**3. Model Validation**

In this section, the numerical models above were studied using a real experiment. Two di fferent sets of operating conditions were used for predicting the spray behavior, including the spray shape, the spray penetration, and the equivalence ratio. The first set involves the model calibration using an evaporation process under experimental conditions at di fferent ambient temperatures. The second set involves the model being calibrated at di fferent rail pressures using the experimental conditions of the Sandia National Laboratory in the ECN [23]. The ambient density, steady flow discharge coe fficient, and nozzle hole diameter are the same in all conditions (22.8 kg/m3, 0.89 mm, and 0.084 mm, respectively) and with the other conditions di fferent, as shown in Table 2.


**Table 2.** The Operating Conditions of the Test Cases.

The injection rate of the test conditions conducted by the Sandia National Laboratory in the ECN was determined by CMT, in which the injection mass flow rate of the Spray A condition was created using the "Virtual Injection Rate Generator" model on the ECN website. The virtual injection rate generator model considers the expected hydraulic fluctuations, including the injector opening times, the pressure, the nozzle diameter, and the discharge coe fficient.

#### *3.1. Ambient Temperature E*ff*ects*

In this section, the low and high ambient temperature conditions are used for model calibration. To demonstrate the predictive efficiency of the model, the spray behavior under different ambient temperatures, as well as at different ambient pressures (case No. 1 and 2 in Table 2) is used as a case study.

A comparison of the fuel spray injection in the cylinder at di fferent ambient temperatures and ambient pressures shows the influence of evaporation and spray fuel di ffusion. Figures 2 and 3 present a comparison of the spray shape and equivalence ratio between the experimental and simulation results for cases No. 1 and 2. The gray background images show the experimental data obtained from high-speed videos using the Schlieren video technique to represent the vapor and liquid for case No. 1. For case No. 2, the experimental data image obtained from the high-speed video using the Schlieren video technique shows vapor and liquid regions, which are stored as MATLAB binary files. The white background images show the simulation result, in which the gradient color region represents the equivalence ratio data. The value of the equivalence ratio is represented by the gradient color bar in the right corner. The black particles are liquid fuel data from the simulation, which the cut-plane from the direction of the spray then rotates 90◦ to the left. Figures 2 and 3 illustrate the shape of the variance by using Re-Normalization Group Theory to determine the small movement effects, while the KH-ACT model calculation captures the impact of cavitation and turbulence on the primary cracks in addition to aerodynamic separation. The calculation results show a smoother distribution for the spray shape boundary simulation than for the experimental data due to the turbulence model's limitations in conjunction with the RNG k-ε turbulence model, where the RNG k-ε turbulence model is used for determining the smaller movements effects. Nonetheless, the simulation results are satisfactory, as these results indicate the effective grid resolution for this simulation. Each comparison image shows the exact thickness of the fuel mass distributed throughout and is consistent with the experimental data. The method of image analysis obtained from this model is sufficient for the study of spray behavior.

The comparison results (Figure 4 and Figure 6) show the spray penetration and spray distribution angle. Black and red represent the results under ambient temperatures of 440 and 900 K, respectively, while dots and solid lines represent the experimental and simulation results, respectively.

The results of vapor penetration are shown in the top graphs of Figures 4 and 5, while the middle and bottom graphs show the liquid penetration and injection rates, respectively.

Figure 4 shows the simulation results that are compatible with the experimental results both during injection and after the EOI. The initial injection is important to consider, as it provides the momentum to change the conditions in the combustion chamber caused by the onset of fuel injection, thereby increasing the injection rate, temperature, and pressure. As shown in Figure 5, the initial spray penetration (0.0–0.3 ms) reveals that both cases cannot properly capture the initial ramp for both vapor and liquid penetration. Due to the very short time error of the simulation results (less than 0.1 ms), the injection rate input data from the virtual injection rate generator may not be as accurate as those of the actual injection rate.

**Figure 2.** Comparison of the spray shapes and equivalence ratio histories of the experimental result [23] and the simulation result under an ambient temperature of 440 K.

**Figure 3.** Comparison of the spray shapes and equivalence ratio histories of the experimental result [23] and the simulation result for an ambient temperature of 900 K.

**Figure 4.** Comparison of the spray penetration of the experimental result [23] and simulation result at different ambient temperatures. (**a**) Maximum vapor penetration, (**b**) liquid spray penetration and (**c**) injection mass flow rate.

**Figure 5.** Comparison of the initial spray penetration (0.0–0.3 ms) of the experimental result [23] and the simulation result under different ambient temperatures. (**a**) Maximum vapor penetration, (**b**) liquid spray penetration and (**c**) injection mass flow rate.

Figure 6 shows a comparison of the spray angle (left graph) and the spray cone angle (right graph) with varying ambient temperatures. The measurement results from experimental data show that the ambient temperature influences the spray angle but not on the spray cone angle. The trend of the measurement results of the spray cone angle is the same for both cases, which means that the spray cone angle is independent of the ambient temperature and ambient pressure. In addition, the simulated spray cone angle results show the same trend as the measured experimental results. These results show that the constructed model effectively predicted spray behavior under varying conditions of ambient temperature and ambient pressure.

#### *3.2. Rail Pressure E*ff*ects*

To ensure that the effects of rail pressure changes are captured by the model when predicting the spray's behavior between the start of the injection (lamping up) and the end of the injection (lamping down), the experimental conditions from previous ECN work under operating conditions No. 2, 3, and 4 (as described in Table 2) are studied in this section.

Figures 7 and 8 show a comparison of the spray shape and equivalence ratio between the simulation results and the experimental data of the rail pressure under 100 MPa and 50 MPa conditions, respectively. The gray background images show the experimental data obtained from high-speed videos using the Schlieren video technique. The white background images show the simulation results. The gradient color region represents the equivalence ratio data, with values shown on the gradient color bar in the right corner.

**Figure 6.** Comparison of the spray distribution angle for different ambient temperatures. (**a**) Spray angle and (**b**) spray cone angle.

**Figure 7.** Comparison of the spray shapes and the equivalence ratio histories of the experimental result [23] and the simulation result under a rail pressure of 100 MPa.

The black particles are the liquid fuel data from the simulation, which the cut-plane from the direction of the spray then rotates 90◦ to the left (which is similar to the display in case No. 2, as mentioned in the previous section (Figure 3)). From these comparisons, the results of the simulation show a better prediction under high rail pressure conditions (150 MPa and 100 MPa) than under a low rail pressure condition (50 MPa).

The results of the spray penetration and spray distribution angle (Figures 9 and 10) shown in the red, blue, and yellow colors indicate the results for rail pressures of 150, 100, and 50 MPa, respectively. The dots and solid lines represent the experimental and simulation results, respectively. The results of vapor penetration are shown in the top graphs of Figures 9 and 10, while the middle and bottom graphs show the liquid penetration and injection rates, respectively.

**Figure 8.** Comparison of the spray shapes and equivalence ratio histories of the experimental results [23] and simulation results for a rail pressure of 50 MPa.

**Figure 9.** Comparison of the spray penetration of the experiment results [23] and the simulation results for different rail pressures. (**a**) Maximum vapor penetration, (**b**) liquid spray penetration and (**c**) injection mass flow rate.

**Figure 10.** Comparison of the initial spray penetration (0.0–0.3 ms) for the experiment results [23] and the simulation results under different rail pressures. (**a**) Maximum vapor penetration, (**b**) liquid spray penetration and (**c**) injection mass flow rate.

Figure 9 shows that the model predictions for the penetration length under high rail pressure conditions are longer than those under low rail pressure conditions, which is consistent with the experimental data. Figure 10 shows the initial spray penetration (0.0–0.3 ms); even under the rail pressure conditions in all three cases, these data cannot properly capture the initial ramp for both vapor and liquid penetration. The simulation results show a trend that is consistent with the experimental data. The spray model and other sub-parameters make this model more effective in its predictions, which is consistent with experimental data.

The rail pressure directly affected the air fluctuation in the injected fuel due to the impulse exchange between the gas and the liquid. The spraying behavior under high rail pressure caused the cavitation flow to efficiently accelerate at the nozzle exit. The high rail pressure cavity also increased the spray distribution angle [22]. Figure 11 shows a comparison of the spray angles (left graph) and the spray cone angles (right graph) for different rail pressures, in which the spray distribution angle is measured by the same technique described in the previous section. It was found that the size of the spray angle is not constant, but the spray cone angle from the measured simulation results shows a similar trend to the experiment. This confirms that the spray cone angle size setup in this model is correct and can thus predict the experimental data with acceptable accuracy.

**Figure 11.** Comparison of the spray distribution angle for different rail pressures. (**a**) Spray angle and (**b**) spray cone angle.

The above results show that different rail pressure conditions affect the spray's infiltration behavior. The generated model shows good predictive performance when there is a change in the working conditions. These results demonstrate that this model can predict the spray's permeability and injection characteristics at an acceptable level. This model will be used for spray behavior predictions to analyze the behavior and mixing processes of diesel spray with different injection rate shapes in the next section.

#### **4. E**ff**ect of the Injection Rate Shape**

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.

**Figure 12.** The varying shape of the fuel injection rate with a constant injection duration and fuel quantity. The rectangular injection rate (RECT), 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).

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 grea<sup>t</sup> 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:

$$Sray\text{ come } angle = 0.05P\_{\text{rail}} + 13.333.\tag{8}$$

**Figure 13.** Comparison spray cone angle for 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.

**Figure 14.** Comparison of the simulated spray penetration with different injection rate shapes. (**a**) Maximum vapor penetration, (**b**) liquid spray penetration and (**c**) injection mass flow rate.

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.

**Figure 15.** Comparison of the spray distribution angle for different injection rate shapes. (**a**) Spray angle and (**b**) spray cone angle.

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 [29–31], 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 di fferent injection rate shape conditions, as shown in Figure 16. The simulation results show that di fferent injection rate shapes result in di fferent 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.

**Figure 16.** Comparing the evaporation ratios from the simulation results. (**a**) Evaporation ratio and (**b**) injection mass flow rate.

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 di fferent 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.

**Figure 17.** Comparison of the Sauter mean diameter (SMD) for different injection rate shapes.

The fuel evaporation phenomena can be understood by considering the temperature distribution phenomena. Figures 18 and 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.

Figures 18 and 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 Figures 18 and 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 grea<sup>t</sup> 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.

**Figure 18.** Comparison of the temperature distribution during injection for different injection rate shapes.

**Figure 19.** Comparison of temperature distribution after the EOI for different injection rate shapes.
