Development of a Model for Propeller Tip Vortex Cavitation and Analysis of the Radiated Pressure Fluctuations

The work presented in this thesis focuses on developing a numerical model for predicting the inception of tip vortex cavitation as well as the dynamics of the developed tip vortex cavity and the associated pressure fluctuations. The inception is predicted by either the comparison of the minimum pressure coeffi-cient and the cavitation number (engineering criterion) or based on monitoring the temporal evolution of a set of spherical nuclei in the tip vortex pressure field (bubble growth approach).

For the latter, the Rayleigh-Plesset equation together with the Johnson-Hsieh equation of motion are solved to predict the trajectory and the growth behaviour of the nucleus. Once inception occurs, the vortex line is divided in numerous segments and the dynamic behaviour of each cavitating segment is predicted using the Rayleigh-Plesset equation for a 2-D cylindrical bubble placed at the center of a vortex.

In this work, the tip vortex cavitation (TVC) model is fully integrated into the DTU-developed boundary element method (BEM), called ESPPRO. The input data to the TVC model, i.e. the blade tip circulation and Reynolds number, are provided by the BEM part of the implementation. It is known that the periodic growth and collapse of the blade sheet cavi-tation contributes mostly to the first and second-order pressure fluctuations (fluctuations occurring at or twice the blade passing frequency).

The third and higher-order fluctuations, however, are assumed to be mainly influenced by the dynamics of the cavitating tip vortex. The higher-order fluctuations can be significant if there is sheet cavitation that extends beyond the trailing edge and interacts with the cavitating tip vortex. This interaction is accounted for in this model by using the span-wise average thickness of the blade sheet cavity at the trailing edge as initial radius of the developed tip vortex cavitation.

The numerical model developed here is shown to be convergent with regards to discretization of the cavitating vortex segments. The calculation results are dependent on the value of the outer domain radius of the vortex flow model. The growth of the viscous core radius and the circulation strength along the tip vortex line downstream of the blade is found to influence the results in terms of the cavity radius and the amplitude of the higher-order pressure fluctuations.

The two methods mentioned above for predicting the inception of tip vortex cavitation are applied to a submarine propeller for which a measured inception curve is available. The results of the two methods are compared to each other and also to the experimental results. The results of both methods are very similar with the bubble growth approach being the more conservative of the two.

Two public well-known benchmark test cases have been used for validation. The first case is the INSEAN E779a propeller in open water that develops a stable long cavitating tip vortex which is reproduced by the model. The second case is the KCS propeller for which experimental results with wake field of the model and the full-scale ship are available.

This propeller develops only a short cavitating tip vortex in the wake peak region. The agreement between the calculation results and the results from the experiment is good for both cavitation extent and pressure fluctuations, especially for model-scale wake field. The calculation results show larger higher-order amplitudes when interaction of sheet and tip vortex cavitation is included.

Propeller designers are highly dependant on the ship wake field for their design. Two marine propellers designed for the same bulk carrier but for the nominal model-scale and the effective full-scale wake fields have been analysed. The axial components of both wake fields are scaled to the same overall wake fraction to ensure the same mean inflow velocity.

It is shown that it is crucial to have the correct wake field distribution as the basis for the design. The dynamics of tip vortex cavitation is pronounced when there is an interaction between sheet and the cavitating tip vortex and it can be seen in the hull pressure fluctuations.