## Dynamic response of very large containerships passing fairways with dunes

### From BAWiki

Author: K. Uliczka

## Contents

### Boundary conditions

The dynamic behavior of very large POST-PANMAX container ships interacting with beds with various dune configurations was investigated in the BAW-DH shallow water basin (length about 100 m, width about 35 m, max water depth 0.7 m) at a model scale of 1 : 40. Selected ship parameters are summarized in the following table:

Name | Length | Beam | Draft | UKCR* | cB** | SG+ | Trim | KG++ |

- | m | m | m | m | - | - | - | m |

JUMBO | 320 | 40 | 14.5 | 1-2 | 0.740 | 6.29 | hard | 11.8 |

MEGA-JUMBO | 360 | 55 | 15.5 | 1-1,5-2 | 0.677 | 6.10 | hard | 10.2 |

*UKCR: Under-Keel-Clearance / cB: block coefficient / SG: slenderness ratio / KG: centre of gravity above ke*

The depth FROUDE Numbers were 0.27 < Fr_{h} < 0.68. The REYNOLDS Numbers were determined to be 3.1 · 10^{6} < Re < 6.2 · 10^{7} (Factor 10 > Re_{KRIT,erf}).

**The investigation's prognosis capability was guaranteed by adhering to the geometric and dynamical conditions dictated by dimensional analysis.**

Graph 1 shows the dune section in the hydraulic model used for simulating the influence of bed structures on ship dynamics in extremely shallow water (example: dune length l = 50 m).

Using a laser target measuring system installed on the model ships, it was possible to record the vertical dynamic behavior of the self-propelled, cable-guided models over a distance of approximately 90 m, from the acceleration to the braking phase. The internal velocity independent prognosis accuracy of the system was DS < 1 mm (Model; corresponds to < 4 cm in nature).

Using the point, laser-geometrical measurement method according to ERYUZLU et al. (1994), prognostized values could also be obtained as a function of ship speed (vS < 18 Kn) with an accuracy of DS < 1 mm (Model).

### Results

The following three graphs show a continuous recording of the vertical movement of the bow and stern of a JUMBO moving over a flat bed as well as over dunes of 50 m and 100 m length. A comparison of the graphs shows the increase in dynamic response as a function of dune length.

While underway over the dune section with l = 50 m the ship showed a slightly disturbed movement (Graphs 2 and 3). For l = 100 m a ratio of dune **l** to ship length **l** of about **l = l / 3** was chosen, so that a pitching of the large PPM container ship with the period of the dunes could be excited (Graph 4). The excitation results from the locally higher bow squat with a smaller UKC over the crest of the dune and the simultaneous lower stern squat with a locally higher water depth in the trough of the dune. The ship velocity dependent amplitudes achieve maximum values of DS = 0.16 m (v_{S} = 15,3 Kn).

The systematic investigations using an array of dune sections of equal length were augmented with ship movement experiments over a bed with dunes of irregular length of l = 50 m - 75 m - 100 m. Graph 5 shows the dynamic behavior of a ship over a distance of 1600 m (about 5 ship lengths or 25 dunes). A light pitching on the order of DS = 0.07 m (v_{S} = 16.8 Kn) was recorded for the JUMBO passing over the irregular dunes. The absolute value for the squat was similarly reduced as with the investigations with dunes of constant length (Graphs 6 and 7).

Graph 6 shows a comparison of the velocity dependent squat for the JUMBO moving over various bed forms (no dunes, l = 50 m, l = 100m, l = 50 m - 75 m - 100 m). The results of the point-wise measurements show a definite reduction of squat for movement over dunes. This is especially clear for a UKC_{R} = 2 m with a resulting squat on the order of up to DS = 0.3 m (v_{S} = 15 Kn).

As is the case with the JUMBO, a reduced velocity dependent squat is also evident for the MEGA-JUMBO (Graph 6) over bedforms with dunes (UKC_{R} = 1.5 m). Different from the JUMBO, the stern squat dominates the bow squat for the MEGA-JUMBO in extreme shallow water, resulting in a negative trim angle. This dynamic behavior is due to the ship having a large width (b = 55 m) and a single screw drive and moving in extremely shallow water (marked pressure minimum from the propeller wake at the stern).

### Discussion

The present results of the fundamental investigations show that formulas of BARRASS and ICORELS, even in modified form, are not suitable when applied to very large PPM container ships moving in laterally unbounded shallow water, as is clearly shown in Graph 8. The formulas do not contain a generally valid parameterization of the geometric crossections in their hydraulic interaction with a moving ship.

The following hydromechanical processes are important for a discussion and explanation of the very low squat values:

- Squat is the depression of the ship moving with the evolving primary wave system, and is at the same time a characteristic parameter of the ship's drag; changes in the width, length and flow-optimized hull forms of modern ships, the geometric conditions for the formation of the primary wave system have changed, and thus the squat - with reference to ship size - has decreased.

- The influence of bed structures (dunes) on the dynamic behavior of very large container ships in extreme shallow water had not been researched to date. For reasons of nautical safety, bed depths were based on the crests of the dunes. A higher form roughness of the system, and thus a higher energy dissipation for the ship generated back current was assumed. This resulted in a stronger primary wave system which in turn increased the squat.

- The systematic model investigations show, however, that in comparison to a flat bed, for a bed with dunes of very small slope (H = 4 m; l = 50 - 100 m), an increased back current crossection with corresponding energy dissipation appears, which in turn leads to a weakening of the primary wave system and thus to a decrease in the squat.

- The supplementary investigations on the influence of irregular dunes on ship behavior show that here also "pitching" - though lower than for regular dunes - was determined for all investigated ship model types and that the absolute squat can decrease in a similar manner as for the previous bed forms.

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