## 3 Methods Used for Identification of Tonal Noise Sources
### Experimental Setup  
The test facility consisted of an open-loop centrifugal compressor test rig placed in a laboratory room used for compressor performance measurement. The compressor's surroundings thus represented a diffuse field that could have a certain influence on the amplitudes of the acoustic signal. Generally, the acoustic impedance of the test environment has a limited effect on the broadband noise, but it has a considerable effect on the tonal noise. The frequency of the signal, however, is affected negligibly. Moreover, these machines  
Figure 1: Schematic overview of the algorithm for evaluating tonal metrics of measured sound pressure. Figure 2: Partial displays of the measured signal at each step of the tonal metric evaluated from a time sub-cycle length of 0.29 s for the operating conditions of a compressor with 11 impeller blades and a vaned diffuser; corresponding blade tip speed \(u_{2}=500\) m\(\cdot\)s\({}^{-1}\). are always placed in non-anechoic chambers when they operate. Thus, this experiment reflected the typical placing and operation of a centrifugal compressor. The compressor drew in the ambient air at atmospheric pressure and contained an 11-bladed unshrouded impeller with a diameter of 0.231 m, a 19-vaned diffuser and a volute. At the outlet of the volute there was a 0.14 m internal diameter pipe 0.8 m in length, followed by a 0.218 m outlet diameter cone, which was followed by a 0.2 m diameter pipe with bellows, elbows and an orifice with a total length of 23 m. Total pressure and temperature sensors were placed at the inlet and outlet of the compressor. In addition, sound recording microphones were placed approximately 1 m away (Figure 3). In this way, the compressor map was measured, and the sound pressure at each operating point was measured by the microphones. During measuring, basic turbocharger operating parameters such as rotor speed, gas pressures and temperatures upstream and downstream of the compressor and turbine, oil temperature and pressure at the turbocharger inlet were also recorded. Each operating point of the compressor map was measured separately in a cycle including the run-up to the operating point, a turbocharger steady state of 10 min and the steady-state measurement of operating variables. The measurement time of the operating variables at the steady-state operating point was 22 s at a sampling rate of 65,536 Hz. Five speed lines \(u_{2}=250,\ 350,\ 450,\ 500\) and 550 m\(\cdot\)s\({}^{-1}\) were measured at four operating points on each speed line (Figure 4). These points were aerodynamically approximately affine; thus, so-called'sweeps' could be introduced, where the relations \(m_{\text{corr}}=f(u_{2})\) and \(\pi_{\text{t-t}}=f(u_{2}^{2})\) were valid. This approximate dependence held between speeds of 450-550 m\(\cdot\)s\({}^{-1}\) with a deviation of less than 15%. Basic information on the sensors used for the experiment is given in Table 1.  
Figure 4: An illustrative overview of measured operating points expressed in the compressor map. Figure 3: Setting up a set of microphones near the turbocharger compressor to be measured. At all analysed speeds, rotating-blade related noise was dominant. This typically dominant noise for compressors was evident in both the blade frequency of the main blades (MBPF) and the blade frequency of the sum of the main blades and splitter blades (MSBPF). However, as the speed increased, the effect of single-integer multiples of the rotational frequency, that is, buzz-saw noise, became more evident. The buzz-saw noise was evident at higher rotor speeds \(u_{2}=550\) m\(\cdot\)s\({}^{-1}\) and \(u_{2}=500\) m\(\cdot\)s\({}^{-1}\) for all operating points (sweeps A-D). Conversely, this noise could not be uniquely identified at rotor speeds \(u_{2}=250\) m\(\cdot\)s\({}^{-1}\) and \(u_{2}=350\) m\(\cdot\)s\({}^{-1}\), which was due to the absence of supersonic aerodynamic conditions in the impeller at this rotor speed.