*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 (rO2= 0). We applied the following equation of chemical combustion:

$$\text{Fuel} + \text{O}\_2 \rightarrow \text{CO}\_2 + \text{H}\_2\text{O}.\tag{9}$$

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 + O2 + 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. Figures 20 and 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.** Comparison of the spray behavior and equivalence ratio histories during injection for different injection rate shapes.

**Figure 21.** Comparison of the spray behavior and equivalence ratio histories after the EOI for different injection rate shapes.

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.

**Figure 22.** Comparison of the turbulence kinetic energy (TKE) for different injection rate shapes. (**a**) TKE and (**b**) 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 Figures 23 and 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.** Comparison of the TKE distribution during injection for different injection rate shapes.

**Figure 24.** Comparison of the TKE distribution after the EOI for different injection rate shapes.

Figures 23 and 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, Figures 23 and 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 Figures 20 and 21. This is because a high injection rate directly affects the crossflow, resulting in significant disintegration and displacement. Figures 23 and 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 o ffer penetration longer than the QIGD injection rate (Figures 23 and 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 e fficiency 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 Figures 18 and 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 e fficiency is very potent when the TKE distribution has high potential due to a su fficiently 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 e fficient 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 a ffect emissions), CO emissions increase when the initial injection rate is low, which will shorten the flame lift-o ff 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 NOx emissions and a higher engine noise level. In our numerical simulation on the influence of injection rates on spray behavior a ffecting 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 e fficiency is greater than that of the other injection rate shapes. The RECT injection rate was used for reducing NOx and engine noise due to lower pressure in the combustion chamber. Future studies will be developed on the e fficiency of injection strategies that can simultaneously reduce NOx emissions, engine noise levels, and soot emissions.
