Eine Plattform für die Wissenschaft: Bauingenieurwesen, Architektur und Urbanistik
Eine Plattform für die Wissenschaft: Bauingenieurwesen, Architektur und Urbanistik
Second-order monopile wave loads at linear cost
https://orcid.org/0000-0001-6961-0753
https://orcid.org/0000-0002-1374-5912
Abstract A method to compute the second-order free surface elevation, depth integrated force and mud line moment for a slender circular vertical cylinder is presented. The method is valid for unidirectional irregular waves and includes inertia loads and viscous loads. We first derive the linear transfer functions for free surface elevation, depth-integrated force and moment from the complex Fourier amplitudes of the velocity potential. Next, the second-order contributions are expressed through closed form quadratic transfer functions, which are further diagonalized through eigen decomposition. Hereby the second-order contributions can be computed as products of pseudo time series calculated by FFT, with the eigenvectors acting as transfer functions on the linear Fourier amplitudes. For a sample 3-hour sea state, we find that eight eigen vectors are sufficient to achieve an accuracy of 1% for the maximum peak value of force and moment and 1.3% for free surface elevation, relative to the standard deviation of each signal. These results are obtained 2500 faster than with the conventional approach and we demonstrate that the computational effort of the new method scales like , similar to linear wave loads, where is the number of frequencies. For the eight mode approximation, the error bound of 1% for loads and 4% for free surface elevation are found to hold across various values of the normalized peak wave number from shallow to deep water. The accuracy is adjustable through the number of modes and is found to be independent of the time series length. The methods potential in practical design is discussed.
Highlights Fast method for second-order loads on vertical cylinders. Method valid for force, moment and free surface elevation. Scales like N Log N, similarly to linear wave loads. Accuracy is adjustable. 2500 times faster calculation of 3 hour load time series demonstrated.
Second-order monopile wave loads at linear cost
https://orcid.org/0000-0001-6961-0753
https://orcid.org/0000-0002-1374-5912
Abstract A method to compute the second-order free surface elevation, depth integrated force and mud line moment for a slender circular vertical cylinder is presented. The method is valid for unidirectional irregular waves and includes inertia loads and viscous loads. We first derive the linear transfer functions for free surface elevation, depth-integrated force and moment from the complex Fourier amplitudes of the velocity potential. Next, the second-order contributions are expressed through closed form quadratic transfer functions, which are further diagonalized through eigen decomposition. Hereby the second-order contributions can be computed as products of pseudo time series calculated by FFT, with the eigenvectors acting as transfer functions on the linear Fourier amplitudes. For a sample 3-hour sea state, we find that eight eigen vectors are sufficient to achieve an accuracy of 1% for the maximum peak value of force and moment and 1.3% for free surface elevation, relative to the standard deviation of each signal. These results are obtained 2500 faster than with the conventional approach and we demonstrate that the computational effort of the new method scales like , similar to linear wave loads, where is the number of frequencies. For the eight mode approximation, the error bound of 1% for loads and 4% for free surface elevation are found to hold across various values of the normalized peak wave number from shallow to deep water. The accuracy is adjustable through the number of modes and is found to be independent of the time series length. The methods potential in practical design is discussed.
Highlights Fast method for second-order loads on vertical cylinders. Method valid for force, moment and free surface elevation. Scales like N Log N, similarly to linear wave loads. Accuracy is adjustable. 2500 times faster calculation of 3 hour load time series demonstrated.
Second-order monopile wave loads at linear cost
https://orcid.org/0000-0001-6961-0753
https://orcid.org/0000-0002-1374-5912
Abstract A method to compute the second-order free surface elevation, depth integrated force and mud line moment for a slender circular vertical cylinder is presented. The method is valid for unidirectional irregular waves and includes inertia loads and viscous loads. We first derive the linear transfer functions for free surface elevation, depth-integrated force and moment from the complex Fourier amplitudes of the velocity potential. Next, the second-order contributions are expressed through closed form quadratic transfer functions, which are further diagonalized through eigen decomposition. Hereby the second-order contributions can be computed as products of pseudo time series calculated by FFT, with the eigenvectors acting as transfer functions on the linear Fourier amplitudes. For a sample 3-hour sea state, we find that eight eigen vectors are sufficient to achieve an accuracy of 1% for the maximum peak value of force and moment and 1.3% for free surface elevation, relative to the standard deviation of each signal. These results are obtained 2500 faster than with the conventional approach and we demonstrate that the computational effort of the new method scales like , similar to linear wave loads, where is the number of frequencies. For the eight mode approximation, the error bound of 1% for loads and 4% for free surface elevation are found to hold across various values of the normalized peak wave number from shallow to deep water. The accuracy is adjustable through the number of modes and is found to be independent of the time series length. The methods potential in practical design is discussed.
Highlights Fast method for second-order loads on vertical cylinders. Method valid for force, moment and free surface elevation. Scales like N Log N, similarly to linear wave loads. Accuracy is adjustable. 2500 times faster calculation of 3 hour load time series demonstrated.
Second-order monopile wave loads at linear cost
Bredmose, H. (Autor:in) / Pegalajar-Jurado, A. (Autor:in)
Coastal Engineering ; 170
21.06.2021
Aufsatz (Zeitschrift)
Elektronische Ressource
Englisch