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Abstract. Vortex-induced vibration (VIV) of wind turbine towers during installation is an aero-structural problem of significant practical relevance. Vibrations may happen in the tower structure, especially when the rotor-nacelle assembly is not yet attached to the tower or if the rotor blades are not yet connected to the tower-nacelle assembly. The complexity of aeroelastic phenomena involved in VIV makes modelling and analysis challenging. Therefore, the aim of the current research is to investigate the fundamental mechanisms causing the onset and sustenance of vortex-induced vibrations. To gain more understanding of the nature of vibrations, a methodology is established that distinguishes between different components of the forces at play. This approach allows for identifying how various force components impact the oscillation of a rigid body. The method is executed using the OpenFOAM open-source software. Numerical simulations are conducted on a two-dimensional smooth cylinder at both subcritical and supercritical Reynolds numbers to establish a correlation between wind turbine tower vibrations and the force mechanism. The analysis involves performing unsteady Reynolds-averaged Navier–Stokes (URANS) simulations using the modified pimpleFoam solver with the k–ω shear stress transport (SST) turbulence model. Both fixed and free-vibrating cases are studied for smooth cylinders. For the high-Reynolds-number cases, a setup matching the tower top segment of the IEA 15 MW reference wind turbine was chosen. Studying the flow around a cylinder at a subcritical Reynolds number reveals that the primary force involved is the vortex-induced force. The combined force due to viscosity, added mass, and vorticity contributes most to the overall force. For a freely vibrating cylinder with a single degree of freedom in the crossflow direction, the analysis indicates that the force component associated with the cylinder's motion is crucial and significantly affects the total force. Moreover, analysing the energy transfer between the fluid and the structure, a positive energy contribution by the vortex-induced force is observed on or before the dominant Strouhal velocity. This confirms observations at low Reynolds numbers in the literature that the vortex shedding predominantly contributes to the initiation of oscillations during VIV. The kinematic force contributes to the energy transfer of the system, but the mean energy transfer per cycle is negligible.

Abstract. Vortex-induced vibration (VIV) of wind turbine towers during installation is an aero-structural problem of significant practical relevance. Vibrations may happen in the tower structure, especially when the rotor-nacelle assembly is not yet attached to the tower or if the rotor blades are not yet connected to the tower-nacelle assembly. The complexity of aeroelastic phenomena involved in VIV makes modelling and analysis challenging. Therefore, the aim of the current research is to investigate the fundamental mechanisms causing the onset and sustenance of vortex-induced vibrations. To gain more understanding of the nature of vibrations, a methodology is established that distinguishes between different components of the forces at play. This approach allows for identifying how various force components impact the oscillation of a rigid body. The method is executed using the OpenFOAM open-source software. Numerical simulations are conducted on a two-dimensional smooth cylinder at both subcritical and supercritical Reynolds numbers to establish a correlation between wind turbine tower vibrations and the force mechanism. The analysis involves performing unsteady Reynolds-averaged Navier–Stokes (URANS) simulations using the modified pimpleFoam solver with the k–ω shear stress transport (SST) turbulence model. Both fixed and free-vibrating cases are studied for smooth cylinders. For the high-Reynolds-number cases, a setup matching the tower top segment of the IEA 15 MW reference wind turbine was chosen. Studying the flow around a cylinder at a subcritical Reynolds number reveals that the primary force involved is the vortex-induced force. The combined force due to viscosity, added mass, and vorticity contributes most to the overall force. For a freely vibrating cylinder with a single degree of freedom in the crossflow direction, the analysis indicates that the force component associated with the cylinder's motion is crucial and significantly affects the total force. Moreover, analysing the energy transfer between the fluid and the structure, a positive energy contribution by the vortex-induced force is observed on or before the dominant Strouhal velocity. This confirms observations at low Reynolds numbers in the literature that the vortex shedding predominantly contributes to the initiation of oscillations during VIV. The kinematic force contributes to the energy transfer of the system, but the mean energy transfer per cycle is negligible.

Abstract. Wake steering is an emerging wind power plant control strategy where upstream turbines are intentionally yawed out of perpendicular alignment with the incoming wind, thereby “steering” wakes away from downstream turbines. However, trade-offs between the gains in power production and fatigue loads induced by this control strategy are the subject of continuing investigation. In this study, we present a multifidelity multiobjective optimization approach for exploring the Pareto front of trade-offs between power and loading during wake steering. An unsteady large-eddy simulation is used as the high-fidelity model, where an actuator line representation is used to model wind turbine blades, and a rainflow-counting algorithm is used to compute damage equivalent loads. A coarser simulation with a simpler loads model is employed as a supplementary low-fidelity model. A multifidelity Bayesian optimization is performed to iteratively learn both a surrogate of the low-fidelity model and an additive discrepancy function, which maps the low-fidelity model to the high-fidelity model. Each optimization uses the expected hypervolume improvement acquisition function, weighted by the total cost of a proposed model evaluation in the multifidelity case. The multifidelity approach is able to capture the logit function shape of the Pareto frontier at a computational cost that is only 30 % of the single fidelity approach. Additionally, we provide physical insights into the vortical structures in the wake that contribute to the Pareto front shape.

Abstract. Wake steering is an emerging wind power plant control strategy where upstream turbines are intentionally yawed out of perpendicular alignment with the incoming wind, thereby “steering” wakes away from downstream turbines. However, trade-offs between the gains in power production and fatigue loads induced by this control strategy are the subject of continuing investigation. In this study, we present a multifidelity multiobjective optimization approach for exploring the Pareto front of trade-offs between power and loading during wake steering. An unsteady large-eddy simulation is used as the high-fidelity model, where an actuator line representation is used to model wind turbine blades, and a rainflow-counting algorithm is used to compute damage equivalent loads. A coarser simulation with a simpler loads model is employed as a supplementary low-fidelity model. A multifidelity Bayesian optimization is performed to iteratively learn both a surrogate of the low-fidelity model and an additive discrepancy function, which maps the low-fidelity model to the high-fidelity model. Each optimization uses the expected hypervolume improvement acquisition function, weighted by the total cost of a proposed model evaluation in the multifidelity case. The multifidelity approach is able to capture the logit function shape of the Pareto frontier at a computational cost that is only 30 % of the single fidelity approach. Additionally, we provide physical insights into the vortical structures in the wake that contribute to the Pareto front shape.

Abstract. This paper presents a comparison study of the simplified model QuLAF (Quick Load Analysis of Floating wind turbines), and a FAST model of the DTU 10MW Reference Wind Turbine mounted on the LIFES50+ OO-Star Wind Floater Semi 10MW floating substructure. The purpose is to investigate how accurate results can be obtained from this simplified model for different load cases. The two models are briefly presented and the limitations of QuLAF are discussed. These are (A) an under-prediction of the wave excitation loads for large sea states; (B) a simplified representation of the rotor-induced forcing and damping; (C) an over-predicted aerodynamic damping for the tower mode motion and (D) restriction to planar motion. All the limitations are linked to approximations applied for achieving the substantial model speed up relative to the state-of-the-art model. The comparative study is based on the planar version of design load cases (DLC) 1.2, 1.3, 1.6, 2.1 and 6.1 and the overall analysis shows that the simplified model is generally very good at estimating the bending moment at the tower base and the floater motions in heave and pitch. The largest tower-base bending moments are slightly over-predicted, but it is observed that while stronger wind leads to an over-prediction, stronger waves lead to an under-prediction. Thus in DLC 1.6, where the largest load was obtained at 10.3 m/s, a perfect match in tower base bending moments between the two models is found. The nacelle acceleration, however, is generally under-predicted, which is likely due to an over-prediction of the aerodynamic damping on the tower mode. Furthermore the floater response in large sea states is influenced by the omission of viscous hydrodynamic drag forcing, which leads to an under-prediction of the wave excitation loads. A further investigation of the model limitations confirms these findings with respect to the tower mode damping and viscous drag loads, while the simplified approach to rotor-induced loads is found to provide remarkable accurate forcing results. Although a full design load basis evaluation with a state-of-the-art model must be carried out for the final design, the present results show the potential of applying the QuLAF model in the preliminary design phase.

Abstract. This paper presents a comparison study of the simplified model QuLAF (Quick Load Analysis of Floating wind turbines), and a FAST model of the DTU 10MW Reference Wind Turbine mounted on the LIFES50+ OO-Star Wind Floater Semi 10MW floating substructure. The purpose is to investigate how accurate results can be obtained from this simplified model for different load cases. The two models are briefly presented and the limitations of QuLAF are discussed. These are (A) an under-prediction of the wave excitation loads for large sea states; (B) a simplified representation of the rotor-induced forcing and damping; (C) an over-predicted aerodynamic damping for the tower mode motion and (D) restriction to planar motion. All the limitations are linked to approximations applied for achieving the substantial model speed up relative to the state-of-the-art model. The comparative study is based on the planar version of design load cases (DLC) 1.2, 1.3, 1.6, 2.1 and 6.1 and the overall analysis shows that the simplified model is generally very good at estimating the bending moment at the tower base and the floater motions in heave and pitch. The largest tower-base bending moments are slightly over-predicted, but it is observed that while stronger wind leads to an over-prediction, stronger waves lead to an under-prediction. Thus in DLC 1.6, where the largest load was obtained at 10.3 m/s, a perfect match in tower base bending moments between the two models is found. The nacelle acceleration, however, is generally under-predicted, which is likely due to an over-prediction of the aerodynamic damping on the tower mode. Furthermore the floater response in large sea states is influenced by the omission of viscous hydrodynamic drag forcing, which leads to an under-prediction of the wave excitation loads. A further investigation of the model limitations confirms these findings with respect to the tower mode damping and viscous drag loads, while the simplified approach to rotor-induced loads is found to provide remarkable accurate forcing results. Although a full design load basis evaluation with a state-of-the-art model must be carried out for the final design, the present results show the potential of applying the QuLAF model in the preliminary design phase.

Abstract. The flexible-membrane kite employed by some airborne wind energy systems uses a suspended control unit, which experiences a characteristic swinging motion relative to the top of the kite during sharp turning manoeuvres. This paper assesses the accuracy of a two-point kite model in resolving this swinging motion using two different approaches: approximating the motion as a transition through steady-rotation states and solving the motion dynamically. The kite is modelled with two rigidly linked point masses representing the control unit and wing, which conveniently extend a discretised tether model. The tether-kite motion is solved by prescribing the trajectory of the wing point mass to replicate a figure-eight manoeuvre from the flight data of an existing prototype. The computed pitch and roll of the kite are compared against the attitude measurements of two sensors mounted to the wing. The two approaches compute similar pitch and roll angles during the straight sections of the figure-eight manoeuvre and match measurements within 3°. However, during the turns, the dynamically solved pitch and roll angles show systematic differences compared to the steady-rotation solution. As a two-point kite model resolves the roll, the lift force may tilt along with the kite, which is identified as the driving mechanism for turning flexible kites. Moreover, the two-point kite model complements the aerodynamic model as it allows for computing the angle of attack of the wing by resolving the pitch. These characteristics improve the generalisation of the kite model compared to a single-point model with little additional computational effort.