Modelling the manoeuvring behaviour of an ULCS in coastal waves
Introduction
When a ship manoeuvres in the close proximity to ports, it will encounter several environmental phenomena such as wind, waves, and shallow water. Determining the influence of such phenomena on the ship's manoeuvrability is of great relevance in order to guarantee safe ship operations.
During the past decades the analysis of manoeuvring has mainly been focused to environmental conditions corresponding to calm water and infinite water depth. Studies as such have been restricted to cover horizontal motions only. At most they have been extended to include roll motion. For the case of finite water depth the study requires additional considerations. For instance, disregarding the effects of the ship's vertical motions from the study is not an option, in such cases the ship experiences a significant induced sinkage and trim due to the squat phenomenon. Bear in mind that the limited water depth will, in addition, change the overall hydrodynamic behaviour of the forces and moments acting on the ship, as reported in Vantorre and Eloot (1996) and ITTC (2002). Models for such scenarios, finite water depth, including the vertical motions are rather scarce in literature. To the authors' best knowledge one of the most recent work addressing this problem can be found in Delefortrie et al., 2016a, Delefortrie et al., 2016b.
In practice, when the ship manoeuvres in coastal areas, approaching or leaving a port, it will also navigate under the influence of waves. Considering the already restricted water depth and the induced squat effects, the estimation of wave effects on the manoeuvring behaviour seems of critical importance.
Manoeuvring in waves has been a constant topic of research during the last years. In literature several works addressing the problem can be found. Among them, one can refer to the works of Hirano et al. (1980), Bailey et al. (1998), Ueno et al. (2003), Skejic and Faltinsen (2008), and Seo and Kim (2011). More recent work has been performed by Cura-Hochbaum and Uharek (2016), Papanikolaou et al. (2016), Tello Ruiz et al. (2016a), Zhang et al. (2017), and Wang et al. (2018). In general, the approaches can be summarised in two main groups, the unified method and the two time scale method. The unified method attempts to integrate the fluid phenomena in a more general formulation valid for manoeuvring as well as for seakeeping, see for instance Bailey et al. (1998) and Sutulo and Guedes Soares (2006). The two time scale method is a more practical approach as it does not consider any further modification of the manoeuvring model obtained from calm water analysis. This approach considers waves effects given by the mean second order wave forces and moments only, e.g. Skejic and Faltinsen (2008), Seo and Kim (2011), Yasukawa and Nakayama (2009) and Papanikolaou et al. (2016). In spite of the fundamental differences between the unified and the two time scale method, it is important to mention that both evaluate wave forces similarly; computing them as in seakeeping studies.
Investigations of the influence of manoeuvring parameters such as the drift angle and yaw velocity on the wave induced forces and motions (as estimated from seakeeping studies) are limited in literature. In general, the drift angle influence is simply disregarded from the analysis. Works addressing this problem numerically can be found in Sutulo and Guedes Soares (2008) and Yasukawa et al. (2010) and experimentally in Yasukawa and Adnan (2006). In the latter, the influence of drift angle on the wave induced ship motions was evaluated for a container ship S-175 in deep water and waves longer than the ship length (). For such characteristics, the influence of the drift angle was found of relevant importance.
Another important concern is with respect to the propeller and rudder performance under the effect of waves. In literature, it is surprising to notice that in spite of their significant importance for manoeuvres only few works can be found, e.g. Nakamura and Naito (1977), Bhattacharyya (2015) and Taskar (2017). The latter are also dedicated to study the problem in deep water; in shallow water, however, relevant research information is scarce.
It is important to point out that in literature the problem of manoeuvring in waves is mostly addressed in deep water. There is limited information on how waves will affect the ship's manoeuvring behaviour in coastal zones where the limited water depth is a fundamental problem. To the authors, the study of manoeuvring in waves in shallow water deserves a great attention because it is in such areas where ships are mostly expected to manoeuvre in waves. Initial results on this topics were presented in Tello Ruiz et al. (2016a). A more extensive analysis was required to have a better view of the influence of waves on the ship's manoeuvrability.
It has been stressed above that there is a lack of research studies addressing the problem of manoeuvring in waves in restricted water depths. The current methods have been mostly developed for deep water scenarios and their fundamental assumptions require yet further investigation to determine their applicability to restricted water depths.
But first, before any further discussion is introduced, it is necessary to mention that in the present study the definition of restricted water depths is adopted from PIANC (2012) where the classification is made based on the water depth () to ship's draft amidships () ratio (). For shallow water this varies between 1.2 and 1.5, for medium deep water this ratio takes the values from 1.5 to 3, and for deep water larger values than 3. The present study is restricted to the limit between shallow to medium deep water depth, where the ratio takes the values of 1.5, corresponding to an under keel clearance of 50% of the ship's draft.
Considering the stated above, the main objective of the present study is to investigate the effect of waves on the ship's manoeuvrability in a finite water depth. The investigation will be conducted mainly experimentally and to some extent numerically.
To investigate the effect of waves on the manoeuvring of the ship the study is conducted by comparing results obtained from tests in calm water and in waves. The parameters evaluated are forces and moments, propeller thrust and torque coefficients, wake fraction at the propeller and rudder, as well as the thrust deduction factor. Further investigations are also required to study the main assumptions, such as the superposition of the wave forces to the manoeuvring forces, commonly used in the unified and two time scale method.
For the present study a selected number of ship speeds, drift angles, wave lengths and amplitudes have been used during experiments. Tests were conducted in head and following waves with a scale model of an ULCS. The ship speeds, the drift angles, and the wave main characteristics are chosen to be representative for the conditions commonly encounter in the Belgian coastal zone of the North Sea. In these navigational areas, the ship is expected to manoeuvre with slow to moderate speed and with a limited drift angles ( less than 20 deg).
For the present study numerical estimations have also been computed for the first and second order wave forces and moments. This has been performed with the software package Hydrostar. Hydrostar uses a 3D boundary element method that incorporates the speed effects by employing the so-called “encounter-frequency” approximation based on the use of the Green function associated to the encounter frequency (Bureau Veritas, 2012).
Section snippets
Modular approach
The governing equations of motion, describing the ship's rigid body motions in six degrees of freedom, are given by:where Eq. (1) is expressed in a body fixed coordinate system (b-frame), of which the origin is fixed amidships, with
The towing tank
The experiments were conducted at the Towing Tank for Manoeuvres in Confined Water at Flanders Hydraulics Research (FHR) in Antwerp, Belgium (in cooperation with Ghent University). The towing tank has a total length of 87.5 m, a width of 7.0 m and a maximum water depth of 0.5 m. Because of the presence of the harbour and the wave maker, the useful length is limited to 68.0 m. See Fig. 1 for better illustration.
The towing tank is equipped with a carriage mechanism which consists of a main
First order forces and moments
The results obtained for the first order forces in surge and heave as well as for the first order pitch moment are presented in Fig. 8 and Fig. 9 for two different speeds, respectively. In both figures, fully captive test results are shown for head and following waves, with and without the influence of the drift angle (). In addition, the numerical results computed with Hydrostar (HS) have also been displayed for comparison. Bear in mind that HS results do not take into account the influence
Conclusions
An extensive experimental study has been conducted to investigate the manoeuvring behaviour of an ULCS in coastal waves. The ship behaviour and environmental characteristics were chosen to represent the most common scenarios encountered when approaching or leaving a port. For an ULCS this represents operating in the range of shorter waves lengths compared to the ship length.
From the analysis of the first order forces and moments, no significant influence on the results was obtained when the
Acknowledgments
The present work is performed in the frame of project WL_2013_47 (Scientific support for investigating the manoeuvring behaviour of ships in waves), granted to Ghent University by Flanders Hydraulics Research, Antwerp (Department of Mobility and Public Works, Flemish Government, Belgium).
For the numerical calculations a Hydrostar licence was put at the main author's disposal by Bureau Veritas through their Antwerp and Paris offices, which is highly appreciated.
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