• Ocean Systems Engineering
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• v.6 no.3
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• pp.233-244
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• 2016

Tension Leg Platform (TLP) is a floating structure that consists of four columns with large diameter. The diffraction theory is used to calculate the wave force of floating structures with large dimensions (TLP). In this study, the diffraction and Froude-Krylov wave forces of TLP for surge, sway and heave motions and wave force moment for roll, pitch degrees of freedom in different wave periods and three wave approach angles have been investigated. From the numerical results, it can be concluded that the wave force for different wave approach angle is different. There are some humps and hollows in the curve of wave forces and moment in different wave periods (different wavelengths). When wave incidents with angle 0 degree, the moment of diffraction force for pitch in high wave periods (low frequencies) is dominant. The diffraction force for heave in low wave periods (high wave frequencies) is dominant. The phase difference between Froude-Krylov and diffraction forces is important to obtain total wave force.

• International Journal of Naval Architecture and Ocean Engineering
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• v.12 no.1
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• pp.297-313
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• 2020

An Arctic Spar is characterized by its conical shape near the waterline. In this case, the nonlinear effects from its irregular hull shape would be significant if there is either a large amplitude floater motion or steep wave conditions. Therefore, in this paper, the nonlinear effects of an Arctic Spar are numerically investigated by introducing a weakly nonlinear time-domain model that considers the time dependent hydrostatic restoring stiffness and Froude-Krylov forces. Through numerical simulations under multiple regular and irregular wave conditions, the nonlinear behavior of the Arctic Spar is clearly observed, but it is not shown in the linear analysis. In particular, it is found that the nonlinear Froude-Krylov force plays an important role when the wave frequency is close to the heave natural frequency. In addition, the nonlinear hydrostatic restoring stiffness causes the structure's unstable motion at a half of heave natural period.

• International Journal of Naval Architecture and Ocean Engineering
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• v.13 no.1
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• pp.86-101
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• 2021

This study examined the effects of buoy shape and Nonlinear Froude-Krylov force (NFK) on a heaving-buoy-type Wave Energy Converter (WEC). Based on the Maclaurin expansion, the theoretical solutions of the NFK were derived for three different buoy shapes; hemispheric buoy, circular vertical cylinder, and truncated conical cylinder. A hydraulic power take-off system was adopted, and the latching control strategy was applied to maximize the extracted power from the WEC. The nonlinear effects of the Froude-Krylov force and restoring force on the heaving point absorber were investigated by comparing the heave Response Amplitude Operator (RAO) and time-averaged power extraction. The results showed that the conventional linear analyses were overestimated by up to 50% under the high amplitude wave condition. The latching control strategy was the most effective when peak wave period of regular or irregular wave was 0.4-0.45 times the heave natural period of the buoy.

• International Journal of Naval Architecture and Ocean Engineering
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• v.8 no.2
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• pp.127-136
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• 2016

Springing is the resonance phenomenon of a ship hull girder with incoming waves having the same natural frequency of the ship. In this study, a simple and reliable calculation method was developed based on quadratic strip theory using the Timoshenko beam approach as an elastic hull girder. Second-order hydrodynamic forces and Froude-Krylov forces were applied as the external force. To improve the accuracy of the strip method, the variation in the added mass along the ship hull longitudinal direction, so called tip-effect, was considered. The J-factor was also employed to compensate for the effect of three-dimensional fluid motion on the two-node vibration of the ship. Using the developed method, the first- and second-order vertical bending moments of the Flokstra ship were compared. A comparative study was also carried out for a uniform barge ship and a 10,000 TEU container ship with the respective methods including the J-factor and tip-effect.

• International Journal of Naval Architecture and Ocean Engineering
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• v.10 no.3
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• pp.259-269
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• 2018

In this study, the second order bending moment induced by sea waves is calculated using the quadratic strip theory. The theory has the fluid forcing terms including the quadratic terms of the hydrodynamic forces and the Froude-Krylov forces. They are applied to a ship as the external forces in order to estimate the second order ship responses by fluid forces. The sensitivity of the second order bending moment is investigated by implementing the quadratic terms by varying the ship side angle for two example ships. As a result, it was found that the second order bending moment changes significantly by the variation of the ship side angle. It implies that increased flare angles at the bow and the stern of ships being enlarged would amplify their vertical bending moments considerably due to the quadratic terms and may make them vulnerable to the fatigue.

• Journal of Ocean Engineering and Technology
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• v.33 no.6
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• pp.518-525
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• 2019

Recently, the Sub-Committee on SDC (Ship Design and Construction) of IMO have discussed actively the technical issues associated with the second-generation intact stability criteria of ships. Generally, second generation intact stability criteria refer to vulnerability five modes ship stability which occurs when the ship navigating in rough seas. As waves passes the ship, dynamic roll motion phenomenon will affect ship stability that may lead to capsizing. Multi-tiered approach for second generation of intact stability criteria of IMO instruments covers apply for all ships. Each ship is checked for vulnerability to pure loss of stability, parametric roll, and broaching/surf-riding phenomena using L1(level 1) vulnerability criteria. If a possible vulnerability is detected, then the L2(level 2) criteria is used, followed by direct stability assessment, if necessary. In this study, we propose a new method to verify the criteria of the surf-riding/broaching mode of small ships. In case, L1 vulnerability criteria is not satisfied based on the relatively simple calculation using the Froude number, we presented the calculation code for the L2 criteria considering the hydrodynamics in waves to perform the more complicated calculation. Then the vulnerability criteria were reviewed based on the data for a given ship. The value of C, which is the probability of the vulnerability criteria for surf-riding/broaching, was calculated. The criteria value C is considered in new approach method using the Froude-Krylov force and the diffraction force. The result shows lower values when considering both the Froude-rylov force and the diffraction force than with only the Froude-Krylov force was considered. This difference means that when dynamic roll motion of ship, more exact wave force needs considered for second generation intact stability criteria This result will contribute to basic ship design process according to the IMO Second-Generation Intact Stability Criteria.

• International Journal of Naval Architecture and Ocean Engineering
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• v.13 no.1
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• pp.718-733
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• 2021

A prediction method, based on the Morison equation as well as Froude-Krylov formula, is presented to simulate the loads acting on the columns and caissons of the semi-submersible platform induced by Internal Solitary Wave (ISW) respectively. Combined with the experimental results, empirical formulas of the drag and inertia coefficients in Morison equation can be determined as a function of the Keulegan-Carpenter (KC) number, Reynolds number (Re) and upper layer depth h₁/h respectively. The experimental and calculated results are compared. And a good agreement is observed, which proves that the present prediction method can be used for analyzing the ISW-forces on the semi-submersible platform. Moreover, the results also demonstrate the layer thickness ratio has a significant effect upon the maximum horizontal forces on the columns and caissons, but both minimum horizontal and vertical forces are scarcely affected. In addition, the incoming wave directions may also contribute greatly to the values of horizontal forces exerted on the caissons, which can be ignored in the vertical force analysis.

• Journal of the Korean Institute of Navigation
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• v.11 no.2
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• pp.61-72
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• 1987

When a ship is running in following seas, the encounter frequency is reduced to a very low one. In that case broaching, surfiding and capsizing phenomena are most likely to occur due to wave exciting forces acting on a ship in following seas. In this paper, the emphasis is mainly laid upon transverse stability of ships following seas, which is related to capszing phenomenon. The authors take the case that ship speed is equal to the wave celerity, i.e., the encounter frequency is zero. Hydrostatic force and moment due to Froude-Krylov hypothesis are calculated by line intergral method. Transverse stability is evaluated from hydrostatic force and moment. Through the application of present calculation method to box-shaped vessel, it is confirmed that the transversestability of a vessel can be reduced to critical level at wave crest.

• Journal of the Society of Naval Architects of Korea
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• v.47 no.3
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• pp.291-305
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• 2010

A three-dimensional time-domain calculation method is of crucial importance in prediction of the motions and wave loads of a ship advancing in a severe irregular sea. The exact solution of the free surface wave-ship interaction problem is very complicated because of the essentially nonlinear boundary conditions. In this paper, an approximate body nonlinear approach based on the three-dimensional time-domain forward-speed free-surface Green function has been presented. The Froude-Krylov force and the hydrostatic restoring force are calculated over the instantaneous wetted surface of the ship while the forces due to the radiation and scattering potentials over the mean wetted surface. The time-domain radiation and scattering potentials have been obtained from a time invariant kernel of integral equations for the potentials which are discretized according to the second-order boundary element method (Hong and Hong 2008). The diffraction impulse-response functions of the Wigley seakeeping model advancing in transient head waves at various Froude numbers have been presented. A simulation of coupled heave-pitch motion of a long rectangular barge advancing in regular head waves of large amplitude has been carried out. Comparisons between the linear and the approximate body nonlinear numerical results of motions and wave loads of the barge at a nonzero Froude number have been made.

• Bulletin of the Society of Naval Architects of Korea
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• v.21 no.3
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• pp.27-34
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• 1984

When a ship is travelling in following seas, the encounter frequency is reduced to be very low. In that case broaching phenomenon is most likely to occur, and it may be due to wave exciting forces acting on ships. It is thought that the wave exciting forces acting on ships in following seas almost consist of two components. One is hydrostatic force due to Froude-Krylov hypothesis, and the other is hydrodynamic lift force due to orbital motion of water particles below the wave surface. In the present paper, the emphasis is laid upon wave exciting sway force, yaw moment and roll moment acting on ships in following seas. The authers take the case that the component of ship speed in the direction of wave propagation is equal to the wave celerity, i.e., the encounter frequency is zero. Hydrostatic force components are calculated by line integral method on Lewis form plane, and hydrodynamic lift components are calculated by lifting surface theory. Furthermore captive model tests are carried out in regular following waves generated by means of a wave making board. Through the comparison between calculated and measured values, it is confirmed that the wave exciting forces acting on ships in following seas can be predicted in terms of present method to a certain extent.