As noted the low amplitudes are expected for high k values because of high harmonic number and k 1 is usually not relevant.
The runner blades 1, 2, 3โ€ฆ. and 11 are first excited by interference with the vanesโ€™ wakes. Runner blades are excited in phase and induce a vibration having a mode with 2 diametrical nodes. The runner provokes a pressure wave rotating at the same runner speed, inducing a characteristic pressure oscillation of frequency\(f_{s}=m\frac{\mathrm{\Omega}}{2\pi}N_{r}\) and\(f_{r}=n\frac{\mathrm{\Omega}}{2\pi}N_{s}\) at every stationary/rotating point. The pressure field presents two diametrical pressure modes ๐‘˜1, ๐‘˜2 indicating the number of high- and low-pressure regions for the frequency component in the circumferential direction estimated in Table 3 for a combination of 19 vanes and 11 blades. When operating at 6000 rpm, the highest RSI calculated diametrical positive mode number (Table 4) occurs fork2 =3, 14, 25, 36, 47, 58, 69, 80, 91, and 102 for the successive frequency 2200 Hz, 3300 Hz, 4400 Hz, 5500Hz, 6600 Hz, 7700 Hz, 8800 Hz, 9900 Hz, 11000 Hz, and 12100 Hz. The highest RSI calculated diametrical negative mode number (Table 5) occurs fork2 = -8, -16, -5, -13, -2, -10, -18, -7, -15, -4 and -12 for the successive frequency 1100 Hz, 2200 Hz, 3300 Hz, 4400 Hz, 5500Hz, 6600 Hz, 7700 Hz, 8800 Hz, 9900 Hz, 11000 Hz and 12100 Hz. This theoretical analysis allow describing the characteristics of pressure mode shape in the frequency domain and the sequences of interactions which may give the expected dominant modes and frequencies, however it is difficult to predict accurately the amplitudes in addition to other interactions frequencies.
Table 3. Sample of expected RSI diametrical mode numbers and frequencies