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, 3โฆ. 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 ๐1, ๐2 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