# Estimation of the Noise Source Level of a Commercial Ship Using On-Board Pressure Sensors
## 2 Method and Validation
### Validation of the Method  
To check the validity of the estimation method, a model-scale measurement was conducted in the Large Cavitation Tunnel (LCT) at the Korea Research Institute of Ships and Ocean Engineering (KRISO). Figure 3 shows a schematic view of the tunnel. The overall dimensions of the tunnel are 60 \(\times\) 22.5 \(\times\) 6.5 m\({}^{3}\), and those of the test section are 12.5 \(\times\) 2.8 \(\times\) 1.8 m\({}^{3}\). A model ship and propeller with a scale ratio of 25.6 were installed in the test section, as shown in Figure 4.  
Figure 3: Schematic view of the Large Cavitation Tunnel (LCT) at the Korea Research Institute of Ships and Ocean Engineering (KRISO). Figure 2: Procedure of the source-level estimation. A set of B&K type 8103 miniature hydrophones were installed at the hull above the propeller plane for the estimation of source strength. The position and the coordinates of the hydrophones on the hull are shown in Figure 5 and Table 1, respectively. As the hydrophones were not flush-mounted, they were expected to be affected by flow noise. This would be small, however, unless cavitation were to occur directly around the hydrophones. All the hydrophone sensors were connected to a B&K type 2692-A charge amplifier and B&K type 3052 data acquisition system, which provided a sampling frequency of up to 204.8 kHz. To obtain the source level from the measurement, a B&K type 8105 hydrophone was used in an acoustic  
noise correction was then applied to obtain valid data (\(SPL_{m}\)). To calculate the source level, it was necessary to measure the transfer function between the source and the receiver. This could be done by replacing the propeller with a sound source of known properties and measuring the source and receiver signals simultaneously. Note that in the transfer function measurement, the flow speed was set to be zero. In this study, an ITC-1032 transducer was used, for which the setup is shown in Figure 6. The transfer function measurement is usually carried out for different source positions along the propeller disk in the circumferential direction. However, only the center position was considered in this study, as the difference was negligible. To obtain more accurate results, one may look at the cavitation pattern to identify possible source locations. The source level in model-scale measurements can be obtained as follows:  
\[SL_{m}=SPL_{m}+TVR-TF\quad\text{(dB)}, \tag{14}\]  
where \(SL_{m}\) is the source level at the model scale, \(TVR\) is the transmitting voltage response of the transducer in free field, and \(TF\) is the transfer function. The transmitting voltage response was provided in the transducer data sheet, as shown in Figure 7. The transfer function between the source and the hydrophone in the tunnel was measured, and the result is shown in Figure 8. Using these two graphs, the source level in free field can be obtained for a given operating condition. Figure 6: Setup for transfer function measurement. Figure 7: Transmitting voltage response of the ITC-1032 (from product data sheet). Three operating conditions were considered in the measurement, as shown in Table 2. Here, the cavitation number \(\sigma_{n,0.7R}\) is defined as  
Figure 3:0  
where \(p_{c}\) is the pressure at the center of the tunnel, \(\rho\) is the density of the fluid, \(g\) is the gravitational acceleration, \(h_{0.7R}\) is the height that is defined from the center of the tunnel to the 0.7\(R\) upward position, \(p_{v}\) is the vapor pressure, \(n\) is the rotational speed of the propeller, and \(D\) is the diameter of the propeller. The flow speed \(V\) was set to be 7 m/s, and the tunnel pressure was controlled to tune the cavitation number. The water temperature was 16.3 \({}^{\circ}\)C. Each run was recorded for 60 s with a sampling frequency of 204.8 kHz. The data were post-processed using MATLAB to obtain the power spectral density (PSD). Figure 9 shows a comparison between the measured signals in operating condition C1 and the background noise.