An improved spectral method and experimental tests for the low-frequency broadband noise of marine propellers

Abstract

Called by Green Ship of the Future to reduce the propeller noise pollution in the subsea environment and avoid the possibility of causing propeller–shaft–ship resonance, the low-frequency broadband noise (LFBN) of marine propellers was studied theoretically and experimentally. The spectral method is improved by considering the blade section thickness and anisotropy in the turbulence spectrum, both of which are found to be effective in improving the prediction accuracy when compared with the experimental results. A series of propellers with the same blade geometry but different blade number were tested in the large cavitation channel at the China Ship Scientific Research Centre. The peak values in all conditions were close to the first-order blade-passing frequency. The effects of blade number and the advance coefficient were investigated by testing the propellers operating under different conditions. The effects were also studied using both the spectral method and experiment, and the results were consistent. Furthermore, the quantitative dependence of the LFBN on the influencing parameters was investigated using the sensitivity analysis. The rotational speed and turbulence intensity were found to be the two main factors, with greater than 10% effects. In addition, the effects of thickness and anisotropy scaling factor were evaluated using the spectral method. The results of this study provide guidance for controlling the LFBN in propeller design and optimisation.

Appendix

The propeller rotates to generate thrust, which has a suction effect on the inflow at the same time. The phenomenon that the streamwise velocity along the X-direction (Fig. 1) in front of the propeller disk is larger than the ship speed is called the induced effect, and the accelerated velocity is named as the induced velocity [27]. To quantitatively evaluate the effect of induced velocity on LFBF, three cases are designed and compared here.

The parameters of the three cases are only different in the streamwise velocity (U_A) in front of the propeller disk, while the other parameters are the same as the typical model test condition as introduced in Sect. 3.2. The model is a 10-blade propeller rotating at 18.13 rps with an inflow speed of 4.69 m/s. The turbulence intensity and turbulence integral length measured at the location of propeller disk without installing the propeller by PIV in the LCC are 3.3% and 0.0298 m, respectively.

For Case 1, U_A equals to the inflow speed of 4.69 m/s. While for Case 2, U_A is obtained based on the ideal propulsion assumption, that is, the maximum induced speed is calculated without considering the actual propeller and energy loss. The induced speed at propeller disk u_a1 can be obtained from [27]:

$$\eta_{iA} = \frac{{U_{A} }}{{U_{A} + u_{a1} }},$$

(25)

where η_iA is the efficiency of idea propulsion and defined as:

$$\eta_{iA} = \frac{2}{{1 + \sqrt {1 + \sigma_{T} } }},$$

(26)

where $\sigma_{T} = \frac{T}{{\tfrac{1}{2}\rho A_{0} U_{A}^{2} }}$ is the load factor with A₀ the propeller disk area. Under the above model test conditions, the thrust coefficient K_T (= T/ρn²D⁴) measured by Sevik [9] is 0.183. Then, u_a1 can be solved to be 0.31. Therefore, U_A equals to be 5 m/s for Case 2.

For Case 3, U_A is obtained by an additional numerical simulation. The computational domain with boundary conditions is shown in Fig. 

Fig. 13

Computational setup

13. The same geometry of the 10-blade propeller (D = 0.2032 m) used in the experiment is simulated. Details about the propeller can be found in Sect. 3.1. The moving reference frame is utilised to realise the rotation of rotor with respect to the laboratory reference frame. Since only the increase in the streamwise velocity caused by the suction of the propeller needs to be evaluated, a steady calculation with the RANS SST-kω model is carried out. The velocity at the inlet is 4.69 m/s and the rotation speed of the propeller is 18.13 rps, which are the same as the experiment conditions. The streamwise velocities in the cross section at a distance of 0.075D in front of the propeller and in the longitudinal section are shown in Fig. 

Fig. 14

Contours of the streamwise velocity in a the cross section in front of propeller and b the longitudinal section

14. The averaged streamwise velocity in the cross section is 4.80 m/s. Therefore, for Case 3 we set U_A to be 4.80 m/s.

The LFBF of the three cases are predicted by the spectral method without correction. The PSD calculated by Eq. 12 are compared in Fig. 

Fig. 15

Comparison of PSD for the three cases with different U_A

15. In addition, the overall SPL at a distance of 1 m between the sound source and the observer calculated by Eq. 9 of the LFBN is compared in Table 3. It is seen from Fig. 8 and Table 3 that the induced velocity has limited effect on LFBF. Even for the Case 2 with the ideal propulsion assumption, the difference in SPL is only about 0.3 dB. For Case 3 that considers the real geometry of the propeller, there is only a difference of 0.1 dB.

A possible explanation is that although the suction effect of the propeller increases the streamwise velocity, the change in the local inflow velocity is not significant by taking the propeller rotation speed into consideration. The local inflow velocities at a radius of 0.7R of the three cases are also listed in Table 7, which is a typical location dominating the overall LFBF.

Table 7 Comparison of the overall SPL

Based on the above results, it can be concluded that the induced velocity does not change essentially the LFBF. Meanwhile, the induced velocity is not easy to obtain without numerical simulation or model test. Therefore, for the applicability and generalizability of the spectral method, the induced velocity is not considered in the present method.