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