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Abstract
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 coefﬁcient 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 RayleighPlesset equation together with the JohnsonHsieh 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 RayleighPlesset equation for a 2D cylindrical bubble placed at the center of a vortex. In this work, the tip vortex cavitation (TVC) model is fully integrated into the DTUdeveloped 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 cavitation contributes mostly to the ﬁrst and secondorder pressure ﬂuctuations (ﬂuctuations occurring at or twice the blade passing frequency). The third and higherorder ﬂuctuations, however, are assumed to be mainly inﬂuenced by the dynamics of the cavitating tip vortex. The higherorder 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 spanwise 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 higherorder 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 wellknown 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 fullscale 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 modelscale wake ﬁeld. The calculation results show larger higherorder 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 modelscale and the effective fullscale 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.
It is known that the periodic growth and collapse of the blade sheet cavitation contributes mostly to the ﬁrst and secondorder pressure ﬂuctuations (ﬂuctuations occurring at or twice the blade passing frequency). The third and higherorder ﬂuctuations, however, are assumed to be mainly inﬂuenced by the dynamics of the cavitating tip vortex. The higherorder 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 spanwise 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 higherorder 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 wellknown 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 fullscale 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 modelscale wake ﬁeld. The calculation results show larger higherorder 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 modelscale and the effective fullscale 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.
Original language  English 

Place of Publication  Kgs. Lyngby 

Publisher  Technical University of Denmark 
Number of pages  113 
ISBN (Electronic)  9788774755579 
Publication status  Published  2019 
Series  DCAMM Special Report 

Number  S258 
ISSN  09031685 
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Dive into the research topics of 'Development of a Model for Propeller Tip Vortex Cavitation and Analysis of the Radiated Pressure Fluctuations'. Together they form a unique fingerprint.Projects
 1 Finished

Development of Improved Cavitation and Noise Radiation Prediction Methods for Marine Propellers
Mirsadraee, Y., Walther, J. H., Bingham, H. B., Bensow, L. R. E., Gomaa, M. A., Shin, K. W., Andersen, P. & Nørgaard, H. H.
01/03/2015 → 06/06/2019
Project: PhD