A simplified modular approach for the prediction of the roll motion due to the combined action of wind and waves

Abstract

In this work a combined analytical-numerical approach is proposed to address the problem of the ship roll motion under the combined action of wind and waves. Roll motion is modelled as a one-degree-of-freedom system non-linear in both damping and restoring. The approach is modular, allowing an easy update of the methodology on the basis of new research outcomes. Realistic environmental conditions regarding the effects of both wind and waves are taken into account and can be easily changed. The spatial correlation of wind gusts is taken into account by means of an 'aerodynamic admittance' function, whereas the moment due to waves is obtained from the sea slope spectrum using the concept of effective wave slope, leading to a 'hydrodynamic admittance' function. Both static and dynamic aspects of the problems are taken into account. The proposed analytical procedure, based on statistical linearization technique, allows approximate statistical averages of the roll motion, assumed to be Gaussian, to be obtained without necessarily resorting to time-consuming Monte Carlo simulations. On the basis of the results obtained, an estimation of the capsize probability can be carried out. It seems that the effect of wind gustiness could be considered very small when compared with the effects of waves and mean wind speed when the metacentric height is sufficiently large. Finally, the presented approach moves towards the concept of 'performance-based analysis', recently introduced at the International Maritime Organization as the basis for future developments of intact stability, in a clear and formal way.

Filter models for prediction of stochastic ship roll response

“…It is the transfer function between the wave energy spectrum and the wave excitation moment spectrum and it depends on ship geometry and frequency ω. Generally, for beam seas, long waves with low frequencies are effective for roll motion, but the excitation due to short waves with high frequencies is almost negligible [27]. Moreover, the wave elevation and the wave excitation moment are assumed to be stationary Gaussian processes.…”

Smoothed particle hydrodynamics (SPH) simulation of a tuned liquid damper (TLD) with angular motion

“…In the field of Naval Architecture, the roll motion equation was coupled with experimentally determined fluid moments for an oscillating free surface tank (Van den Bosch and Vugts 1966) whilst Francescutto and Contento (1999) exploited the mechanical equivalence developed by Graham and Rodríguez (1952) to provide a 2-DOF analytical model which is nonlinear in respect to roll, and linear in respect to the DOF associated to the fluid sloshing. SDOF models for roll are often used to simúlate the roll behaviour in beam seas (Bulian and Francescutto 2004) and an example of analytical nonlinear SDOF descriptions of roll motion coupled with direct CFD calculations for the free surface tank can be found in (Armenio et al 1996). Rognebakke and Faltinsen (2003) analyzed the coupled problem in the sway case of a box excited by waves, in comparison to experimental data.…”

Estimation of Effective Wave Slope Coefficient of Ships with Large Breadth and Draught Ratio

“…The wavelength corresponds to the wave frequency of 3.0 rad/s is 6.85 meters smaller than a half of the ship breadth. Bulian, et al [15] shows that this coefficient can be neglected when the wavelength is smaller than a half of ship breadth. Figure 8 shows the effective wave slope coefficient as a function of ratio between vertical distance of center of gravity from the sea surface and the ship draught.…”

“…Those damping coefficients are obtained following the method recommended by International Towing Tank Conference (ITTC) [12], The Bertin s coefficient is then calculated by using the following equation: (14) where and are the linear and the nonlinear coefficients of polynomial equation of decay amplitude of roll as function of average two consecutive roll amplitude of roll decay test results. The effective wave slope coefficient is calculated by using the equation as follows [8]: (15) is the maximum roll angle obtained by drift test in regular beam seas with wave steepness, . The drift test is conducted for several different wave slope with wave frequency of 0.8 to 1.2 of the natural frequency of roll.…”