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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.
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.