During an entire revolution each of \(N_{r}\) blades interacts with all\(N_{s}\)vanes so that there are a total of \(N_{s}N_{r}\) interactions
separated by an angle\({\ \theta}_{\text{RSI}}=\left(\frac{1}{N_{s}}-\frac{1}{N_{r}}\right)\)which in our case\({\ \theta}_{\text{RSI}}=0.03827\ rad\). The
time\({\ \ t}_{\text{RSI}}=\frac{2\pi}{{(N}_{r}N_{s}\mathrm{\Omega})}\)=\(\ 47.84\ \mu s\)for a rotating speed of 6000 rpm. The phase difference between two
consecutive interactions is constant for the same harmonic [33]. For
a given frequency\(\text{\ f}=\frac{\mathrm{\Omega}}{2\pi}\) occurring
after an angular rotation equivalent to\({\ t}_{\text{RSI}}\) the order
of interaction depends on the first position of blade [32, 34, 35].
The sequences of interactions between 19 vanes and 11 blades are listed
in Table 2. By considering that the 1st vane first
interacts with the 1st blade, the sequence of
interactions depicts that one blade interacts with another vane after\(11{t}_{\text{RSI}}\) and the 1st blade interacts
again with the 1st vane
after\(\ 209{t}_{\text{RSI}}\).
Table 2. Order of interaction of 19 vanes with 11 blades, at
t=0 the 1st blade is near 1st vane