Prediction of Hydro-Acoustic Radiation
Underwater noise induced by human behavior raises the underwater background noise level significantly and is very likely to damage marine life. Especially the operation of marine propellers is considered one of the main sources of underwater radiated noise. The development of efficient numerical methods which are able to predict the radiated noise caused by an operating propeller can assist to understand the mechanism and to optimize propellers in regard to hydro-acoustic radiation and thus reduce the noise to a minimum.
Hybrid Method for Noise Prediction
The panel code panMARE has been extended by a hybrid method, in which the Ffowcs Williams-Hawkings (FW-H) analogy is coupled with the Boundary Element Method (BEM) approach, as described in detail in Göttsche (2020). This extension of panMARE for the prediction of underwater radiated noise caused by operating propellers utilizes the hydrodynamic results of the panMARE propeller calculation and can thus be integrated into the propeller design process easily.
Using panMARE as the BEM, the propeller flow can be calculated as well as propeller-induced pressure pulses on the ship's hull. Furthermore, a viscous correction of the potential flow results can be applied to include a ship's wake, and finally, the prediction of sheet cavitation on the propeller blades is also possible. All of these important aspects can be included in the prediction of hydro-acoustic radiation implemented in panMARE.
For the prediction of underwater radiated noise the hydro-acoustic pressures are evaluated using the Ffowcs Williams-Hawkings equation (formulation 1A by Farassat). Hereby, both the displacement as well as the lifting forces of the bodies are included in the hydrodynamic calculation. The method's main principle is visualized in Figure 1. In addition to the direct path from the noise source to the point of observation, also noise reflections at the free water surface and at the seabed are modeled and used as part of the hydro-acoustic radiation's prediction.
Noise Prediction for Propellers with Sheet Cavitation
While a further development of the method is recommended, so that other types of cavitation can also be included in the underwater noise prediction, the hybrid method is already able to predict the hydro-acoustic radiation of propellers with sheet cavitation well.
In case sheet cavitation occurs, the sheet cavitation influences the displacement as well as the forces in the FW-H equation. The displacement is affected due to the cavity's expansion and sheet thickness and the lifting forces are influenced, since vapour pressure is acting on the blades within the area of the cavity.
This way, sheet cavitation can be included in the prediction of underwater radiated noise.
Noise Prediction for Non-Cavitating Propellers
For non-cavitating propellers the prediction method for hydro-acoustic radiation implemented in panMARE has been developed further and also presented to the public.
In this approach, the noise prediction is based on the calculation of the acoustic pressure generated by the propeller's wake sheet, as is elaborated and discussed in Göttsche, Wang (2020). It is possible to perform calculations for both uniform (open water case) and non-uniform (behind-hull case) inflow conditions. The dominant sound source terms and the decay rate of the radiated noise depending on the distance to the propeller's center can be investigated for both conditions.
Validation of the Prediction
The quality of the prediction has been validated successfully using the following different scenarios:
Firstly, a pulsating sphere was used to check the displacement-part of the FW-H equation resulting from the hydrodynamic simulation against analytical results. Hereby, the interference patterns predicted by the simulation, which result from the sound's reflections, are as expected.
Secondly, a propeller in open water was calculated, in which the lift-generating part of the FW-H equation was included.
Based on the open water case the same propeller was simulated in its natural environment behind a ship in various operating conditions. Hereby, both sheet cavitation as well as the influence of a restricted water depth were included. The resulting noise pressure levels were compared with measured data of the examined ship and showed good agreement.
The predicted hydro-acoustic noise pressure levels and their interference patterns correspond well with the measured data (incl. reflections and interference).