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Prediction and optimisation of non-cavitating marine propeller noise at low frequency are important for design of submarine propellers that are required to operate in the non-cavitating condition. The low-frequency discrete- and broadband-spectrum forces of propellers have different generation mechanisms, and thus have not previously been studied within a unified framework. In this work, the strip method is applied to simultaneously predict and optimise these two forces. First, the panel method is applied to predict the discrete-spectrum forces of different strips in the time domain. Then, the unsteady force of the whole propeller is obtained as the linear superposition of the shifted unsteady forces of all the strips, according to a skew distribution. The strip method is then used to numerically solve an integral equation for the broadband-spectrum force, derived via the spectral method. On the basis of experimental results, the predictions of low-frequency discrete- and broadband-spectrum forces are verified to have high accuracies. An analysis of the effect of propeller skew on the unsteady forces of different strips, and the effect of strip-cutting strategy on the broadband-spectrum force, is also performed. It is found that the skew of a strip is approximately equal to the angle of the circumferential phase shift of the unsteady force of that strip, and that the strip-cutting method has an insignificant effect on the predicted broadband-spectrum force. The optimisation of propeller performance under several constraints is then considered, with the particular objectives of maximising the propulsion efficiency and minimising the low-frequency discrete- and broadband-spectrum forces. The circumferential phase-shift effect of the skew allows the optimisation model to be decoupled into two steps. The discrete-spectrum force of the whole propeller can thus be computed using linear superposition rather than a hydrodynamic calculation, which significantly improves the computational efficiency. The effectiveness of the optimisation is verified by two optimization cases. For HSP, the propulsion efficiency is increased by 2.5%, the broadband-spectrum noise is reduced by approximately 0.6 dB, and the first- and second-order values of discrete-spectrum thrust are decreased by 9% and 27%, respectively. Similarly, for E1619, the first- and second-order values of the discrete-spectrum thrust are reduced by 13% and 18%, respectively. |
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