Session: 06-01-01 Computational Mechanics and Design Applications

Submission Number: 180613

A Linear Time Complexity Algorithm for Implicit Time-Domain Simulations of Submarine Power Cable Motions in Offshore Wind Power Applications 

During the past decades, offshore wind energy has become a key contributor to renewable energy. However, it poses significant technical challenges, particularly in the reliable transmission of electricity. A key challenge arises from the fact that the cables are not completely buried beneath the seafloor, but instead include a free-span section near the connection of the cables to the wind turbines or converter platforms, respectively. Considering current developments, this is even more relevant in floating offshore wind energy applications. Thus, subsea high-voltage cables face harsh environmental conditions due to periodic hydrodynamic loads and platform displacements in the case of floating systems, which can lead to mechanical fatigue damage and ultimately failure.

Consequently, suitable methods are required that are able to predict the cables’ motions and resulting internal stresses, in order to perform fatigue lifetime analyses and carry out corresponding optimisations if needed. However, commercially available solutions are often either computationally expensive or based on simplified lumped-mass approaches, resulting in a physically inaccurate depiction of local deformations and stresses. To this end, custom-tailored open-source simulation tools were developed for the transient simulation of cable motions under arbitrary hydrological conditions, forming the basis for detailed fatigue and damage analyses. Specifically, numerically efficient, geometrically non-linear finite element models based on the floating frame of reference formulation were implemented to replace simplified spring-mass models, enabling a more accurate assessment of local deformations and stresses.

Since the floating frame of reference formulation originates from the field of flexible multibody system dynamics, a common problem when setting up the equations of motion is the presence of algebraic constraints in addition to the differential equations, which often leads to numerical drift and constraint violations. Although various methods exist to address this issue (e.g. the so-called Baumgarte stabilisation), in this work the coordinates were chosen such that a direct formulation of ordinary differential equations without algebraic constraints is possible, thus completely avoiding the problem of numerical drift.

Moreover, another challenge arises from the fact that the resulting equations usually pose a stiff initial-value problem due to the cables’ large differences in longitudinal and lateral stiffness. Accordingly, when using explicit numerical integration schemes, it is often unavoidable to reduce the integration time-step sizes to unnecessarily low values that are orders of magnitude smaller than the time periods associated with the typically low excitation frequencies of hydrodynamic loads. To address this issue, the elastic restoring forces are linearised in each time step, which enables the use of the implicit Newmark integration scheme. In doing so, numerical stability is greatly increased without sacrificing physical accuracy for the case at hand.

In this paper, the model is verified against commercial codes and analytical reference solutions, and computational performance is compared. For reasons of confidentiality, only generic configurations roughly based on typical real ones are analysed. Finally, based on the derived algorithm, fatigue lifetime estimations can be carried out using component-specific fatigue resistance curves, allowing for reliable lifetime predictions. As an illustrative example, the model is used to simulate different generic cable configurations under identical hydrodynamic loads, and the resulting load spectra are compared.

Presenting Author: Christoph Otto University of Rostock

Presenting Author Biography: Christoph Otto studied mechanical engineering at the university of Rostock from 2005 until 2012 and started working there as a researcher in 2012. During his internship at Suzlon Energy in the course of his studies he started developing a keen interest in custom derived physical models that he carried over to his research carrier at the university.

Authors:

Christoph Otto University of Rostock
Lars Radtke University of Rostock
Sascha Kosleck University of Rostock