Suresh Rajendran

Time Domain Comparison With Experiments for Ship Motions and Structural Loads on a Container Ship in Abnormal Waves

The paper presents experimental results from model tests with a containership advancing in abnormal wave conditions and comparisons with numerical simulations. A nonlinear time domain method based on strip theory is used for the calculation of vertical ship responses induced by abnormal waves. This code combines the linear diffraction and radiation forces with dominant nonlinear forces associated with vertical response arising from Froude-Krylov forces, hydrostatic forces and shipping of green water. The time domain simulations are compared directly with experimental records from tests with a model of a container ship in deterministic waves for a range of Froude numbers. Extreme sea conditions were replicated by the reproduction of realistic abnormal waves like the New Year Wave and abnormal wave from North Alwyn. Head sea condition is considered and the comparisons include the wave elevation, the vertical motions of the ship and the vertical bending moment at midship.Copyright

Estimation of Short Term Probability Distributions of Wave Induced Loads Acting on a Cruise Vessel in Extreme Seas

A time domain code based on strip theory is applied to calculate the probability distributions of relative motions and bending moments of a cruise ship in a set of extreme seas. The code includes two levels of complexity. The simpler one combines linear radiation and diffraction forces with nonlinear Froude-Krylov forces, hydrostatic forces and shipping of green water on the bow. Cummins formulation is used to represent the radiation forces. The second approach is a generalization of the first one and, although the formulation is based on the linear assumption (of the radiation forces), the effects of body nonlinearity are considered by a simplified method: the memory functions, infinite frequency added masses and the radiation restoring coefficients are assessed at each time instant as function of the instantaneous wetted surface. A similar procedure is used to calculate the diffraction forces.The code is used to analyze the responses of a cruise ship in a set of extreme sea conditions. The nonlinear radiation and diffraction effects on the responses are analyzed by comparing the “fully nonlinear” results with the numerical predictions assuming linear radiation and diffraction forces. The short term nonlinear responses are represented by empirical probability distributions, obtained from time domain simulations, and the quality of the predictions is assessed by comparing with model tests experimental data.Copyright

Analysis of Vertical Bending Moment on an Ultra Large Containership Induced by Extreme Head Seas

This paper discusses the numerical analysis of an ultra large containership model in severe head seas. A body nonlinear time domain code based on the strip theory is used for the calculation of the rigid body response of the vessel. The radiation, diffraction, Froude-krylov and hydrostatic forces are calculated for the exact wetted surface area of the ship at each time step. A practical engineering approach is followed to calculate the body nonlinear radiation and diffraction forces. The numerical vertical bending moment is compared with the experimental results. The experiment was conducted on a flexible model in both regular and irregular waves. The model comprised six segments that were joined with an aluminum backbone of variable stiffness characteristics in order to replicate the hydroelastic behavior of the real ship. The model was tested for two ship speeds, 15 and 22 knots. For the first three harmonic values of the vertical bending moment, a good agreement between the numerical and the experimental results are found. However, higher harmonics significantly contributed to the total experimental vertical bending moment, in regular waves with 8m wave height and a ship speed of 15 knots. Similarly, the value of the fourth harmonic was 32% of the first harmonic values when the ship encountered a 5m regular wave with 22 knots speed. On comparison of the rigid body response in irregular seas, the hydroelastic loads resulted in 49% increase in the maximum value of the vertical bending moment.© 2014 ASME

Calculation of Vertical Bending Moment Acting on an Ultra Large Containership in Large Amplitude Waves

The time domain method is further extended here in order to calculate the hydroelastic response of an ultra large containership in regular waves. Based on strip theory, the hydrodynamic and the hydrostatic forces are calculated for the instantaneous wetted surface area. Slamming forces are calculated using a Von Karman approach in which the water pile up during slamming is neglected. Timoshenko beam which takes into account the shear deformation and rotary inertia is used to model the structural dynamic characteristics of the hull. The beam is discretized using the finite element method and the ship vibration is solved using the modal analysis. The method is used to calculate the vertical bending moment acting on an ultra large containership in large amplitude regular waves. The results are compared with the experimental results measured in wave tank.Copyright

Short Term Distribution of Loads Acting on a Cruise Vessel in Extreme Seas Using a Body Nonlinear Time Domain With Second Order Froude-Krylov Pressure

Short term probability distribution of the vertical bending moment acting on a cruise vessel in extreme seas is calculated using a body nonlinear time domain method based on strip theory. The hydrodynamic forces are calculated for the exact wetted surface area under the incident wave profile. The incident potential satisfies the weakly nonlinear free surface condition based on the Stokes expansion. The disturbance potential satisfies the linear free surface and body boundary conditions. Certain practical engineering techniques are employed for the calculation of the body nonlinear forces. The statistics and the probability of distribution of the numerical vertical bending moment are compared with the experimental results measured in the wave tank.© 2015 ASME

Prediction of Ship Responses in Large Amplitude Waves Using a Body Nonlinear Time Domain Method With 2nd Order Froude-Krylov Pressure

The paper analyzes the effect of 2nd order waves on the vertical ship responses in extreme seas. The numerical simulations are carried out using a body nonlinear time domain code based on strip theory. The radiation, diffraction, Froude-krylov and hydrostatic forces are calculated for the exact wetted surface area of the ship for each time step. A practical engineering approach is followed to calculate the body nonlinear radiation and diffraction forces. First order Froude Krylov pressures are replaced with a second order model for the present study. The 2nd order Froude-Krylov pressures are integrated upto the exact wetted surface area for each time instant. The ship responses in regular waves with varying steepness are analyzed. Finally, the vertical ship responses are compared with the responses in design waves measured in the wave tank.© 2014 ASME

Experimental Investigation of the First and Second Order Wave Exciting Forces on a Restrained Body in Long Crested Irregular Waves

The paper presents an experimental investigation of the first order and second order wave exciting forces acting on a body of simple geometry subjected to long crested irregular waves. The body is axis-symmetric about the vertical axis, like a vertical cylinder with a rounded bottom, and it is restrained from moving. Second order spectral analysis is applied to obtain the linear spectra, coherence spectra and cross bi-spectra of both the incident wave elevation and of the horizontal and vertical wave exciting forces. Then the linear and quadratic transfer functions (QTF) of the exciting forces are obtained. The QTF obtained from the analysis of irregular wave measurements are compared with results from experiments in bi-chromatic waves and with numerical predictions from a second order potential flow code.Copyright

Estimation of Short-and Long-Term Probability Distributions of Wave-Induced Loads Acting on a Cruise Vessel in Extreme Seas

ABSTRACT A time domain code based on strip theory is applied to calculate the probability distributions of relative motions and bending moments of a cruise ship in a set of extreme seas. The code includes two levels of complexity. The simpler one combines linear radiation and diffraction forces with nonlinear Froude-Krylov forces, hydrostatic forces and shipping of green water on the bow. Cummins formulation is used to represent the radiation forces. The second approach is a generalization of the first one and, although the formulation is based on the linear assumption (of the radiation forces), the effects of body nonlinearity are considered by a simplified method: the memory functions, infinite frequency added masses and the radiation restoring coefficients are assessed at each time instant as function of the instantaneous wetted surface. A similar procedure is used to calculate the diffraction forces. The code is used to analyze the responses of a cruise ship in a set of extreme sea conditions. The nonlinear radiation and diffraction effects on the responses are analyzed by comparing the “fully nonlinear” results with the numerical predictions assuming linear radiation and diffraction forces. The short term nonlinear responses are represented by empirical probability distributions, obtained from time domain simulations, and the quality of the predictions is assessed by comparing with model tests experimental data.