An inverse tracing method (ITM) to solve the radiating noise induced by the marine propeller sheet cavitation with experimental verifications

Abstract

This paper develops and proposes an Inverse Tracing Method (ITM) in the time domain to tackle the problem of the radiating noise caused by unsteady propeller sheet cavitation, in which the relationship between the time of the noise source and the time of the propagated sound can be inversely traced by the piecewise cubic-spline functions. By applying the inversely traced relationship into the solution of the wave equation, the Dirac delta function is assumed to simplify to delta (0), so the time integral is assumed to vanish. In addition, the unlimited differential terms also can be replaced by differentiating the piecewise cubic-spline functions. In order to validate the corrections of the ITM, the far-field noise calculated by the ITM is compared with that predicted by the farfield method proposed by Nobel et al. (1986), and good agreement is shown. The near-field noise obtained by the ITM is checked by the experimental results of a container ship, and the ITM overestimates the experimental data by about 2 dB. A workboat is also taken as a computing sample to predict the radiating noise caused by unsteady propeller sheet cavitation. Because the cavity volumes are over-predicted, the predicted noises by the ITM are obviously stronger than the measured noises. As the numerical cavity volumes are modified to meet the measured volumes, by adjusting the cavitation number, the predicted Sound Pressure Level (SPL) at the first blade passing frequency (i.e. the maximum SPL) by the ITM is smaller than the measured value, by 4 dB. At higher blade passing frequencies, the measured SPLs are remarkably stronger than the predicted levels, due to the appearance of tip vortex cavitation in the model test.