6 results
Wave front perturbation effect on the variability of monopile wave impact loads
- Arefhossein Moalemi, Henrik Bredmose, Trygve Kristiansen, Fabio Pierella
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- Journal:
- Journal of Fluid Mechanics / Volume 984 / 10 April 2024
- Published online by Cambridge University Press:
- 12 April 2024, A65
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The slamming wave force and pressure variabilities for monopile wave impacts are studied as functions of wave breaking shape and transverse perturbations on the breaking wave front. The impacting wave topology is characterized as slosh, flip-through, $\varOmega$, overturning and fully broken. Fifty test repetitions are conducted for each type of wave impact to assess the variability of force impulse, force and pressure. The results for the unperturbed cases show that the slamming force is highest among the nominal slosh, flip-through and $\varOmega$ tests, and that the slamming force variability is highest for the first two. We demonstrate that the slamming force and pressure variabilities decrease notably after selecting and regrouping the tests by similar crest heights and temporal slopes measured at an upstream wave gauge. The group representing $\varOmega$ wave impacts shows the largest mean slamming force and peak pressure, and their variability is the highest among all groups. Further, the effect of lateral perturbations on the pressure, force and impulse variabilities is investigated. Due to the perturbations, the slamming pressure variability for the wave impacts in which the wave front hits the monopile surface increases significantly. The variability of the slamming force is also increased for the perturbed impacts; however, it is smaller than the slamming pressure variability. The force impulse variability shows a low sensitivity to perturbations, and its magnitude is smaller than that of the force variability. Finally, the slamming pressure using fifteen pressure sensors for five selected events is studied. For these tests, oscillations at frequencies associated with structural or bubble oscillations are seen. Further, the air entertainment is documented through video recordings.
Resonant response of a flexible semi-submersible floating structure: experimental analysis and second-order modelling
- Christine Lynggård Hansen, Henrik Bredmose, Maude Vincent, Stefan Emil Steffensen, Antonio Pegalajar-Jurado, Bjarne Jensen, Martin Dixen
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- Journal:
- Journal of Fluid Mechanics / Volume 982 / 10 March 2024
- Published online by Cambridge University Press:
- 01 March 2024, A7
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The dynamics and nonlinear wave forcing of a flexible floating structure are investigated experimentally and numerically. The floater was designed to match sub-harmonic rigid-body natural frequencies of typical floating wind turbine substructures, with the addition of a flexible bending mode. Experiments were carried out for three sea states with phase-shifted input signals to allow harmonic separation of the measured response. We find for the weakest sea states that sub-harmonic rigid-body motion is driven by even-harmonic difference frequency forcing, and by linear forcing for the strongest sea state. The flexible mode was tested in a soft, linearly forced layout, and a stiff layout, forced by second-, third- and fourth-harmonic frequency content, for increasing severity of the sea state. Further insight is gained by analysis of the amplitude scaling of the resonant response. A new simplified approach is proposed and compared with the recent method of Orszaghova et al. (J. Fluid Mech., vol. 929, 2021, A32). We find that resonant surge and pitch motions are dominated by even-harmonic potential-flow forcing and that odd-harmonic response is mainly potential-flow driven in surge and mainly drag driven in pitch. The measured responses are reproduced numerically with second-order forcing and quadratic drag loads, using a recent and computationally efficient calculation method, extended here for the heave, pitch and flexible motions. We are able to reproduce the response statistics and power spectra for the measurements, including the subharmonic pitch and heave modes and the flexible mode. Deeper analysis reveals that inaccuracies in the even-harmonic forcing content can be compensated by the odd-harmonic loads.
Cylinder water entry on a perturbed water surface
- Aref H. Moalemi, Henrik Bredmose, Amin Ghadirian, Trygve Kristiansen
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- Journal:
- Journal of Fluid Mechanics / Volume 965 / 25 June 2023
- Published online by Cambridge University Press:
- 16 June 2023, A16
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The perturbations existing on a breaking wavefront can be a potential explanation for the slamming pressure variability in wave impacts. Here, we investigate the effect of these perturbations by forced vertical slamming of a two-dimensional circular cylinder with constant downward velocity on standing waves. Through experimental modelling and numerical simulation, the slamming force is measured for several standing wave amplitudes and wavelengths. The standing wave phase is tuned such that the impact occurs symmetrically at the instant of maximum crest or trough. Our observations show that slamming coefficients vary with the standing wave amplitude when the wavelength is kept constant and vice versa. The trough impact slamming coefficient can be more than two times the flat impact, and up to four times the crest impact. The experimental results are reproduced by numerical simulations and they agree reasonably well in general. Two analytical approaches based on the von Kármán (NACA, vol. 321, 1929, pp. 1–8) and Wagner (Z. Angew. Math. Mech., vol. 12, 1932, pp. 913–215) methods, which consider the effect of water surface curvature, are introduced. The slamming coefficient calculated from these methods can provide a bound in which the slamming coefficient can be found for each standing wave amplitude and wavelength. Further insight is achieved by numerical simulations of impact on the shorter wavelength to diameter ratio of $0.05<\lambda /D<0.4$. As the wavelength to diameter ratio becomes smaller, the cylinder impacts the water surface at several locations. As a result, multiple peaks occur, and the trapped air at different locations between the cylinder and the water surface yields oscillations with different frequencies on the slamming coefficient time history.
Wave- and drag-driven subharmonic responses of a floating wind turbine
- Jana Orszaghova, Paul H. Taylor, Hugh A. Wolgamot, Freddy J. Madsen, Antonio M. Pegalajar-Jurado, Henrik Bredmose
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- Journal:
- Journal of Fluid Mechanics / Volume 929 / 25 December 2021
- Published online by Cambridge University Press:
- 27 October 2021, A32
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The nonlinear hydrodynamic responses of a novel spar-type soft-moored floating offshore wind turbine are investigated via analysis of motion measurements from a wave-basin campaign. A prototype of the TetraSpar floater, supporting a $1:60$ scale model of the DTU 10 MW reference wind turbine, was subjected to irregular wave forcing (with no wind) and shown to exhibit subharmonic resonant motions, which greatly exceeded the wave-frequency motions. These slow-drift responses are excited nonlinearly, since the rigid-body natural frequencies of the system lie below the incident-wave frequency range. Pitch motion is examined in detail, allowing for identification of different hydrodynamic forcing mechanisms. The resonant response is found to contain odd-harmonic components, in addition to the even harmonics expected a priori and excited by second-order difference-frequency hydrodynamic interactions. Data analysis utilising harmonic separation and signal conditioning suggests that Morison drag excitation or third-order subharmonic potential flow forcing could be at play. In the extreme survival-conditions sea state, the odd resonant responses are identified to be drag-driven. Their importance for the tested floater is appreciable, as their magnitude is comparable to the second-order potential flow effects. Under such severe conditions, the turbine would not be operating, and as such neglecting aerodynamic forcing and motion damping is likely to be reasonable. Additionally, other possible drivers of the resonant pitch response are explored. Both Mathieu-type parametric excitation and wavemaker-driven second-order error waves are found to have negligible influence. However, we note slight contamination of the measurements arising from wave-basin sloshing.
Detailed force modelling of the secondary load cycle
- Amin Ghadirian, Henrik Bredmose
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- Journal:
- Journal of Fluid Mechanics / Volume 889 / 25 April 2020
- Published online by Cambridge University Press:
- 21 February 2020, A21
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Steep wave passage around vertical circular cylinders is associated with an additional force peak occurring after the main peak: the secondary load cycle. The secondary load cycle for a focused wave group typical of offshore wind turbine foundations at 33 m full-scale water depth is investigated in scale 1 : 50. Ensemble-averaged force, front face pressures and free surface elevation measurements are used as the basis for the investigation. A two-phase free-surface Reynolds-averaged Navier–Stokes solver is validated against generic cases of turbulent flow over a wall, wave-boundary layer flow for a Reynolds number, $Re$, of $1\times 10^{4}<Re<1\times 10^{7}$, two-dimensional (2-D) drag on a cylinder for $1\times 10^{2}<Re<2.5\times 10^{5}$ and 2-D oscillatory flow for three combinations of $Re=\{5.8\times 10^{4},9\times 10^{4},1.7\times 10^{5}\}$ and Keulegan–Carpenter number, $KC=\{6,12,18\}$, respectively. The solver is next applied to reproduce ensemble-averaged experimental results of the focused wave group and a good match for the inline force and free surface elevation is found along with a good match for the measured front face pressures. The numerical solution for the focused wave is next analysed in detail to explain the cause of the secondary load cycle. We find that the secondary load cycle is confined to an upper region ranging from just above the still water level to 1.5 cylinder diameters below. By a further break down of the pressure field into contributions from the individual terms of the vertical Navier–Stokes equation, we find that the local force peak in the secondary load cycle is mainly caused by suction effects around the still water level on the back side, contributed through the material time derivative of the vertical velocity, $\text{D}\unicode[STIX]{x1D70C}u_{z}/\text{D}t$. The suction occurs due to the rapid decrease of water level below the generated water column at the back of the cylinder, which at this time has only just begun its downward motion. The first force local minimum in the secondary load cycle is aided by the hydrostatic pressure from the water column while the second local minimum of the secondary load cycle is aided by wash-down effects on the front side. Finally, the role of the observed vortices behind the cylinder is discussed and compared to reference computations with slip conditions. The results confirm findings from earlier slip boundary studies that the global force history through the secondary load cycle is not strongly affected by the boundary layer. The source of vortices behind the cylinder, observed in both sets of computations is discussed.
Pressure impulse theory for a slamming wave on a vertical circular cylinder
- Amin Ghadirian, Henrik Bredmose
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- Journal:
- Journal of Fluid Mechanics / Volume 867 / 25 May 2019
- Published online by Cambridge University Press:
- 20 March 2019, R1
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A pressure impulse model is presented for wave impact on vertical circular cylinders. Pressure impulse is the time integral of the pressure during an impact of short time scale. The model is derived for a simplistic geometry and has relative impact height, crest length and cylinder radius as effective variables. The last parameter, the maximum angle of impact, is free and can be calibrated to yield the right force impulse. A progression of simpler pressure impulse models are derived in terms of a three-dimensional box generalization of the two-dimensional wall model and an axisymmetric model for vertical cylinders. The dependence on the model parameters is investigated in the simpler models and linked to the behaviour of the three-dimensional cylinder model. The model is next validated against numerical results for a wave impact for a phase- and direction-focused wave group. The maximum impact angle is determined by calibration against the force impulse. A good match of the pressure impulse fields is found. Further comparison to the force impulse of two common models in marine engineering reveals improved consistency for the present model. The model is found to provide a promising representation of the pressure impulse field, based on a limited number of input parameters. Its further validation and potential as a robust tool in force and response prediction is discussed.