## 3 Spray Development from Nozzle Orifices
### Velocity and Size Measurement with Laser 2-Focus Velocimetry  
After primary breakup, the spray droplet or ligaments are fragmented to small droplets aerodynamically. It is possible to obtain the velocity of the droplets by a laser 2-focus velocimeter (L2F) [43], based on the measurement of time-of-flight when a droplet passes through two foci. The L2F has a highly concentrated measurement volume and therefore it is possible to adverse the effect of multiple scattering from the droplets in dense sprays. [PERSON] et al. showed that the velocity and the size of droplets can be simultaneously obtained by adding the measurement of time-of-scattering to the L2F [44]. The light probe of the L2F consists of two highly focused laser beams, as shown in Figure 17a. The size \(F\) of the focus is about 3 \(\upmu\)m, the distance \(S\) between two foci is 25 \(\upmu\)m, and the length \(L\) is about 20 \(\upmu\)m in the direction of the optical axis. When a droplet flies through both upstream and downstream foci, time-of-flight \(t_{1}\), time-of-scattering \(t_{2}\) on the upstream focus and time-of-scattering \(t_{3}\) on the downstream focus are measured. The velocity of a droplet is obtained by dividing the distance between two foci \(S\) with the measured time-of-flight \(t_{1}\). The schematic diagram of the time counter of L2F is shown in Figure 17b. The ratio of the time-of-flight and the time-of-scattering corresponds to the ratio of the distance between two foci \(S\) and the droplet size \(L_{dp}\) plus the focus size \(F\). The time-of-scattering can be estimated by averaging two time-of-scattering values. Then, the droplet size \(L_{dp}\) can be estimated. Figure 17: Schematic diagram and measurement principle of L2F: (**a**) Measurement prove of L2F; (**b**) Diagram of the time counter of L2F. According to the basic L2F measurement principle, it is possible to measure droplets correctly only in the case that the same droplet appears at the foci sequentially. In order to exclude signals from different droplets or from droplets passing diagonally, the data which has an imbalance of time-of-scattering at both foci is filtered out. After this process, a velocity bias correction and a statistical processing for cutting outliers is applied. Due to this multi-stage processing, the valid data rate is around 10%. Therefore, 20,000 samples were collected on each measurement position to obtain enough valid data. The details of this data processing and its effectiveness have been discussed in [45]. Figure 18 shows the time resolved velocities on 50 MPa injection pressure condition. The measurements were performed under a collaborate research with Nagasaki university. The solid line shows the result from the L2F measurement. The dotted line indicates the velocity calculated from the mass flow rate measurement at the same condition. The droplet measurement by L2F is carried out 10 mm downstream from the nozzle (\(z=10\) mm) on the spray axis. For comparison, the calculated velocity from the measured mass flow rate is shown, assuming an averaged velocity at the nozzle exit without any losses. The velocity profile by L2F shows a similar curve to that from mass flow rate. Figure 19a shows the spatial distribution of the droplet velocity at \(t=1.2\) ms ASOE on three planes of \(z=5\), 10 and 15 mm from the nozzle exit at 50 MPa injection pressure condition. The velocity data were averaged in a period of 0.1 ms from \(t=1.15\) to 1.25 ms (middle of the injection period). The velocity was highest at \(x=0\) mm on \(z=5\) mm and decreased with increasing the distance from the nozzle exit. The velocities in the spray periphery are lower, as is expected. Figure 19b shows the spatial distribution of the droplet size at the same conditions of Figure 19a. The droplet at the spray center decreased with the distance from the nozzle exit. At the \(z=5\) mm plane, the droplets show the highest sizes at the spray center, decreasing to the sides. This tendency does not appear on the other measurement planes.