Pitch Degrees Of Freedom Research Articles

Quantifying the impact of modeling fidelity on different substructure concepts for floating offshore wind turbines – Part 1: Validation of the hydrodynamic module QBlade-Ocean

Abstract. To realize the projected increase in worldwide demand for floating offshore wind, numerical simulation tools must capture the relevant physics with a high level of detail while being numerically efficient. This allows engineers to have better designs based on more accurate predictions of the design driving loads, potentially enabling an economic breakthrough. The existing generation of offshore wind turbines is reaching a juncture, where traditional approaches, such as the blade element momentum theory, are becoming inadequate due to the increasing occurrence of substantial blade deflections. QBlade is a tool that includes a higher-fidelity aerodynamic model based on lifting-line theory, capable of accurately modeling such scenarios. In order to enable the simulation of offshore conditions in QBlade and to make use of this aerodynamic capability for novel offshore wind turbine designs, a hydrodynamic module called QBlade-Ocean was developed. In the present work, this module is validated and verified with two experimental campaigns and two state-of-the-art simulation frameworks on three distinct floating offshore wind turbine concepts. The results confirm the implementation work and fully verify QBlade as a tool to be applied in offshore wind turbine simulations. Moreover, a method aimed to improve the prediction of non-linear motions and loads under irregular wave excitation is analyzed in various conditions. This method results in a significant improvement in the surge and pitch degrees of freedom in irregular wave cases. Once wind loads are included, the method remains accurate in the pitch degree of freedom, while the improvements in the surge degree of freedom are reduced. A code-to-code comparison with the industry-designed Hexafloat concept highlights the coupled interactions on floating turbines that can lead to large differences in motion and load responses in otherwise identically behaving simulation frameworks.

The nonlinear effects of spinning on the dynamics of a pitching cantilever

We investigate the structural dynamics of a pitching cantilever as it spins about a fixed axis, emulating the motion of the rotor blades of wind turbines or rotorcraft to some extent. From first principles, we derive a system of equations consisting of a nonlinear partial differential equation (PDE) coupled with a nonlinear ordinary differential equation (ODE) that describes the motion of the system in bending and pitch as it spins according to a prescribed rotor velocity and acceleration. The equations of motion consider the interaction between dynamics of a flexible body in bending, rigid body motion in pitch, and the nonlinear effects of spinning, concurrently. This simplified model of a rotor blade permits an intuitive understanding of the various nonlinear terms that arise in the equations of motion, and their relative influence on the system dynamics. In a series of numerical experiments, we study the effects of the coupling between the bending and pitch degrees of freedom, the influence of rotor velocity, and rotor acceleration on the system dynamics. We compare the full nonlinear simulation results to those of the underlying linear system, obtained by imposing a small angle assumption in pitch and excluding all remaining nonlinear terms. The numerical experiments are performed by non-dimensionalizing the equations, discretizing the non-dimensionalized equations in space by applying the Galerkin method, discretizing the resulting system of ODEs in time using the Houbolt method and finally solving the resulting system of implicit algebraic equations using Newton’s method.

A reduced-order multi-body model with electromechanical-aeroelastic coupling for mechanism-free ornithopters

Piezoelectric material-actuated so-called solid-state (i.e., mechanism-free) ornithopters do not need conventional motors and mechanisms, potentially saving weight and energy consumption, reducing mechanical complexity, and improving wing flexibility. In solid-state ornithopters, wing flapping can be achieved by surface-mounted piezoelectric actuators. The design of a solid-state ornithopter is a complex multi-disciplinary task, and optimization of wing topology, actuator placement, and excitation parameters requires a computationally efficient model to predict its dynamic response and performance metrics. In this paper, effectively, a novel flight simulation model is presented based on a reduced-order lumped parameter multi-body model coupled with a vortex lattice program. The proposed lumped parameter model can be represented by an equivalent multi-body mechanical model or a circuit model. The coupling considered in the lumped parameter model includes: (1) the body-wing momentum interaction, (2) bend–twist​ coupling of the piezocomposite wings, (3) fluid–structure interactions between the flapping wings, oscillating body, and the ambient fluid, and (4) electromechanical coupling between a resistive–inductive–capacitive driving circuit and the piezocomposite wings. The wing motion is described using the Rayleigh–Ritz method, in which the representative wing modes are identified as spanwise plunge, chordwise curvature, and twist. The body-wing interaction is modeled using Hamilton’s principle. The fluid-induced effects on the wings have three contributions: added mass and damping, quasi-steady aerodynamic forces obtained using the vortex lattice program, and unsteady aerodynamic forces calculated using the Theodorsen formulation, which is integrated into the wing heave and pitch degrees of freedom in the lumped parameter model. The proposed reduced-order model proposed is computationally efficient, suitable for trade studies and multi-disciplinary design optimization, and can be easily converted to state representation for controller development purposes. The capabilities of this model are demonstrated through tethered and gliding flight simulations. System properties such as circuit parameters, structural parameters, excitation frequency ratio, etc., are investigated. Phugoid and short period modes are observed in gliding flight simulations. The contribution of active flapping is found by the comparison of flight simulations with and without active flapping. A net thrust contributed by unsteady lift is demonstrated even though the thrust-lift ratio is low. The proposed model serves as an extensible framework for modeling and design optimization of ornithopters.

PIV investigations of shock-buffet dynamics on a supercritical airfoil with a pitching degree of freedom

The interaction between the transonic flow around a spring mounted OAT15A airfoil model and the resulting pitching motion of the model was investigated with the goal of understanding the dynamics of the occurring phenomena. The experiments were performed at free-stream Mach numbers from 0.70 to 0.77 and at a Reynolds number of Rec ≈ 3 × 10^6. The dominant structural frequency of the airfoil’s pitch motion was adjusted to be in the range of the natural buffet frequency of the flow with inhibited pitching motion of the model. The variation of the Mach number allowed for an investigation in the pre-buffet, buffet and post-buffet regime. A periodic pitch motion with an amplitude of the angle of attack of up to ±1.17° was observed for buffeting flow conditions while it was significantly less in pre-buffet and post-buffet conditions. Velocity field measurements by means of high repetition rate particle image velocimetry (PIV) were used to capture the motion of the shock and to determine the state of the boundary layer flow for the different phases of the model motion. For the Mach number range Ma = 0.72 − 0.75 the change of the angle of attack and the shock position correlate strongly with each other. From the measurements, the delay of both quantities during the coupled motion could be determined.

Aeroelastic analysis and nonlinear characterization of three-degree-of-freedom systems with discontinuous nonlinearities

The effects of freeplay, multi-segmented, and impact nonlinearities in the pitch and control surface degrees of freedom on the nonlinear responses of a three-degree of freedom aeroelastic system are investigated to characterize the nonlinear behavior and possible bifurcations. The system consists of a plunging and pitching rigid airfoil supported by a linear spring in the plunge degree of freedom, a nonlinear torsional spring in the pitch degree of freedom, and a control surface with a nonlinear spring in the trailing edge. The unsteady representation based on the Duhamel formulation is used to model the aerodynamic loads. Nonlinear characterization is performed to identify the system’s response, under different representations of the nonlinear springs, below the linear flutter speed. The results show that grazing/sliding bifurcations are present and nonlinear coupling of the system’s frequencies lead to complex responses including sudden transitions between harmonic and chaotic responses as the freestream velocity is increased. These responses, which include the sudden amplitude jumps, generation of higher harmonics and broadband oscillatory behavior, could result in catastrophic structural failures of aeroelastic systems even when operating below the linear flutter speed.

Estimating Flutter Bifurcation Diagrams Using the State Velocity

This paper introduces a method for estimating flutter bifurcation diagrams of systems described by time-domain state-space models. The method estimates the bifurcation diagram by quantifying changes in the recovery rate in the preflutter regime. The recovery rate is approximated from the state velocity, overcoming the need for transient output data in existing methods that use this quantity. Demonstration examples involve an analytical system and a typical section with smooth nonlinearities in the pitch degree of freedom. The proposed method captures the bifurcation type and the amplitude trend of the bifurcation diagram without transient or iterative calculations, and with no assumed knowledge of the postflutter dynamics. These features ease applications that involve flutter bifurcation analyses for many parameter choices and in automated processes, from design space exploration to optimization.

Shock-buffet analysis on a supercritical airfoil with a pitching degree of freedom

The interaction between the transonic flow around a spring mounted OAT15A airfoil model and the resulting pitching motion of the model were investigated with the goal of understanding the dynamics of the occurring phenomena. The experiments were performed at a free-stream Mach number of 0.74, a Reynolds number of mathrm{Re}_mathrm {c}=3.1times 10^6, and a mean angle of attack of 5.8^circ. A periodic pitch motion with an amplitude of the angle of attack of pm ,0.9^circ was observed for these flow conditions. The dominant structural frequency of the airfoil’s pitch motion was adjusted to be in the range of the natural buffet frequency of the flow with inhibited pitching motion of the model. The structural motion locks into the frequency of the shock buffet with the pitching degree of freedom at a dominant frequency of 115.5 Hz. Velocity field measurements by means of high repetition rate particle image velocimetry (PIV) were used to capture the motion of the shock and to determine the state of the boundary layer flow for the different phases of the model motion. The PIV results with high temporal resolution allow the detailed observation of the evolution of the different phases of the buffet cycle. Mean values and statistical quantities, spectra and space-time correlations were determined from the measurement data to analyze the flow effects. It was possible to estimate the convection velocity of turbulent structures in the detached boundary layer.Graphical abstract

On the importance of nonlinear hydrodynamics and resonance frequencies on power production in multi-mode WECs

Multi-mode Wave Energy Converters (WECs) are able to harvest energy from multiple Degrees-of-Freedom (DOFs) simultaneously, which increases the power that can be absorbed from the incident wave compared to single-DOF WECs. However, nonlinear coupling between hydrodynamic modes, which occurs when the WEC oscillates simultaneously in multiple directions, means that simply applying the typical control strategies used for single-DOF WECs can lead to sub-optimal performance. This study investigates the multi-DOF dynamic control of a submerged, flat cylindrical WEC subjected to hydrodynamic coupling effects modelled under the weakly nonlinear potential flow theory based on the weak-scatterer approximation. Results show that, at low incident wave frequencies, tuning the surge, heave and pitch modes of the WEC to the same natural frequency can result in power losses of up to 30% in the weakly nonlinear model compared to results obtained from a fully linear model. These discrepancies are attributed to the pitching motions of the WEC, which changes the projected surface area of the device relative to the equilibrium position and hence violates the assumptions of the linear theory. From these findings, a suggested design strategy where the surge, heave and pitch DOFs were all decoupled and tuned to different natural frequencies was therefore proposed. In the presence of weakly nonlinear hydrodynamic coupling, it was found that this design may result in significant improvements in power absorbed for the multi-mode WEC, compared to a case where all DOFs are simply tuned to match the peak frequency of a given sea state.

Effects of soft marine fouling on wave-induced forces in floating aquaculture cages: Physical model testing under regular waves

Previous experiments on the fouling/current and fouling/wave interactions were mostly limited to two dimensional (2D) net panels or isolated twines. The current paper deals with the wave-induced forces/moments in three dimensional (3D) physical models of a gravity net-cage. The colonial hydroid Ectopleura larynx, a common fouling organism in the aquaculture industry, was artificially modelled and considered in the current experiments. A clean cage and cages with different fouling lengths were tested under deep-water regular wave trains. The time series of the wave-induced forces/moments in the surge, sway, roll and pitch degrees of freedom were recorded and analysed. The experimental results showed that the surge force amplitude increased up to 72% by the fouling, but the sway force amplitude decreased up to 26%. The asymmetry of the surge and sway force waveforms increased by the fouling, respectively. The effects of the fouling on the force/moment response amplitude operators (RAO) were also studied. Pixel histogram analysis was performed to define equivalent net solidities of the fouled nets. In general, the tests under regular waves were found to underestimate the soft fouling effects on the wave-induced forces/moments, as compared to those carried out under irregular waves.

Coupled Mode Flutter of a Linear Compressor Cascade in Subsonic and Transonic Flow Conditions

Flutter onset in turbomachinery is typically investigated numerically via decoupled methods due to a high mass ratio of structure to air. The unsteady aerodynamic response of a forced motion vibration is evaluated for a positive or negative work entry. The forced motion simulations assume vacuum mode shape vibrations at certain amplitudes without modal coupling due to aerodynamic forces. This approach, also known as the energy method, is valid for a high blade mass ratio and small logarithmic decrement values. An aeroelastic study of a multi-passage linear compressor cascade was performed. In fluid-structure-coupled time-marching CFD, generic heave and pitch degrees of freedom are allowed to vibrate freely in reaction to any aerodynamic forces. For one subsonic and one transonic flow condition predicted to be stable by the classical energy method approach, aerodynamically coupled-mode flutter is observed. It is shown that variations in the starting conditions, i.e. the initial vibration and inter-blade phase angle of the system, can have a strong influence on the number of CFD iterations required until amplitudes grow. However, if coupled-mode flutter is present in the system, it will ultimately set in at a distinct inter-blade phase angle.

Fuzzy control of nonlinear aeroelastic system based on neural network identification

This article presents a fuzzy control method for the limit cycle oscillation (LCO) suppression of nonlinear aeroelastic systems based on the neural network identification algorithm. A prototypical 2D wing section with a single control surface at the trailing edge of the main wing, which contains a symmetrical free play nonlinearity in the pitch degree of freedom, is modeled to illustrate the proposed method. A neural network is used to identify the fuzzy control rules from the existing LCO suppression input and output data. A new fuzzy control rate of the nonlinear aeroelastic system is obtained by adjusting the parameters of the fuzzy control surface. Numerical simulations are conducted to verify the effectiveness of the proposed method.

Adaptive fuzzy control of nonlinear aeroelastic system with measurement noise

This paper presents a limit cycle oscillation (LCO) suppression method of nonlinear aeroelastic system based on adaptive neuro-fuzzy control. A prototypical 2D wing section with a single control surface at the trailing edge of the main wing, which contains a symmetrical freeplay nonlinearity in the pitch degree of freedom, is modelled by SIMULINK (Matlab 2016R) to illustrate the proposed method. Proportional integral differential (PID) controller is used to suppression the LCO of nonlinear aeroelastic system. The control law of the PID controller is identified by neural network. A new fuzzy control law of the nonlinear aeroelastic system is obtained by adjusting the parameters of the fuzzy control system. A nonlinear aeroelastic system with measurement noise in the measurement feedback loop is conducted to verify the effectiveness of the proposed method.

Integrated study of triboelectric nanogenerator for ocean wave energy harvesting: Performance assessment in realistic sea conditions

Ocean related activities are often supported by offshore equipment with particular power demands. These are usually deployed at remote locations and have limited space, thus small energy harvesting technologies, such as photovoltaic panels or wind turbines, are used to power their instruments. However, the inherent energy sources are intermittent and have lower density and predictability than an alternative source: wave energy. Here, we propose and critically assess triboelectric nanogenerators (TENGs) as a promising technology for integration into wave buoys. Three TENGs based on rolling-spheres were developed and their performance compared in both a “dry” bench testing system under rotating motions, and in a large-scale wave basin under realistic sea-states installed within a scaled navigation buoy. Both experiments show that the electrical outputs of these TENGs increase with decreasing wave periods and increasing wave amplitudes. However, the wave basin tests clearly demonstrated a significant dependency of the electrical outputs on the pitch degree of freedom and the need to take into account the full dynamics of the buoy, and not only that of TENGs, when subjected to the excitations of waves. This work opens new horizons and strategies to apply TENGs in marine applications, considering realistic hydrodynamic behaviors of floating bodies. • Three rolling-sphere-based TENGs were implemented inside of a rescaled-buoy. • The electrical outputs of TENGs depend on the wave periods and wave amplitudes. • Wave basin tests showed a dependency of the electrical outputs on the pitch degree of freedom. • UL-TENG was the most efficient to harvest wave energy under realistic conditions.

Spatially localized vibrations in a rotor subjected to flutter

The current push toward lightweight structures in aerospace and aeronautical engineering is leading to slender design airfoils, which are more likely to undergo large deformation, hence experiencing geometrical nonlinearities. The problem of vibration localization in a rotor constituted by N coupled airfoils with plunge and pitch degrees of freedom subjected to flutter instability is considered. For a single airfoil, it is shown that depending on the system parameters, multiple static and dynamic equilibria coexist which may be a fixed point, a limit cycle, or irregular motion. By elastically coupling N airfoils, a simplified rotor model is obtained. The nonlinear dynamical response of the rotor is studied via time integration with particular attention to the emergence of localized vibrating solutions, which have been classified introducing a localization coefficient. Finally, the concept of basin stability is exploited to ascertain the likelihood of the system to converge to a certain localized state as a function of the airstream velocity. We found that homogeneous and slightly localized states are more likely to appear with respect to strongly localized states.

Investigating amplitude death in a coupled nonlinear aeroelastic system

Coupling nonlinear dynamical systems can lead to a host of phenomena, one of which leads to the complete cessation of their oscillations. This phenomenon is referred to as amplitude death (AD) in the dynamical systems literature. Recently, there is a growing interest to mitigate oscillatory or dynamic instabilities in a variety of engineering systems using AD. Deriving impetus from the same, we investigate the possibility of cessation of oscillatory instabilities in aeroelastic systems using the concept of AD. In specific, the suppression of flutter instability that arises in aeroelastic systems due to highly nonlinear fluid–structure interactions is investigated from the purview of AD. To that end, we consider two identical airfoils that are exposed to input fluid forces along the axial directions. The airfoils, via translational and rotational springs, are allowed to oscillate in plunge and pitch degrees of freedom. To augment the findings to in-field scenarios, we consider the individual cases of the input flow to be either uniform (deterministic) or possess randomly time varying components, respectively. To promote coupled interactions, the airfoils are coupled using a linear torsional spring. The coupled interaction of the airfoils at the flutter regime are then studied by obtaining the pitch and plunge responses. Further, the strength of the coupling and the time delay between the airfoils are systematically varied to investigate its effect on the regime of AD. The ability of AD to suppress flutter instability and thereby serve as a possible flutter suppression mechanism in both deterministic and stochastic input flow cases is then demonstrated. Finally, the phase delay values between the airfoils is computed to heuristically present a relationship between the coupling parameters and the post coupling signatures.

Nonlinear Dynamic and Kinematic Model of a Spar-Buoy: Parametric Resonance and Yaw Numerical Instability

Mathematical models are essential for the design and control of offshore systems, to simulate the fluid–structure interactions and predict the motions and the structural loads. In the development and derivation of the models, simplifying assumptions are normally required, usually implying linear kinematics and hydrodynamics. However, while the assumption of linear, small amplitude motion fits traditional offshore problems, in normal operational conditions (it is desirable to stabilize ships, boats, and offshore platforms), large motion and potential dynamic instability may arise (e.g., harsh sea conditions). Furthermore, such nonlinearities are particularly evident in wave energy converters, as large motions are expected (and desired) to enhance power extraction. The inadequacy of linear models has led to an increasing number of publications and codes implementing nonlinear hydrodynamics. However, nonlinear kinematics has received very little attention, as few models yet consider six degrees of freedom and large rotations. This paper implements a nonlinear hydrodynamic and kinematic model for an archetypal floating structure, commonplace in offshore applications: an axisymmetric spar-buoy. The influence of nonlinear dynamics and kinematics causing coupling between modes of motion are demonstrated. The nonlinear dynamics are shown to cause parametric resonance in the roll and pitch degrees of freedom, while the nonlinear kinematics are shown to potentially cause numerical instability in the yaw degree of freedom. A case study example is presented to highlight the nonlinear dynamic and kinematic effects, and the importance of including a nominal restoring term in the yaw DoF presented.

Response of triceratops to impact forces: numerical investigations

Triceratops is one of the new generations of offshore compliant platforms suitable for ultra-deepwater applications. Apart from environmental loads, the offshore structures are also susceptible to accidental loads. Due to the increase in the risk of collision between ships and offshore platforms, the accurate prediction of structural response under impact loads becomes necessary. This paper presents the numerical investigations of the impact response of the buoyant leg of triceratops usually designed as an orthogonally stiffened cylindrical shell with stringers and ring frames. The impact analysis of buoyant leg with a rectangularly shaped indenter is carried out using ANSYS explicit analysis solver under different impact load cases. The results show that the shell deformation increases with the increase in impact load, and the ring stiffeners hinder the shell damage from spreading in the longitudinal direction. The response of triceratops is then obtained through hydrodynamic response analysis carried out using ANSYS AQWA. From the results, it is observed that the impact load on single buoyant leg causes periodic vibration in the deck in the surge and pitch degrees of freedom. Since the impact response of the structure is highly affected by the geometric and material properties, numerical studies are also carried out by varying the strain rate, and the location of the indenter and the results are discussed.

Investigation of TLP's hydrodynamic response with different tendon connection angles

ABSTRACT This paper aims to investigate the hydrodynamic behavior of a tension leg platform (TLP) when the tendon connection angles are varied at 90°, 70°, 50°, and 30°. Three different types of loading conditions are applied to the TLP. Conditions include 100-year hurricane storm period, regular waves and no loading. The TLP displayed major response in the pitch degree of freedom. A maximum reduction of 14% in pitch rotation is achieved when 100-year hurricane storm conditions are applied to the TLP. This occurred in 0° loadings at 30° tendon connection angle as compared to 90° tendon connection angle. Reduction in pitch rotation is also achieved in the regular wave loadings. A maximum of 9% in pitch rotation is achieved during 0° wave loading at 30° tendon connection angle as compared to 90°. When the tendon connection angle is reduced from 90° to 30°, the natural frequency of the TLP increased both in pitch and yaw degrees of freedom by 2.55% and 2.40%, respectively.

On intermediate-scale open-sea experiments on floating offshore structures: Feasibility and application on a spar support for offshore wind turbines

Experimental investigation of floating structures represents the most direct way for achieving their dynamic identification and it is particularly valuable for relatively new concepts, such as floating supports for offshore wind turbines, in order to fully understand their dynamic behaviour. Traditional experimental campaigns on floating structures are carried out at small scale, in indoor laboratories, equipped with wave and wind generation facilities. This article presents the results of an open-sea experimental activity on a 1:30 scale model of the OC3-Hywind spar, in parked rotor conditions, carried out at the Natural Ocean Engineering Laboratory (NOEL) of Reggio Calabria (Italy). The aim of the experiment is two-fold. Firstly, it aims to assess the feasibility of low-cost, intermediate-scale, open-sea activities on offshore structures, which are proposed to substitute or complement the traditional indoor activities in ocean basins. Secondly, it provides useful experimental data on damping properties of spar support structures for offshore wind turbines, with respect to heave, roll and pitch degrees of freedom. It is proven that the proposed approach may overcome some limitations of traditional small-scale activities, namely high costs and small scale, and allows to enhance the fidelity of the experimental data currently available in literature for spar floating supports for offshore wind turbines.

Nonlinear modes of large-amplitude ship motion with roll-pitch coupling

This research pertains to the dynamics of a ship taking into account the nonlinear coupling of roll and pitch degrees of freedom. Such nonlinearity has critical implications for large-amplitude ship motion, and can thus be useful in understanding conditions leading to capsize. The nonlinear normal modes of the conservative system are determined numerically and are displayed in a frequency-energy plot, which clarifies the bifurcations that connect the various branches of periodic orbits. Numerical simulations show that, although the solutions on most branches result in capsize if their energy is beyond a common critical value, a few branches contain stable solutions at higher energies that do not lead to capsize, suggesting possible methods of capsize mitigation. We study a class of solutions analytically using a complexification-averaging technique. Finally, we run a simulation in the case of light damping in roll with high-energy initial conditions, illustrating transitions between branches that occur in the direction of decreasing energy on the frequency-energy plot.