Added mass coefficient of a moored ship
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Abstract:
Added mass is an important component for impact force of a moored ship.In order to establish a more reasonable load design standard for moored ships,it is necessary to perform systemic researches on added mass coefficient of a ship.Based on three dimensional frequency-domain theory,hydrodynamic problems of different types of moored ships were calculated in beam seas.The influences of those factors,such as ship size,water depth,loading condition and wharf type on added mass coefficient were analyzed.It is shown that added mass coefficient increases with ship size(loading) and decreases with water depth.It is higher in semi-infinite domain than in infinite domain.Based on regression analysis,an approximate estimate of added mass coefficient of a moored ship is presented.Keywords:
Added mass
Morison equation
Response amplitude operator
Wharf
Mooring
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The equations of motion of a spring-mass system are used to describe a vessel’s mooring system. These equations employ added mass and hydrodynamic damping coefficients, which depend on vessel shape and the proximity of free-surface and solid boundaries. The present study has experimentally determined these coefficients for barge tows moored in the chamber of navigation locks. Seven lock chamber configurations were tested in which the width, depth, and length of the chamber and the beam width and length of the tow were varied. Values of the added mass coefficient and a nondimensional form of the damping coefficient are presented. Subsequent to modeling flow in a lock chamber, these coefficients can be used in conjunction with hawser properties (spring constants) to estimate hawser forces generated during locking operations.
BARGE
Mooring
Lock (firearm)
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Fetch
Sea spray
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Buoy
Mooring
Tension (geology)
Added mass
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In the present study, as a novel and alternative form of foundation for offshore wind turbines, the air-floating characteristics of a large-diameter multi-bucket foundation (LDMBF) in still water and regular waves are investigated. Following the theory of single degree of freedom (DOF)-damped vibration, the equations of oscillating motion for LDMBF are established. The spring or restoring coefficients in heaving, rolling and pitching motion are modified by a dimensionless parameter ϑ related to air compressibility in every bucket with the ideal air state equation. Combined with the 1/25 scale physical model tests and the numerically simulated prototype models by MOSES, the natural periods, added mass coefficients and damping characteristics of the LDMBF in free oscillations and the response amplitude operator (RAO) have been investigated. The results shown that the added mass coefficients between 1.2 and 1.6 is equal to or larger than the recommended values for ship dynamics. The coefficient 1.2 can be taken as the lower limit 1.2 for a large draft and 1.6 can be taken as the upper limit 1.6 for a small draft. The resonant period and maximum amplitudes for heaving and pitching motions decrease with increasing draft. The amplitudes of heaving and pitching movements decrease to a limited extent with decreasing water depth.
Response amplitude operator
Dimensionless quantity
Added mass
Foundation (evidence)
Morison equation
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A series of calculations were carried out to investigate the hydrodynamic loads and responses of FPSO and shuttle tanker moored in side-by-side,in which the steady wave drift force was calculated based on the near field.Because of the shielding effect,it was found that the diffraction force on the shuttle tanker is significantly affected by the hydrodynamic interaction,and the steady wave drift force in the high wave frequencies has the same regular as the diffraction force.However the steady wave drift force in the low wave frequencies is slightly affected by the hydrodynamic interaction,the added mass,radiation damping,and vessel's RAOS are only affected marginally.In addition,the effect of the hydrodynamic interaction does not change greatly as the relative distance between the FPSO and shuttle tanker increases.
Added mass
Ship motions
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Ensuring safe ships berthing and loading-unloading operations at berths need reliable mooring systems. The choice of its parameters corresponds to calculating of the maximum displacements of the boat, which are caused by external impact of extreme waves, winds, and currents. Ship motions are described by system of differential equations, which contain disturbing, inertia, damping, and restoring forces, which magnitude strongly depends on the berth design and configuration of its elements. The major impact on the boat movements is caused by sea waves. In the given paper, an interaction between sea waves and ship located near the berth is studied. The cross-sectional shape of the boat is assumed to be rectangular and under-berth slope profile is approximated by finite number of steps. Different types of berth constructions are taken into account: containing impermeable or partially permeable front vertical wall, wave attenuation camera behind it with or without under-berth slope. The fluid is assumed ideal and incompressible, and its motion is potential. The stated problem is reduced to the determination of the velocity potential that satisfies the Laplace equation; the boundary condition on the free surface; the condition of non-flux through the impermeable bottom, the ship and berth elements; the condition on the surface of the permeable wall that is in proportionality between the wave flow velocity through the wall and pressure drop from its front to back faces. The problem is solved by dividing of the region into sub-domains with conditions of the hydrodynamic pressure and velocity continuity on its boundaries. In each sub-domain the solution is found using Fourier method in the form of functional series with unknown coefficients which are found from the system of linear algebraic equations. Calculated velocity potentials are used to determine different hydrodynamic characteristics of ship motions, such as horizontal and vertical components of disturbing force and moment, added masses and damping coefficients for all types of boat motions. The results of calculations are presented and they are compared with experimental data performed by authors.
Mooring
Velocity potential
Free surface
Potential flow
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Experimental investigations of unsteady ship motion in shallow water have been carried out at the Institute of Hydromechanics AN UkrSSR. Large-scale models were towed through a gravitational-type research pool at various depths. The changes in resistance as a function of model speed during acceleration and consequent inertial path, starting from the instant of automatic removal of the driving force, were studied. A reduction in resistance during acceleration was noticed in the region of critical velocities. Formulas were obtained for the calculation of the instantaneous and average over-a-given-interval arguments for the value of the coefficient of added mass. In general, the work represents a search for approaches to further investigation
Fictitious force
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In order to study the characteristics and law of green water impact pressure of ship,a water tank experiment was carried out for the ITTC international standard containership model S-175. In the model test,the self-propulsion ship model was utilized. The wave elevation,ship motions,wave height of green water,the impact pressure on the deck were synchronously measured during the model test. During the experiment,the green water phenomenon was analyzed by using the measured data through parameter variation of a series of factors including incident wave height,wave headings,ship speed and the bow shapes. It was shown by model testing that the effectiveness was limited in reducing the impact loads from deck green water by increasing the flare of the ship's bow. On the contrary,the phenomena of green water could get intensified in a high sea state. In the model test,the impact pressure from rolling waves of green water was observed internationally for the first time. The measured data shows that the slamming pressure by the direct impact of rolling waves on deck is far seriously destructive,in comparison with the impact loads induced by the deck swell of green water. The impact of rolling waves on the deck requires further study.
Slamming
Ship motions
Swell
Impact pressure
Wave height
Sea state
Water pressure
Bow wave
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By employing the method of bimodal spectrum to simulate the mixed waves that swell and wind wave appearing at the same time,the experiments were performed for a 266,000 m3 LNG ship moored to an island berth.A special effort was made to measure the mooring ship's motion responding the mixed waves.The result shows that when the energy of mixed waves is definite,the movement of the mooring ship will generally increase with the increase of low-frequent wave energy;when the loading condition is fixed,the surge and heave of the mooring ship will increase with the increase of period of swells in mixed waves.The peak values of sway,roll,and yaw are in proportion to the natural roll period of the mooring ship.When the condition of wind waves in mixed waves is definite,the movement of the mooring ship will rapidly increase with the increase of wave height of swells in most cases.When the condition of swells in mixed waves is fixed,the changes of wave height of wind waves have small effect on the movement of the mooring ship.In transverse waves,the pitch of the mooring ship is little influenced with the changes of mixed waves.
Mooring
Swell
Infragravity wave
Wave height
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Abstract : As part of the Navy's program to develop mobile port facilities, an analytical model was developed which can be used to compute the relative motion between vessels in regular and random head seas. The model, based on strip theory, is suitable for analyzing all single hull, linearly moored slender vessels. Since symmetry of moorings (if present) is assumed throughout, the motion is restricted to heave, surge and pitch. Deep-water added mass and damping coefficients are used in the equations of motion, and the resulting model predictions are considered valid provided that the draft-to-mean depth ratio does not greatly exceed 0.50. Typical results from the analysis are presented. These include graphs and tables of: the relative horizontal and vertical motion between two moored ocean-going vessels in shoal water, the relative horizontal and vertical motion between a moored ship and an unmoored beach discharge lighter, and the shoal water surge response of vessels as a function of mooring stiffness. (Author)
Shoal
Mooring
Response amplitude operator
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