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Abstract
Breaking waves cause the largest forces on marine structures. Research on the impact pressure and force caused by the breaking waves has demonstrated that the maximum impact pressure and force show stochastic variability even for nominally identical waves in laboratory conditions. The source of the variability is not well known; however, the variability associated with wavebreaking shapes is considered to be the main cause. The motivations behind the study conducted in this thesis are: understanding the source of the variability, addressing the significance of the local variations on the breaking wavefront on the variability, and quantifying the impact pressure, force, and impulse variability as a function of the breaking wave shape and the local variations on the breaking wave surface.
The sources of the breaking wave variability, as documented in the literature, are presented. The shape of the breaking wave crest has been reported to be highly sensitive to any variation in the lab condition, which is partly responsible for the impact pressure and force variability observed in several studies on wave impact. However, even in highly controlled laboratory tests where the variation of the breaking wave crest shape is minimized, notable variations in the impact pressure have still been reported. We assume the variations are related to the lateral perturbations on the breaking wavefront. The perturbations are intrinsic to the wave breaking, and they are created by several pairs of counterrotating vortices parallel to the wave propagation direction that is generated during the breaking process. In nature, the perturbations on the wavefront are more prominent than in the lab due to other factors, such as the wavewind interaction and highfrequency waves. Further, residual vortices from the previous wave breaking are also a source of variability, which will not be present for lab tests of singlewave episodes.
The effect of the perturbations on the impact force is first assessed by investigating the slamming force and impulse for a cylinder vertically impacting on standing waves in two dimensions. The choice of the standing wave is to model the perturbations in a simplified setting. For a long horizontal cylinder, the slamming force is measured experimentally for the impact on various standing wave amplitudes and wavelengths. The results show that the trough impact slamming coefficient can be more than two times the value for flat impact and up to four times the value for crest impact. Adopted from von Karman (1929) and Wagner (1932), two analytical initial slamming coefficients are derived in which the effect of the water surface curvature is considered. These methods provide insight into the range of variation of the slamming coefficients.
The experimental results are numerically reproduced, showing a good agreement with the measurements. The study is extended with numerical simulations of the impacts with air entrapment between the cylinder and the water surface. The oscillations in the force time series due to the compressibility of air inside the air pockets are considered. For the cylinder impact on a short wavelength standing wave, multiple spatial and temporal slamming pressure peaks are observed, which cause multiple temporal slamming force peaks.
Given that the modelling of the perturbations in the twodimensional setup demonstrated that deviations from a nonflat water surface has a considerable influence on the slamming force, the effect of perturbations on the impact pressure, force, and impulse is investigated for a threedimensional wave impact on a monopile. The breaking wave shape varies globally and locally for a threedimensional wave impact. Thus, the impact pressure and force are investigated, on the one hand, as a function of the breaking wave shape and, on the other, as a function of the breaking wave shape and lateral perturbations on the breaking wavefront.
To study the breaking wave shape variation effect on the impact variability, the impact topology is characterized by the impact type. Five wave impact types, namely slosh, flipthrough, Ω, overturning, and fully broken, are defined. Fifty test repetitions are carried out for each impact type, and the slamming force, pressure, and impulse variability are evaluated. The mean and variability of the slamming force peaks are found to be the largest for the impact of type slosh and flip through. The coefficient of variation (CV) for these two impacts is in order of 10%. The high sensitivity of the impact force to the wave height and slope variation is the reason for the high force variability. The wave height and slope variation is mainly due to residual wave motion in the basin and wave prebreaking close to the wave paddle.
It is demonstrated that minimizing the wave height and slope variation by choosing the tests with similar wave height and slope decreases the slamming force and pressure variability. The group representing Ω impact shows the largest mean slamming force and pressure peak, and its variability is the highest among all groups. For the slamming force, the CV is in order of 4.5%, while for the slamming pressure, the CV is in order of 30%.
The experiments are repeated for the case of having perturbations in the breaking wavefront. The perturbations are introduced by a purposebuilt mechanical perturber device. Because of the perturbations, the slamming force peak variability increases, and the CV is approximately 5.7% for the Ω impacts. The slamming pressure variability for wave impacts significantly increases when the wavefront directly hits the monopile surface. The CV of the slamming pressure peak is in the order of 50% for the perturbed tests. The spatial variation of the slamming pressure peak for the perturbed tests is larger than for the unperturbed ones. For the former, the difference between the pressure measured for the Ω impact by the left and right pressure sensors at the front face of the monopile at the impact zone is found to have a CV of more than 10%, while the corresponding unperturbed CV is 1.7
The results of this study contribute to the further understanding of the loads associated with wave breaking and to the development of more accurate mathematical models to estimate slamming loads.
The sources of the breaking wave variability, as documented in the literature, are presented. The shape of the breaking wave crest has been reported to be highly sensitive to any variation in the lab condition, which is partly responsible for the impact pressure and force variability observed in several studies on wave impact. However, even in highly controlled laboratory tests where the variation of the breaking wave crest shape is minimized, notable variations in the impact pressure have still been reported. We assume the variations are related to the lateral perturbations on the breaking wavefront. The perturbations are intrinsic to the wave breaking, and they are created by several pairs of counterrotating vortices parallel to the wave propagation direction that is generated during the breaking process. In nature, the perturbations on the wavefront are more prominent than in the lab due to other factors, such as the wavewind interaction and highfrequency waves. Further, residual vortices from the previous wave breaking are also a source of variability, which will not be present for lab tests of singlewave episodes.
The effect of the perturbations on the impact force is first assessed by investigating the slamming force and impulse for a cylinder vertically impacting on standing waves in two dimensions. The choice of the standing wave is to model the perturbations in a simplified setting. For a long horizontal cylinder, the slamming force is measured experimentally for the impact on various standing wave amplitudes and wavelengths. The results show that the trough impact slamming coefficient can be more than two times the value for flat impact and up to four times the value for crest impact. Adopted from von Karman (1929) and Wagner (1932), two analytical initial slamming coefficients are derived in which the effect of the water surface curvature is considered. These methods provide insight into the range of variation of the slamming coefficients.
The experimental results are numerically reproduced, showing a good agreement with the measurements. The study is extended with numerical simulations of the impacts with air entrapment between the cylinder and the water surface. The oscillations in the force time series due to the compressibility of air inside the air pockets are considered. For the cylinder impact on a short wavelength standing wave, multiple spatial and temporal slamming pressure peaks are observed, which cause multiple temporal slamming force peaks.
Given that the modelling of the perturbations in the twodimensional setup demonstrated that deviations from a nonflat water surface has a considerable influence on the slamming force, the effect of perturbations on the impact pressure, force, and impulse is investigated for a threedimensional wave impact on a monopile. The breaking wave shape varies globally and locally for a threedimensional wave impact. Thus, the impact pressure and force are investigated, on the one hand, as a function of the breaking wave shape and, on the other, as a function of the breaking wave shape and lateral perturbations on the breaking wavefront.
To study the breaking wave shape variation effect on the impact variability, the impact topology is characterized by the impact type. Five wave impact types, namely slosh, flipthrough, Ω, overturning, and fully broken, are defined. Fifty test repetitions are carried out for each impact type, and the slamming force, pressure, and impulse variability are evaluated. The mean and variability of the slamming force peaks are found to be the largest for the impact of type slosh and flip through. The coefficient of variation (CV) for these two impacts is in order of 10%. The high sensitivity of the impact force to the wave height and slope variation is the reason for the high force variability. The wave height and slope variation is mainly due to residual wave motion in the basin and wave prebreaking close to the wave paddle.
It is demonstrated that minimizing the wave height and slope variation by choosing the tests with similar wave height and slope decreases the slamming force and pressure variability. The group representing Ω impact shows the largest mean slamming force and pressure peak, and its variability is the highest among all groups. For the slamming force, the CV is in order of 4.5%, while for the slamming pressure, the CV is in order of 30%.
The experiments are repeated for the case of having perturbations in the breaking wavefront. The perturbations are introduced by a purposebuilt mechanical perturber device. Because of the perturbations, the slamming force peak variability increases, and the CV is approximately 5.7% for the Ω impacts. The slamming pressure variability for wave impacts significantly increases when the wavefront directly hits the monopile surface. The CV of the slamming pressure peak is in the order of 50% for the perturbed tests. The spatial variation of the slamming pressure peak for the perturbed tests is larger than for the unperturbed ones. For the former, the difference between the pressure measured for the Ω impact by the left and right pressure sensors at the front face of the monopile at the impact zone is found to have a CV of more than 10%, while the corresponding unperturbed CV is 1.7
The results of this study contribute to the further understanding of the loads associated with wave breaking and to the development of more accurate mathematical models to estimate slamming loads.
Original language  English 

Place of Publication  Risø, Roskilde, Denmark 

Publisher  DTU Wind and Energy Systems 
Number of pages  167 
Publication status  Published  2023 
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 1 Finished

Slamming Loads on Offshore wind monopiles
Moalemi, A. (PhD Student), Lugni, C. (Examiner), Raby, A. (Examiner), Bredmose, H. (Main Supervisor), Ghadirian, A. (Supervisor) & Kristiansen, T. (Supervisor)
01/02/2020 → 31/08/2023
Project: PhD