## 2 Typical Aerodynamic Noise Characteristics of High-Speed High-Pressure Centrifugal Compressors
### Buzz-Saw Tonal Noise  
If a centrifugal compressor is operated under conditions where the relative velocity at the leading edges of the impeller blades approaches the local speed of sound, shock pressure waves are generated in the passage between the impeller blades [36]. The main cause of buzz-saw noise is the rotor's pressure field, which is stable in the rotating (relative) coordinate system, that is, the pressure field coupled with the rotor. In the case of a completely ideal rotor operating in a uniform flow field, the individual shock waves generated by all blades are the same. In such a case, the shock waves can be simplified in the form of repeating the one-dimensional sawtooth waves. An analytical description of this idealised case can be found in the research by [PERSON] and [PERSON] [37]. Their work was followed by that of many other authors, who gradually expanded the description of buzz-saw type noise. A summary of the development of methods describing this type of noise can be found in a study by [PERSON] and [PERSON] [38], for example. However, in real rotating machines, individual blades exhibit minor geometric variations. These deviations result in different amplitudes and different shifts between the individual shocks and therefore affect their propagation, which is nonlinear. Thus, these small irregularities ultimately lead to spectral components present at integer multiples of the rotational frequency. The frequency ratio of the individual tonal components of the buzz-saw noise can be defined as  
\[\varepsilon_{\rm R,BS}=i, \tag{5}\]  
where \(i=1,2,3\ldots\) is the order of the harmonic component.  
The resulting acoustic character can be observed in the form of tonal sounds at integer multiples of the rotational frequency; thus, it is a super-harmonic type of noise. These conclusions were also stated by [PERSON] et al. [39], [PERSON] and [PERSON] [28] and [PERSON] et al. [40]. The description of buzz-saw noise is still a current research topic, as this type of noise is dominant in aircraft engines. In the field of aeronautics, research on the description of this noise is especially important because it is present during take-off and climb, as that is when the rotating machine is in its transonic regime. [PERSON] and [PERSON] [28] stated that the dominant source of noise at the inlet of the compressor at 'high' rotor speeds is buzz-saw noise, in addition to rotational frequency and BPF. It should also be noted that there is no well-defined boundary, for example, in terms of rotor speed, that would determine the occurrence of buzz-saw noise. For example, [PERSON] and [PERSON] [28] only stated that this noise occurs at'supersonic tip speeds'. However, the occurrence of shock waves is caused by the exceedance of the sound speed of the flowing gas, which is local and depends to some extent on the geometry of the impeller channel. For this reason, buzz-saw noise does not occur suddenly. On the contrary, a gradual increase in the individual tonal components with an increasing compressor speed can be expected.  
Additionally, [PERSON] and [PERSON] [28] stated that when supersonic flow conditions occur at the inlet of a centrifugal compressor, that is, \(\text{Ma}_{1}>1\), buzz-saw noise and BPF are dominant, and RSI may be present at the outlet, whereas in the case of subsonic flow conditions, that is, \(\text{Ma}_{1}<0.95\), the noise associated with the interaction of the blade tip and the shroud, also known as the TCN, is evident.