HYDRODYNAMIC DAMPING AND 'ADDED MASS' FOR FLEXIBLE OFFSHORE PLATFORMS
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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.Keywords:
Morison equation
Added mass
Oscillation (cell signaling)
Harmonic
Velocity potential
Simple harmonic motion
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Laboratory experiments were carried out to research drag and inertia coefficients of a vertical circular cylinder in random waves. The results were compared with those of field experiments and numerical simulations to discuss the characteristics of the random wave force. This comprehensive study showed that the drag and inertia coefficients obtained from the least squares fit on a wave-by- wave basis scattered widely as a result of shedding vortices during the previous wave cycle, the so-called history effect. Coefficients determined by least squares fit of the complete force time series of a random wave record were well ordered as a function of Keulegan- Carpenter number defined by significant orbital displacement or significant wave height and showed good agreement with the values in regular waves. This study enabled the authors to apply the results of extensive studies in regular waves or in harmonic flow to estimate wave forces acting on an ocean structure in random waves.
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The spectral properties of nonlinear drag forces of random waves on vertical circular cylinders are analyzed in this paper by means of nonlinear spectral analysis. The analysis provides basic parameters for estimation of the characteristic drag forces. Numerical computation is also performed for the investigation of the effects of nonlinearity of the drag forces.The results indicate that the wave drag forces calculated by linear wave theory are larger than those calculated by the third order Stokes wave theory for given waves. The difference between them increases with wave height. The wave drag forces calculated by use of linear approximation are about 5％ smaller than their actual values when measured in the peak values of spectral densities. This will result in a safety problem for the design of offshore structures. Therefore, the nonlinear effect of wave drag forces should be taken into consideration in design and application of important offshore structures.
Wave drag
Drag equation
Airy wave theory
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This paper presents results from experimental works to investigate wave loading on a vertical circular cylinder in random wave conditions in a wave flume with different water depths . In-line force coefficients (drag and inertia coefficient) are estimated from the measured pressures on cylinder's surface at different elevations along the length of the cylinder. The wave kinematics are estimated by using different wave theories. Methods of max-min and least-squares (simplified by fit on wave-by-wave basis) are applied to determine force coefficients.
Wave flume
Morison equation
Flume
Added mass
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Morison equation
Lift (data mining)
Added mass
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Morison equation
Added mass
Hydroelasticity
Square (algebra)
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The research into hydrodynamic loading on ocean structures is concentrated mostly
on circular cross section members and relatively limited work has been carried out on
wave loading on rectangular sections, particularly in waves and currents. This
research work is therefore carried out focussing on the evaluation of hydrodynamic
force coefficients for sharp edged rectangular cylinders of various cross-sections
(aspect ratios), subjected to waves and currents. Three cylinders with three different
cross-sections are constructed and tested vertically, as surface piercing and
horizontally, as fully submerged with the cylinder axis parallel to the wave crests.
The aspect ratios considered for this investigation are 1.0, 112, 2/1, 3/4 and 4/3. The
length of each cylinder is 2000mm. The sectional loadings are measured on a 100mm
section, which is located at the mid-length of the cylinder. The forces are measured
using a force measuring system, which consists of load cells, capable of measuring
wave and current forces. The in-line & transverse forces (for vertical cylinders) and
horizontal & vertical forces (for horizontal cylinders) have been measured. For
horizontal cylinder, to study the effect of depth of variation on submergence of the
cylinder, the tests are carried out for two depths of submergence.
The experiments are carried out at the Hydrodynamic Laboratory, Department of
Naval Architecture and Ocean Engineering, University of Glasgow. The tests are
carried out in a water depth of 2.2m with regular and random waves for low
Keulegan-Carpenter (KC) number up to 4.5 and the Reynolds number varied from
6.397xl03 to 1.18xl05
• The combined wave and current effect has been produced by
towing the cylinders in regular waves, along and opposite to the wave direction at
speeds of ± 0.1 mis, ± 0.2 mls and ± 0.3 mls. Based on Morison's equation, the
relationship between inertia and drag coefficients are evaluated and are presented as a
function of KC number for various values of frequency parameter, {3.
For the vertical cylinders, the drag coefficients decrease and inertia coefficients
increase with increase in KC number up to the range of KC tested for all the
cylinders. For the horizontally submerged cylinders, the drag coefficients showed a
similar trend to vertical cylinders, whereas the inertia coefficients decrease with
increase in KC number for all the cylinders. This reduction in inertia force is
attributed to the presence of a circulating flow [Chaplin (1984)] around the cylinders.
The random wave results are consistent with regular wave results and the measured
and computed force spectrum compares quite well.
While computing the force coefficients in the case of combined waves and currents,
only the wave particle velocity is used, as the inclusion of current velocity tends to
produce unreliable drag force coefficients. For vertical cylinders, the drag and the
inertia coefficients in combined waves and currents are lower than the drag and the
inertia coefficients obtained in waves alone. For horizontal cylinders the drag
coefficients are larger than those obtained for waves alone and the inertia coefficients
are smaller than those measured in waves alone.
The Morison's equation with computed drag and inertia coefficients has been found
to predict the measured forces well for smaller KC numbers. However, the
comparison between measured and computed positive peak forces indicate that the
computed forces are underestimated. It is suggested that if the wave particle
kinematics are directly measured, this discrepancy between measured and computed
forces might well be reduced.
Wave excitation forces are also reported in non-dimensional forms in the diffraction
regime, using 3D-Green function method. Wave induced pressure distribution around
the cylinder in regular waves have been measured and are reported as normalised
pressures. Wave run-up on the cylinder surfaces has been measured and simple
empirical formulae are presented for run-up calculations on the cylinder surfaces. The
results of this investigation show that the cylinder aspect ratio plays major role on
hydrodynamic force coefficients, dynamic pressure distribution and on wave run-up
on cylinder surfaces.
Wave height
Wave loading
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Morison equation
Added mass
Potential flow
Line (geometry)
Moment of inertia
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Prediction of the total force on a vertical cylinder in waves has been investigated. Drag and inertia coefficients on a small section of span have been measured for a range of orbital shapes. There is considerable scatter but rms in-line force is in reasonable agreement with U-tube data unless orbital shape approaches circular when local and total force is markedly overestimated on a quasi-2-D basis. For surface Kc less than about 12 lift is predominantly at twice the wave frequency. A quasi-2-D calculation using U-tube data underestimates total force for deep-water waves and in general lift prediction is somewhat unreliable.
Lift (data mining)
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We measure the wave drag acting on fully submerged spheres as a function of their depth and velocity, with an apparatus that measures only the component of the drag due to the proximity of the free surface. We observe that close to the surface the wave drag is of the order of the hydrodynamic drag. In our range of study, the measured force is more than one order smaller than predictions based on linear response. In order to investigate this discrepancy, we measure the amplitude of the waves at the origin of the wave drag, comparing the measurement with a theoretical model. The model captures the measurements at “large depth” but the wave’s amplitude saturates at “small depth,” an effect that partially accounts for the difference between the predicted and measured wave drag.
Wave drag
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Slamming
Froude number
Added mass
Potential flow
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