The expanded Morison equation considering inner and outer water hydrodynamic pressure of hollow piers
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Morison equation
Added mass
Velocity potential
Morison equation
Added mass
Velocity potential
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Morison equation
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Earthquake shaking table
Offshore geotechnical engineering
Fictitious force
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Potential flow
Tension (geology)
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Flume
Oscillation (cell signaling)
Wave flume
Offshore geotechnical engineering
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Abstract In offshore engineering, the design of effective marine platforms compatible with the offshore environmental condition is a challenging task, especially accurate estimation of hydrodynamic coefficients that affect the viscous forces. Practically, the well-known Morison’s equation is often adopted by designers to calculate wave loads on slender structures, where the values of drag and inertia coefficients are selected as constant values based on the design code of practice’s recommendations. However, the mass and drag coefficients must be determined empirically based on specific met-ocean data for the operation location. Thus, the objective of this study is to evaluate the Hydrodynamic Forces on Circular Cylinders fitted with sacrificial anodes using empirical methods, and validate the results using Computational Fluid Dynamic (CFD). It is found that the major parameters that affect the drag and inertia coefficients are the water depth, wave heights, wave frequencies, the pipe diameters, and the presence of anode fittings.
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Abstract : The dynamic response of deepwater flexible platforms due to wind-generated ocean waves appears to be an important design consideration; therefore, a theoretical and experimental study was made of hydrodynamic damping and 'added mass.' Classical potential theory with linearized boundary conditions was used to study the hydrodynamic damping due to wavemaking and the coefficient of added mass on a vertical surface-piercing cylinder as a function of oscillation frequency, cylinder diameter, water depth, and mode shape. Experiments were conducted to verify the results of potential theory. Rigid vertical cylinders were oscillated with simple-harmonic motion in calm water. Total forces and radiated waves were measured. They compared very well with theoretical values. Other investigators' data also verified the theory. A small experimental study was made in an attempt to verify the hydrodynamic damping implied by the quasi-steady drag-force interaction term of the presently used modified Morison equation to represent the drag force on an oscillating cylinder in waves. Damping was measured for an elastically supported circular cylinder in a steady current. The measured values were up to 4 times lower than the theoretical values. The disagreement appears to be that the experiments were outside the range for which the quasi-steady assumption is valid. Coefficients of added mass were also measured and were found equal to the potential theory value irrespective of the velocity of the current.
Morison equation
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Morison equation
Wave loading
Oscillating Water Column
Mode (computer interface)
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Slosh dynamics
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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.
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Morison equation
Response amplitude operator
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Mooring
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Radiation wave surrounding a horizontally submerged truncated circular cylinder with harmonic sway motion is analyzed using the linear potential wave theory. Using the method of separation of variables, harmonic expressions of the velocity potential in terms of the unknown constants are obtained in three subregions of the domain occupied by the water. A simple matching technique is used to satisfy the continuity of pressures and normal velocities at the common boundary of the subregions. The velocity potential is thus obtained, and consequently, the hydrodynamic force on the side of the cylinder expressed as a function of equivalent added mass and damping is determined. The solution presented not only is able to consider the gravity wave on the water surface, but also can be applied to truncated circular cylinder submerged in the arbitrary depth of water. Results of examples illustrated the accuracy of the solution and showed that using coefficient of hydrodynamic added mass in Morison equation would over-evaluate the hydrodynamic force on the side of the cylinder.
Velocity potential
Added mass
Radiation damping
Morison equation
Harmonic
Separation of variables
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