## 3 Results
### Velocity Vectors and Turbulence Kinetic Energies  
Figure 7 shows the velocity vectors in the cylinder on the central plane at the TDC of the engine. The simulation results showed that the velocity inside the engine cylinder reached the maximum value at the SA of 45 degrees in all three IP cases (IP = 0.01, 0.015, and 0.02 mm) in both diesel and DF modes. This tendency can be explained by the fact  
Figure 6: Comparison between the simulation and experimental results: (**a**) Peak pressure; (**b**) IMEP; (**c**) NO emission.  
that since the environment inside the cylinder is the same in all cases, the velocity of the injected fuel will be affected only by SA and IP. SA and IP specify the direction and the target region of the injection in the engine cylinder. The direction and the target region of the injection are very important because they affect the interaction between fuel injection streamlines from radial nozzles in this engine, as well as between fuel injection streamlines and the piston surface. When the SA was 40 degrees, the target region of the injection became closer to the piston surface. Meanwhile, when the SA was 50 degrees, the target regions of radial injections interacted with each other. Higher interactions among radial injections and between the injected fuel and piston surface led to a reduction in the fuel velocity inside the engine cylinder. These interactions can be observed in Figure 7.  
Figure 7: Velocity vectors in the engine cylinder at the TDC in all simulation cases with various SA and IP: (**a**) Diesel modes, (**b**) DF modes.  
Figure 8 shows the TKEs in the engine cylinder in all simulation cases. It can be observed from the figure that the TKEs in the diesel modes were higher than those in the DF modes at each SA in all three IP cases. Moreover, in both diesel and DF modes, TKE tended to increase as SA decreased from 50 to 40 degrees. As is known, in fluid dynamics, TKE is the average kinetic energy in one unit of mass associated with vortexes in turbulent flows. Physically, TKE is characterized by the fluctuations of the measured root-mean-square (RMS) velocities. Generally, TKE is defined as half the sum of the fluid flow velocity component variances (square of standard deviations), as expressed in Equation (4) [46].  
\[k=\frac{1}{2}\big{(}\overline{(\mathbf{u})^{2}}+\overline{(\mathbf{v})^{2}}+\overline{ (\mathbf{\omega}\prime)^{2}}\big{)} \tag{4}\]  
where, \(k\), \(\mathbf{u}\), \(\mathbf{v}\), and \(\mathbf{\omega}\prime\) are the TKE and the velocity components according to the horizontal (\(x\)- and \(y\)-axis) and vertical (\(z\)-axis) directions of vortexes in turbulence flows, respectively. As can be seen, TKE is proportional to the square of the turbulence velocity components of fluid flows. In other words, TKE indicates the turbulence intensity of fluid flows.  
In this study, when the SA was reduced from 50 to 40 degrees, the target region of injection shifted closer to the piston surface. Since the piston surface was U-shaped, the target injection region closer to the piston surface led to increases in the vortex intensity of the fluid flow. As a result, the increase in vortex intensity led to an increase in the TKEs in all three IP cases in both diesel and DF modes, as shown in Figure 8. In addition, in each SA case, the increase in IP from 0.01 to 0.02 m also shifted the target injection regions closer to the piston surface. Both the increase in TKE and the target injection region shifting closer to the piston surface will affect the soot formation of the engine. This will be analyzed in detail in Section 3.4.