Thomas E. Schellin

Numerical Prediction of Impact-Related Wave Loads on Ships

We present a numerical procedure to predict impact-related wave-induced (slamming) loads on ships. The procedure was applied to predict slamming loads on two ships that feature a flared bow with a pronounced bulb, hull shapes typical of modern offshore supply vessels. The procedure used a chain of seakeeping codes. First, a linear Green function panel code computed ship responses in unit amplitude regular waves. Ship speed, wave frequency, and wave heading were systematically varied to cover all possible combinations likely to cause slamming. Regular design waves were selected on the basis of maximum magnitudes of relative normal velocity between ship critical areas and wave, averaged over the critical areas. Second, a nonlinear strip theory seakeeping code determined ship motions under design wave conditions, thereby accounting for the nonlinear pressure distribution up to the wave contour and the frequency dependence of the radiation forces (memory effect). Third, these nonlinearly computed ship motions constituted part of the input for a Reynolds-averaged Navier-Stokes equations code that was used to obtain slamming loads. Favorable comparison with available model test data validated the procedure and demonstrated its capability to predict slamming loads suitable for design of ship structures.

A Rankine Panel Method for Added Resistance of Ships in Waves

A new Rankine panel method and an extended Reynolds-Averaged Navier–Stokes (RANS) solver were employed to predict added resistance in head waves at different Froude numbers of a Wigley hull, a large tanker, and a modern containership. The frequency domain panel method, using Rankine sources as basic flow potentials, accounts for the interaction of the linear periodic wave-induced flow with the nonlinear steady flow caused by the ships forward speed in calm water, including nonlinear free surface conditions and dynamic squat. Added resistance in waves is obtained by the pressure integration method. The time domain RANS solver, based on a finite volume method, is extended to solve the nonlinear equations of the rigid body six-degrees-of-freedom ship motions. The favorable comparison of the panel and RANS predictions demonstrated that the Rankine method is suitable to efficiently obtain reliable predictions of added resistance of ships in waves. Comparable model test predictions correlated less favorably, although the overall agreement was felt to be acceptable, considering the difficulties associated with the procedures to obtain accurate measurements.

Simulation of Sloshing in LNG-Tanks

The purpose of this paper was to demonstrate the application of a procedure to predict internal sloshing loads on partially filled tank walls of liquefied natural gas (LNG) tankers that are subject to the action of sea waves. The method is numerical. We used a moving grid approach and a finite-volume solution method designed to allow for arbitrary ship motions. An interface-capturing scheme that accounts for overturning and breaking waves computed the motion of liquid inside the tanks. The method suppressed numerical mixing. Mixing effects close to the interface were buried in the numerical treatment of the interface. This interface, which was at least one cell wide, amounted to about 20–50 cm at full scale. Droplets and bubbles smaller than mesh size were not resolved. Tank walls were considered rigid. The results are first presented for an LNG tank whose motion was prescribed in accordance with planned laboratory experiments. Both two-dimensional and three-dimensional simulations were performed. The aim was to demonstrate that (1) realistic loads can be predicted using grids of moderate fineness, (2) the numerical method accurately resolves the free surface even when severe fragmentation occurs, and (3) long-term simulations over many oscillation periods are possible without numerical mixing of liquid and gas. The coupled simulation of a sea-going full-sized LNG tanker with partially filled tanks demonstrated the plausibility of this approach. Comparative experimental data were unavailable for validation; however, results were plausible and encouraged further validation.

Nonlinear effects on long term distributions of wave induced loads for tankers

A method of long-term formulation of the nonlinear wave induced vertical load effects on ships was applied to three tanker hulls of different sizes. For large tanker hulls the nonlinear effect is not significant and thus linear theories can continue to be used for earlier studies on these kind of ships, contrary to what was shown earlier for containership hulls. However, for smaller tanker significant nonlinear values were obtained, with the particularity that both sagging and hogging nonlinear results were larger than the linear ones.

Wave Load and Structural Analysis for a Jack-Up Platform in Freak Waves

This paper analyzed the effects of freak waves on a mobile jack-up drilling platform stationed in exposed waters of the North Sea. Under freak wave conditions, highly nonlinear effects, such as wave run-up on platform legs and impact-related wave loads on the hull, had to be considered. Traditional methods based on the Morison formula needed to be critically examined to accurately predict these loads. Our analysis was based on the use of advanced computational fluid dynamics techniques. The code used here solves the Reynolds-averaged Navier-Stokes equations and relies on the interface-capturing technique of the volume-of-fluid type. It computed the two-phase flow of water and air to describe the physics associated with complex free-surface shapes with breaking waves and air trapping, hydrodynamic phenomena that had to be considered to yield reliable predictions. Lastly, the finite element method was used to apply the wave-induced loads onto a comprehensive finite element structural model of the platform, yielding deformations and stresses.

CRANE SHIP RESPONSE TO WAVE GROUPS

The motion response of a shear-leg crane ship lifting a heavy load in wave groups was investigated. The 9-DOF dynamic model incorporated hull motions coupled with nonlinear large-angle load swing and elastic stretch of the hoisting rope assembly. Hydrodynamic response forces and wave excitation forces were taken to be frequency dependent, and nonlinear mooring system restoring forces were allowed for. Closed-form linearized results about the system equilibrium state verified our nonlinear simulation algorithm; simulation results in comparison with scale model test measurements, our mathematical model. Wave groups were idealized in two different ways: 1) as continuous wave groups produced by pairs of beating waves of equal amplitude and slightly different periods, and 2) as isolated wave packets generated by superimposing a large number of regular wave components derived from a Gauss-modulated amplitude spectrum. Simulations show that hook load response, strongly coupled with ship motions, was mainly influenced by first-order wave-exciting forces. Low-frequency horizontal ship motions caused by second-order wave (drift) forces did not generally affect hook load response, i.e., first-order and second-order responses were independent.

LONG TERM DISTRIBUTION OF NON-LINEAR WAVE INDUCED VERTICAL BENDING MOMENTS ON A CONTAINERSHIP

A method is proposed for the long-term formulation of non-linear wave induced vertical bending moments. The non-linearity of the response is represented by an uncertain modelling factor that is deduced from calculations of transfer functions that account for non-linear effects in the prediction of wave induced vertical bending moments. Long term predictions are obtained for a containership hull showing that the response is clearly non-linear and is reproduced in the long-term predictions.

Comparison of experimental and theoretical wave actions on floating and compliant offshore structures

Presentation et discussion des methodes de calcul, en hydrodynamique lineaire, pour une sphere flottante, avec la methode diffraction/radiation, pour une plateforme semisubmersible et deux tours articulees, avec la formule de Morison, et pour une structure flottante pouvant etre traitee selon les deux methodes

Experimental investigation of impact loads during water entry

Abstract The objective of the present investigation was to provide reliable experimental data suitable to validate numerical tools aimed at predicting impact loads on and elastic deformations of wedge-shaped structures. To investigate impact-induced hydroelastic effects on slamming pressure peaks, four test bodies were examined. Two bodies were fitted with stiffened, rigid bottom plating and two bodies with thin elastic bottom plating, each case with 5° and 10° deadrise angles. Results comprised impact-induced pressures, accelerations, forces, and structural strains. Measurement repeatability, sampling rate effects, and hydroelastic effects were emphasised. Measured pressures and forces were compared with published experimental data. Additionally, this paper documents body geometries, test rig set-ups including instrumentation, and experimental procedures.

UNCERTAINTY ASSESSMENT OF LOW FREQUENCY LOAD EFFECTS FOR CONTAINERSHIPS

Abstract For a fast containership, linear response to regular waves obtained from three (two-dimensional) strip theories and one (three-dimensional) panel method was compared with model test measurements. The purpose was to assess the uncertainty of these (existing) methods to analytically predict first-order wave induced load effects. There was no clear tendency indicating more accurate results obtained from strip theories or from the panel method. The effect of uncertainty on transfer functions was assessed by calculating long-term distributions. The uncertainty was quantified by obtaining characteristic values. A relatively large degree of uncertainty was associated with predicted midship wave induced sectional loads. For another containership, combined stresses at selected control points in the hull plating were determined based on wave induced loads from one strip theory and the panel method. Differences between two- and three-dimensionally calculated principal stresses were generally smaller than the corresponding differences between two- and three-dimensionally calculated wave induced loads. This was due to the combined action of wave induced load effects.