the Quick Increase Gradual Decrease injection rate (QIGD), the Gradual Increase Gradual Decrease injection rate (GIGD), and the Gradual Increase Quick Decrease injection rate (GIQD). These shapes were designed to examine the effects of an increase and a decrease of the injection rate over a short injection duration to study the influence of spray and combustion behavioral control factors based on previously reviewed research. The above factors include the peak injection rate, the initial injection rate, and the injection velocity of each injection period, which are useful for understanding the spray and fuel mixing behavior. The four injection rate shapes must have the same injection duration and fuel quantity to be used as a benchmark. The three shapes (QIDG, GIGD, and GIQD) had peak injection rates higher than the experimental conditions in case No. 2, which means that the rail pressure would be higher than 150 MPa. As shown in the simulation model, these injection rate shapes can create a peak rail pressure of approximately 600 MPa. A maximum rail pressure of 600 MPa is too high for current engine technology. In this study, the maximum rail pressure generated by the injection rate was determined from the study conditions according to the constant value of the injection duration with the same amount of fuel as used in the experimental data to ensure that the model calibrated from the experiment data would be accurate. The injection pressure can be increased by changing the injection rate of the fuel pump and adjusting the injector area. If the injection pressure is too high, the ignition delay period will be shorter. This may cause a homogeneous decrease in mixing and reduce the combustion efficiency. In practice, changing the injection rate and injector area is necessary to help reduce these effects.
As a result that the newly created injection rate shape for this study is determined by a constant injection duration and fuel mass (including under ambient conditions, which are similar to those of the experimental data), under some conditions, this novel injection rate provides a peak injection rate that is higher than the injection rate of the experimental data used to calibrate the model. This means that higher injection rates will also result in higher rail pressure. Although this study explored the maximum rail pressure conditions up to 600 MPa, the results calibrated with the experimental data for rail pressure of 50, 100, and 150 MPa showed that the model can provide reliable simulation results, even under conditions where the pressure is different. In particular, the simulation results show that the study conditions at a maximum rail pressure of 150 MPa can provide better simulation results than under conditions of a lower maximum rail pressure. This means that the newly created model is effective for high rail pressure conditions. In addition, in this paper, all case studies (including the cases of maximum rail pressure conditions of 600 MPa) use ambient conditions. The injection timing and the fuel mass are the same as those of the experimental conditions at a rail pressure of 150 MPa because the simulation results for the calibration under rail pressure conditions of 150 MPa give good results for both quantity and volume. The prediction results for the spray shape are compatible with the photos from the experimental data; this shape reflects the accuracy of the distribution angle, penetration, and evaporation of the spray. The injection rate and injection pressure have a great influence on these physical characteristics. Therefore, the model created can predict the spray behavior very well, especially under high rail pressure conditions. Based on the study of the effects of different rail pressures, the spray shape data from the experiment demonstrate that the size of the spray cone angle is different under the same ambient conditions, as shown in
Figure 13.
Figure 13 shows the spray cone angle size obtained from the spray picture of the experiment data. The result indicates that the spray cone angle used as the input data in this study depends on the size of the maximum rail pressure. The model calibration demonstrated that using the spray cone angles obtained from the experimental spray images as inputs can provide good predictive results (consistent with the experimental data). Therefore, this study used the prediction equation (Equation (8)) to predict the size of the spray cone angle at different rail pressures:
4.1. Microscopic Spray Characteristics
In spraying simulations, the turbulent distribution has a significant impact on the spray parameters. The spray penetration distance depends on the surrounding conditions, including the injection rate, the injection time, the injected mass quantity, and others. The injection rate design affects the spray penetration and spray distribution angle. This section presents the spray penetration distance consisting of liquid and vapor penetration both during the injection time (0–1.54 ms) and after the EOI, by comparing the results of different injection rate shapes and using these shapes to analyze their effects on the microscopic spray characteristics.
Figure 14 shows the simulation results of the spray penetrations. The black, red, blue, and yellow lines represent the simulation results for the RECT, QIGD, GIGD, and GIQD injection rates, respectively. The results of vapor penetration are shown in the top graph, while the middle and bottom graphs show the liquid penetration and injection mass flow rates, respectively.
Figure 14 (top graph) shows the vapor penetration for the four injection rates with different shapes. The QIGD injection rates show the longest vapor penetration (approximately 25 mm), with an injection rate of around 4.5 mg/ms. Vapor penetration lengths with the same peak injection rates will ultimately lead to the same vapor penetrations. This occurs because, during injection, vapor penetration increases with the injection acceleration rate. After the EOI, the vapor penetration distance increases along with the injection rate at the EOI, when the spray penetration distance is affected by the momentum flux ratio. For the GIQD injection rate shape after the EOI, the vapor penetration continues to increase continuously, and a high injection rate results in rapid fuel movement, while the vapor penetration of the QIGD injection rate shape decreases continuously because of the injection rate at the EOI.
Figure 14 (middle graph) shows the liquid spray penetration, for which the different injection rates also have a significant impact on liquid penetration. The QIGD injection rate provides the longest initial liquid penetration due to having the highest injection rate, while the GIQD injection rate shows the opposite. Liquid spray penetration increases relative to the injection rate shape and terminates at the end of injection. The liquid spray penetration results show the same trend as the injection rate for all cases. Since the greatest penetration distance is primarily affected by the momentum flux ratio, the liquid penetration distance will increase when the injection rate increases and decrease when the injection rate decreases. This is due to slowdown in the movement of the liquid fuel.
In addition, because the spray penetration is a phenomenon that occurs in conjunction with the spray distribution, the spray distribution angle is an important parameter that affects the spray mixing process and is important for the analysis of spray performance. Therefore, the spray distribution angle was investigated by measuring the distribution angle via the spray shape obtained from the simulation.
Figure 15 shows the spray distribution angles from the simulation results, where the black, red, blue, and yellow dots represent the measurement results of the RECT, QIGD, GIGD, and GIQD injection rates, respectively. As shown in the
Figure 14, comparisons were made between the spray angle (left graph) and spray cone angle (right graph) under different injection rate shapes. Similar techniques to those in the previous section were used to measure the spray distribution angles.
The same spray cone angle measurement results are shown in
Figure 15 (right graph) for the same peak injection rate (same peak rail pressure) with different injection rate shapes; the results agree with those in the previous section. The shape with a peak rail pressure of 600 MPa and a spray cone angle of 43° will have spray cone angle larger than approximately twice that of the peak rail pressure of 150 MPa (21°).
Figure 15 (left graph) shows a difference in the spray angle event under the same peak rail pressure. The spray angle increases when the acceleration of the injection rate increases. It can be observed that the QIGD injection rate is significantly small but features a continuous decrease in the spray angle compared to the other injection rates. On the other hand, the GIQD injection rate recorded the largest spray angle at the beginning, followed by a slight decrease, and then remained constant (compared to the other injection rates). This phenomenon demonstrates that the increased injection acceleration rate has a significant effect on the fuel distribution ability, which directly affects the spray angle size. The spray angle is higher when the injection rate is higher because the injection rate can increase the rail pressure, thereby resulting in a higher particle force that can cause a higher penetration force leading to better distribution. The spray angle is an important parameter that helps us understand the global characteristics of the spray. The spray angle and quantity evaluation provide useful information about the airflow in the spray [
29,
30,
31], where the spray angle is an indicator of gas. In general, the greater the spray angle, the higher the increase in gas entrainment, resulting in improved mixing [
32]. Another interesting observation is the effect of the injection rate shapes on spray penetration. The simulation results reveal longer vapor penetration at a higher peak injection rate due to the efficient spray distribution, while the lower peak injection rate yielded poor vapor penetration because the low injection rate resulted in poor spray distribution and spray penetration performance. A spray tip that penetrates too long will result in wet combustion chamber walls, causing excessive soot formation and a waste of fuel. On the other hand, if the penetration time is too short, the mixing efficiency and optimum combustion will be compromised. In addition, the simulation results show that the QIGD injection rate with a high initial fuel injection rate quickly causes the initial penetration. This suggests that the injected fuel is very well atomized and has a significant effect on the onset speed of the combustion phenomenon. In the case of the GIQD injection rate, a very low initial injection rate may result in poor fuel atomization and cause an increase in the ignition delay. The evaporation process and mixing behavior will be discussed further in the next section.
4.2. Evaporation Process
We next studied the evaporation process influenced by the fuel injection rate by considering the distribution of droplet sizes. This section presents the simulation results of the evaporation ratio under different injection rate shape conditions, as shown in
Figure 16. The simulation results show that different injection rate shapes result in different evaporation ratios. The results of the evaporation ratios are shown in the top graph, and the injection mass flow rates are shown in the bottom graph, where the black, red, blue, and yellow lines represent the simulation results of the RECT, QIGD, GIGD, and GIQD injection rates, respectively.
Figure 16 shows that the RECT and the QIGD injection rate shapes undergo more rapid evaporation than the other injection rate shapes. As demonstrated by the RECT and the QIGD injection rate shapes, the evaporation ratio increases to nearly one before approximately 0.01 ms. For the GIGD and GIQD injection rates, the evaporation ratio increases to nearly one at approximately 0.1 ms. These results are due to both injection rate shapes having a quickly increasing initial injection rate, thereby resulting in high rail pressure, which can improve the evaporation rate because higher rail pressure results in a high shear of the fuel particles, which can change the fuel state from liquid to gas very quickly with higher mass flow rates, as well as accelerate the fuel evaporation process.
To better understand the spray breakup characteristics, the SMD is an important parameter that should be considered to reflect the spray performance. The size of the SMD is related to droplet breakup, in which a smaller SMD result in better droplet breakup. Due to the lack of experimental data to calibrate the simulated SMD results, only the relationship between the SMD and injection rate have been considered.
Figure 17 shows the relationships of the SMD values for different injection rate shapes, where the black, red, blue, and yellow lines represent the simulation results of the RECT, QIGD, GIGD, and GIQD injection rates, respectively. The results show that the SMD decreases rapidly when the injection rate increases sharply, at the same time, the SMD gradually decreases as the injection rate gradually increases. This occurs because the droplet tends to breakup under conditions with higher injection rates. A high initial injection rate can clearly reduce the SMD. As can be considered from the high initial injection rate conditions (RECT, QIGD), the SMD decreases to nearly zero at approximately 0.02 ms; with gradual increases in the injection rate conditions (GIGD, GIQD), the SMD decreases to nearly zero at approximately 0.1 ms. These values are worth noting for the RECT and QIGD injection rates. Although the initial injection rates are not the same, the injection rate is sufficiently higher to result in a rapid decrease in the SMD. These behaviors support the spray breakup phenomenon. The evaporation rate is higher for the droplet under a higher initial injection rate, as shown in
Figure 16. From
Figure 17, it can be concluded that the initial injection rate is the main factor affecting the size of the droplets, as an increase in the injection rate results in a decrease in the SMD. Therefore, under higher initial injection rates, the droplets will become smaller and lead to faster evaporation.
The fuel evaporation phenomena can be understood by considering the temperature distribution phenomena.
Figure 18 and
Figure 19 show the simulation results comparing the temperature distribution with different injection rate shapes during injection and after the EOI. The spray images were obtained from the cut-plane in the direction of the spray. The gradient color region represents the temperature data and shows the temperature value as a gradient color bar in the bottom right corner.
Figure 18 and
Figure 19 show that the spray penetration area is cooler than the surrounding combustion chamber, as the fuel absorbs heat for vaporization. The RECT and QIGD injection rates show better vapor penetration at the beginning when considering the temperature distribution contours and comparing them with the other injection rate shapes. This phenomenon occurs due to the higher initial injection rate compared to the GIGD and GIQD injection rates. In addition, the area near the nozzle exit showed different vapor penetration values for each case. The very high injection rate that resulted in initial vapor penetration also occurred further away from the nozzle exit. In
Figure 18 and
Figure 19, under the GIQD injection rate, the vapor penetration at the nozzle exit is farther away from the nozzle exit and clearly farther from the injector exit than other shapes after the EOI. This is because the gradual increase in the injection rate results in fuel breakup capability.
These phenomena occur because faster injection rates can accelerate the evaporation of fuel, with the airflow in the cylinder having a great impact on the evaporation and atomization of the fuel. Therefore, under the conditions of higher injection rates, the droplets will be smaller and evaporate faster, resulting in better acceleration in the formation of the air–fuel mixture. It can be predicted that a high initial injection rate would result in a decrease in the ignition delay period due to better fuel atomization at the beginning of the injection, which may more quickly lead to the start of combustion. The influence of injection rate shapes on the characteristics of the mixture properties will be studied in the next section.
4.3. Mixture Properties
For a deeper understanding of the diesel spray mixing process, the mixture properties are studied in this section by comparing their equivalence ratios and turbulence kinetic energy (TKE) values at different injection rates.
The mixture properties are analyzed by considering the region of the equivalence ratio predicted from the 3D model, which plays an important role in the analysis of the diesel spray mixing process. Therefore, the equivalence ratio is calculated from the basic data of the mass fraction. In this study, the conditions of the case study are the conditions under which the ambient component does not contain oxygen (r
O2 = 0). We applied the following equation of chemical combustion:
Here, we assume that by replacing the oxygen ratio with the total gas ratio (including the oxygen ratio), the general air contains 21% oxygen and 79% other gases. Therefore, the mass fraction is given as Fuel/(Fuel + O
2 + other gases), where the equivalence ratio is equal to 1. From the simulation results, the different injection rate shapes show different spray behaviors and equivalence ratio histories, although the injection duration and injection mass quantity are the same.
Figure 20 and
Figure 21 provide a comparison of the spray behavior and equivalence ratio histories of the simulation results during injection (
Figure 20) and after the EOI (
Figure 21). The spray images were obtained from the cut-plane in the direction of spray. The gradient color region represents the equivalence ratio data and shows the equivalence ratio values as a gradient color bar in the bottom right corner, while the black particles are the liquid fuel data from the simulation.
Figure 20 shows the spray behavior and equivalence ratio histories for the four injection rates. It can be observed that although the injection mass and time for all simulated cases are the same, the spray behavior and equivalence ratio histories for each injection rate shape are very different. There is a high fuel distribution near the nozzle exit of the injection rate shapes with a high peak rail pressure (QIGD, GIGD, and GIQD), which is different from the case with the lower peak rail pressure (RECT). In general, fuel distribution is influenced by changes in the fuel injection rates. These phenomena are clearly reflected in
Figure 21.
Figure 21 clearly shows that the GIQD injection rate with the highest injection rate at the EOI provides the leanest equivalence ratio near the nozzle exit. This is due to the influence of the injection rate, which affects the fuel breakup and the surrounding air crossflow. The momentum arising from increasing the injection rates yields a complementary momentum. The initial injection rate is related to the droplet breakup. For example, for high initial injection rate conditions (RECT and QIGD), the black particles represent the liquid fuel intensely near the nozzle exit and descend quickly when the injection time has passed. This is an example of quick SMD reductions, as shown in
Figure 17.
For a better understanding of the spray behavior in diesel spray mixing, TKE is an important influencing factor that can explain the phenomenon of the equivalence ratio. TKE can reflect the intensity of the turbulent movement in the cylinder.
Figure 22 shows a comparison of TKE with different injection rates. The TKE is displayed as the average value of the TKE in the control volume model, where the black, red, blue, and yellow lines represent the simulation results of the RECT, QIGD, GIGD, and GIQD injection rates, respectively. The top graph shows the TKE and the bottom graph shows the injection mass flow rate.
The injection rate has a significant relationship with the TKE. At low mass flow rates, the field flow will be smooth without a recirculation zone. On the other hand, when the mass flow rate increases, the vortex will increase. This intense recirculation will increase heat transfer compared to the smooth channels.
Figure 22 shows the strongest TKE during the initial injection under the QIGD injection rate, while the RECT injection rate shows the strongest TKE during the injection. Subsequently, after the EOI, the GIQD injection rate shows the strongest TKE. These phenomena can be explained by the influence of TKE production, which is related to the effect of the spray structure. The simulation results of TKE distribution with different injection rates, both during injection and after the EOI, are shown in
Figure 23 and
Figure 24, respectively. The turbulence phenomenon is considered in the boundary of the spray region, where the model provides sufficient mesh density. The spray images were obtained from the cut-plane of the direction of the spray. The gradient color region represents the TKE distribution, which presents the TKE data as a gradient color bar in the bottom right corner.
Figure 23 and
Figure 24 show the contour of the TKE with different injection rate shapes. The state of turbulence distribution affects the proportions of the length and width of the spray shape. For example,
Figure 23 and
Figure 24 show the strong TKE of the QIGD injection rate case that moved to the area along the length of the spray, which resulted in long spray penetration and a lean equivalence ratio in the spray tip area, as can be seen in
Figure 20 and
Figure 21. This is because a high injection rate directly affects the crossflow, resulting in significant disintegration and displacement.
Figure 23 and
Figure 24 show that the TKE production of the RECT injection rate is strong in the axial area of the spray, which indicates that the TKE distribution occurs along the width of the spray. Although the TKE of the RECT injection rate is the strongest during the injection period (see
Figure 22), the TKE produced cannot offer penetration longer than the QIGD injection rate (
Figure 23 and
Figure 24). The QIGD injection rate initially shows the strongest TKE; then, the TKE distribution moves along the length of the spray faster than the other injection rates and has the highest TKE at the spray tip area. This is due to this spray’s high speed and acceleration, causing more increased turbulence levels in the downstream areas than in other injection rate shapes. This gives the QIGD injection rate the highest efficiency of spray turbulence, providing the leanest equivalence ratio at the spray tip area.
The phenomenon of TKE distribution can be well illustrated by the temperature distribution in
Figure 18 and
Figure 19, which show that the QIGD injection rate has a higher temperature in the spray tip area than other shapes. When considering the temperature distribution behavior after the EOI in
Figure 19, the RECT injection rate shape retains the lowest temperature at the spray tip area compared to the other injection rate shapes. The highest temperature at the spray tip area of the QIGD injection rate and the lowest temperature at the spray tip area of the RECT injection rate can predict the spray turbulence behavior. A high temperature means that the area may produce high turbulence results with a lean equivalence ratio but show opposite spray behavior at low temperatures. These results are due to the high temperature influencing the droplet size and evaporation. These phenomena occur when the increased fuel injection rate causing the TKE grows, thereby leading to faster fuel spread and resulting in faster fuel and air mixing. The TKE can reflect the intensity of the turbulent motion in the cylinder, with a large TKE indicating that the agitation is more intense in the cylinder. Examination of the turbulence demonstrates that a high TKE flow provides a clear driving force for mixing and evolution. In addition, strong turbulent mixing leads to the highest chance of saturation, which results in better mixing opportunities. Therefore, the higher the initial injection rate, the greater the variability of the cutting force field in the spray area. This phenomenon is related to the fact that the shape of the injection rate has a significant impact on the potential of spray behavior and TKE production. The mixing efficiency is very potent when the TKE distribution has high potential due to a sufficiently large increase in rail pressure.
The results of this simulation study show that high initial injections will produce high turbulence energy. The GIQD injection rate is highly efficient in atomization and creating good fuel–air mixing, thus resulting in good combustion. The duration of the combustion at each injection rate can be arranged, from long to short, as follows: GIQD, GIGD, RECT, and QIGD. Since the QIGD injection rate has the highest initial injection rate, combustion may start earlier, while the GIQD injection rate has the lowest initial injection rate, which will result in less atomization and poorer combustion.
In addition, when analyzing the mixing behavior of sprays (which can affect emissions), CO emissions increase when the initial injection rate is low, which will shorten the flame lift-off length [
6]. This means that the fuel-injection does not have enough time for good air entrainment before the start of combustion, resulting in higher CO emissions levels. A high initial injection will result in high NO because a high initial injection will lead to an earlier start of combustion and a higher peak heat-release. We expect that the QIGD injection rate will have the highest amount of heat released because the temperature contours and the QIGD injection rate case will provide the fastest mixing. This mixing will result in the shortest ignition delay duration with the highest observed heat-release. The strategy for creating high initial injection rates often results in NO
x emissions and a higher engine noise level. In our numerical simulation on the influence of injection rates on spray behavior affecting the mixing and combustion processes, we chose the QIGD injection rate as the optimal rate for the injection strategy, which requires the injection time and combustion to be short, because this injection rate’s mixing efficiency is greater than that of the other injection rate shapes. The RECT injection rate was used for reducing NO
x and engine noise due to lower pressure in the combustion chamber. Future studies will be developed on the efficiency of injection strategies that can simultaneously reduce NO
x emissions, engine noise levels, and soot emissions.