As wall attachment flow, boundary layer flow, and cavitation phenomena had significant relationships with vortexes in the deflector, how these vortexes influence the performance of the flow field were studied in the following sections.
The snapshot POD analysis were mentioned in the previous researches[2427]. To better verify the snapshot number independence, the energy ratio of the first four modes in the Vgroove is listed in Table 2. It is known that the energy ratios of Mode 1 and Mode 3 increase with increasing snapshot numbers, whereas those of Mode 2 and Mode 4 decrease. The differences between 400 and 500 snapshots are negligible. In this work, transient datasets of 400 snapshots were chosen as the basis for snapshot POD analysis.
Table2. Results of the snapshot number independence study
Snapshot number

300

400

500

600

Energy ratio of mode 1

0.92290

0.92315

0.92344

0.92451

Energy ratio of mode 2

0.02339

0.02330

0.02329

0.02327

Energy ratio of mode 3

0.00761

0.00767

0.00768

0.00770

Energy ratio of mode 4

0.00550

0.00540

0.00538

0.00537

6.2 Analysis of snapshot POD of velocity field
For ease of analysis, the origin of the coordinate system of the flow field was fixed at the center of the shunt wedge, and the streamwise (y) and lateral (x) distances from the origin were normalized by the nozzle length (n). The flow filed of the deflector is located in the region of 0 < y/n < 4.7, where the velocity data from LES are conducted by snapshot POD. The snapshot POD results of the first five modes were obtained, as shown in Figure 12.
Mode 1 consists of the mean flow field with most energy. From snapshot POD results of different inlet pressures, it is shown that the velocity distribution of the first modes is very close, whereas differences in the higher modes are clearly observed. As inlet pressure increases, the energy of Mode 1 decreases, and the energy of the high modes increases. The high modes contain coherent flow fields and turbulent flow fields, which are related to the instability of the flow fields.
To determine the truncation order between the coherent flow field and the turbulent flow field, this paper defined the correlation coefficient between the reconstructed flow field obtained by selecting the number of adjacent modes as:
Figure 13 shows the relationship between the correlation coefficient of the reconstructed flow field and the number of corresponding adjacent modes. With the increase in mode number, the correlation coefficient starts to increase rapidly. In either case, the correlation coefficient between the flow field reconstructed from Mode 2 to Mode 5 and the flow field reconstructed from Mode 2 to Mode 6 was above 95%. The rate of increase in the correlation coefficient became very slow when the mode number continued to increase. The result shows that starting from Mode 6, the vortex structure of the higher mode had a very weak effect on the first five modes, so the boundary truncation order of the coherent structure in the pilot stage could be determined as five. The flow field reconstructed from Modes 2–5 could characterize the coherent flow field of the transient flow field. Since the coherent flow field carried a large proportion of the turbulent kinetic energy, most information about the turbulent pulsation flow field could be described from the flow field reconstructed from Modes 2–5.
To further study the influence of coherent structures, streamlines from Modes 2–5 for inlet pressures of 10 MPa and 14 MPa are presented in Figure 14.
In Mode 2, a largescale wallattached vortex existed near the downstream part of the side wall of the Vgroove, while the vortex core was located at 2 < y/n < 2.4. With the inlet pressure increasing, the locations of vortex cores increased in the y direction. At the inlet of the Vgroove, the free submerged jet was deflected to the wall side and then attached to the wall while flowing downward. It could be seen that this jet deflection was due to the effect of the bigscale clockwise vortex in Mode 2. In Mode 3, a counterrotating vortex pair (a smallscale wallattached vortex and a counterclockwise vortex) became the major factor. Snapshot POD analysis results showed a full ability to directly visualize details of the counterrotating vortex pair. In Mode 4, in the upper right region near the wall, there was a vortex, which was close to the position of the traveling cavitation in Part 5.2. Whether they are rated is discussed further. With the mode increasing, the vortexes became smaller and more turbulent, and their positions rose with the inlet pressure increasing.
6. 4 Analysis of POD coefficients of coherent structures
Since the POD mode is related to the corresponding flow field structure, we can deeply study the influence of coherent structures of various scales through the spectral analysis of mode coefficients. Figure 15 showed the FFT results of the corresponding coefficients of the first four modes at different inlet pressures, which meaned the pulsation frequency of each mode. When the inlet pressure was 6 MPa, the frequency domain of a1, a2, a3, and a4 peaked at 3,380 Hz, 1,170 Hz, 976 Hz, and 3,710 Hz, respectively. For inlet pressure 10 MPa, the frequency domain of a1, a2, a3, and a4 peaked at 2,343 Hz, 976 Hz, 976 Hz, and 1,367 Hz, respectively, while at 2,832 Hz, 1,269 Hz, 1,269 Hz, and 2,832 Hz for 14 MPa.
Figure 16 showed the FFT results of surface mean velocity in the Vgroove. Compared to Figure 15, the frequencies were very close to those of the first modes, which meaned that the oscillation in the Vgroove primarily came from the first mode with the most energy.
The traveling cavitation caused the pressure to fluctuate. Point A (0.2 mm, 0.7 mm, 0) was located near the vortex core of the traveling cavitation. The pressure at Point A varied with time, as shown in Figure 17(a). The pressure fluctuated more when the inlet pressure increased. To verify the assumption of the relationship between the vortex in Mode 4 and the traveling cavitation, the FFT analysis of pressure at Point A was conducted, as shown in Figures 17(b) and (c). The FFT results of 1,376 Hz and 2,834 Hz were close to those of a4 for 10 and 14 MPa, which were 1,367 Hz and 2,832 Hz, respectively. It could be concluded that the traveling cavitation was generated by the lowpressure vortex in Mode 4.