Hydrodynamic force coefficients for rectangular cylinders in waves and currents
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Abstract:
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.Keywords:
Wave height
Wave loading
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Evaluation of wave induced forces on tubular members of offshore structures is sensitive to the choice of hydrodynamic coefficients involved in the Morison's equation. This study is based on experiments conducted in a wave flume to evaluate the coefficients of drag, inertia and lift for rough as well as inclined cylinders. Within the experimental range it was observed that the magnitude of the drag coefficient is more influenced by the degree of cylinder inclination along the 'in-line' direction than by its roughness. The inertia and lift coefficients however are affected by the cylinder inclination as well as by its roughness at high Reynolds numbers.
Morison equation
Flume
Lift (data mining)
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The hydrodynamic forces on a cylinder exposed to oscillatory flow have been determined at Reynolds numbers (Re) in the range 2.5×105 to 1.0×106 (supercritical and transcritical regimes) and Keulegan‐Carpter (KC) numbers in the interval from 1 to 16. One smooth and two rough cylinders were tested. Inline force coefficients and rms lift coefficients are given as a function of KC, Re, and surface roughness. Time series of both force components are shown, and different flow regimes are identified. These force traces are linked to characteristic vortex shedding modes in different KC‐intervals. Both force components are found to vary considerably in the KC‐range under investigation, with the transverse force sometimes being as large in magnitude as the in‐line force.
Lift (data mining)
Vortex shedding
Aerodynamic force
Body force
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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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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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The wave-induced hydrodynamic forces on a pair of vertical cylinders of different diameters in close proximity are investigated experimentally. The smaller cylinder is placed at various circumferential positions around the larger one. The effects of the wall-to-wall gap between the 2 cylinders are also investigated. The wave forces, including drag, inertia forces and mean lift, are measured on each cylinder independently and at 2 different depths below the mean water level for each cylinder. The Keulegan-Carpenter numbers vary from 0.4 to 14 based upon the larger cylinder diameter, and the Reynolds numbers are in the subcritical regime. It is found that there is significant interference effect upon the cylinder drag and inertia coefficients.
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This paper presents the results of an extensive experimental investigation of the in-line and transverse forces acting on sand-roughened circular cylinders placed in oscillatory flow at Reynolds numbers up to 1,500,000, Keulegan-Carpenter numbers up to 100, and relative roughnesses from 1/800 to 1/50. The drag and inertia coefficients have been determined through the use of the Fourier analysis and the least squares method. The transverse force (lift) has been analysed in terms of its maximum and root-mean-square values. In addition, the frequency of vortex shedding and the Strouhal number have been determined. The results have shown that all of the coefficients cited above are functions of the Reynolds number, Keulegan-Carpenter number, and the relative roughness height. The results have also shown that the effect of roughness is quite profound and that the drag coefficients obtained from tests in steady flow are not applicable to harmonic flows even when the loading is predominantly drag.
Strouhal number
Lift (data mining)
Vortex shedding
Aerodynamic force
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Wave forces on small sections of vertical tubes were measured in a wave tank test. The tube sizes and the wave parameters were such that both the inertia and the drag dominated areas were covered in the test. The surface of the tubes was sand-roughened to simulate the marine growth on these tubes. The hydrodynamic coefficients from these forces were computed with the help of the Morison equation. The roughnesses of the tubes were varied to show their effects on the inertia, drag, and lift coefficients. Mean values of these coefficients versus the Keulegan-Carpenter number were used to compute total forces on the tubes which were compared with the measured total forces. The drag and lift coefficients increased with the increased roughness of the tubes, while the inertia coefficients were relatively unaffected.
Morison equation
Lift (data mining)
Added mass
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Hydrodynamic forces on a smooth horizontal circular cylinder exposed to oscillating flow were investigated experimentally at Reynolds numbers (Re) in the range 20,000 - 260,000 (subcritical and transcritical regimes) and Keulegan-Carpenter numbers (Kc) in the interval from 5 to 40. In the tests, the Re number and Kc number were varied systematically. The drag force coefficient CD and inertia force coefficient CM in Morison equation were determined through the use of the Least Squares Method. Both total in-line force coefficient CF and transverse force (lift) coefficient CL were analysed in terms of their maximum and root means square values. All the in-line and lift force coefficients were given as a function of Re and Kc number, and also their deviations with the average value were shown. The principal results are as follows: for the Re greater than or equal 80,000m, all the hydrodynamic force coefficients, including CD, CM, CF and CL, are at best very weak functions of Reynolds number, and each of them tends towards a certain constance with increasing Kc number; for the Re 80,000, the drag force coefficient CD decreases with increasing Re number, and inertia force coefficient CM increases with increasing Re number. The tendencies of drag and inertia coefficients versus Kc number for the Re less than or equal 105 are very similar to the others, which are very close to Rodenbusch and Cutierrez's (1983) but are somewhat larger than Sarpkays's (1976 and 1986) and Bearman et al's (1985).
Morison equation
Lift (data mining)
Strouhal number
Fictitious force
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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.
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