Narakorn Srinil

Characterization of Variable Hydrodynamic Coefficients and Maximum Responses in Two-Dimensional Vortex-Induced Vibrations With Dual Resonances

A phenomenological model and analytical-numerical approach to systematically characterize variable hydrodynamic coefficients and maximum achievable responses in two-dimensional vortex-induced vibrations with dual two-to-one resonances are presented. The model is based on double Duffing and van der Pol oscillators which simulate a flexibly-mounted circular cylinder subjected to uniform flow and oscillating in simultaneous cross-flow/in-line directions. Depending on system quadratic and cubic nonlinearities, amplitudes, oscillation frequencies and phase relationships, analytical closed-form expressions are derived to parametrically evaluate key hydrodynamic coefficients governing the fluid excitation, inertia and added mass force components, as well as maximum dual-resonant responses. The amplification of the mean drag is ascertained. Qualitative validations of numerical predictions with experimental comparisons are discussed. Parametric investigations are performed to highlight the important effects of system nonlinearities, mass, damping and natural frequency ratios.

Nonlinear Hybrid-Mode Resonant Forced Oscillations of Sagged Inclined Cables at Avoidances

We investigate non-linear forced oscillations of sagged inclined cables under planar 1:1 internal resonance at avoidance. To account for frequency avoidance phenomena and associated hybrid modes actually distinguishing inclined cables from horizontal cables, asymmetric inclined static configurations are considered. Emphasis is placed on highlighting nearly tuned 1:1 resonant interactions involving coupled hybrid modes. The inclined cable is subjected to a uniformly distributed vertical harmonic excitation at primary resonance of a high-frequency mode. Approximate non-linear partial-differential equations of motion, capturing overall displacement coupling and dynamic extensibility effect, are analytically solved based on a multi-mode discretization and a second-order multiple scales approach. Bifurcation analyses of both equilibrium and dynamic solutions are carried out via a continuation technique, highlighting the influence of system parameters on internally resonant forced dynamics of avoidance cables. Direct numerical integrations of modulation equations are also performed to validate the continuation prediction and characterize non-linear coupled dynamics in post-bifurcation states. Depending on the elasto-geometric (cable sag and inclination) and control parameters, and on assigned initial conditions, the hybrid modal interactions undergo several kinds of bifurcations and non-linear phenomena, along with meaningful transition from periodic to quasi-periodic and chaotic responses. Moreover, corresponding spatio-temporal distributions of cable non-linear dynamic displacement and tension are manifested.

EXPERIMENTAL INVESTIGATION OF THE VORTEX-INDUCED VIBRATION OF A CURVED CYLINDER

Experiments have been conducted in a water channel in order to investigate the vortex-induced vibration (VIV) response of a rigid section of a curved circular cylinder. Two curved configurations were tested regarding the direction of the approaching flow, a concave or a convex cylinder, in addition to a straight cylinder that served as reference. Amplitude and frequency response are presented versus reduced velocity for a wide Reynolds number range between 750 and 15,000. Trajectories in the cross-flow and streamwise direction are presented as well for several reduced velocities. Results show a distinct behaviour from the typical VIV of a straight cylinder highlighting the effect of curvature on vortex formation and excitation. The concave configuration presents relatively high amplitudes of vibration that are sustained beyond the typical synchronisation region. The mechanism behind the response is not yet clear, although authors suggest it might be related to some kind of buffeting excitation due to the disturbed flow from

WAKE-INDUCED TRANSVERSE VIBRATION OF TWO INTERFERING CYLINDERS IN TANDEM ARRANGEMENT: MODELLING AND ANALYSIS

A considerable number of numerical and experimental studies have been performed on the problem of vorte x induced vibration (VIV) of an isolated circular cylinder. A very few studies have considered a practical situation where cylinders are deployed in clusters. This study presents a mat hematical fluid-structure interaction modelling and analysis of two flexibly-mounted circular cylinders arranged in tan dem and subject to fluid cross flows. The hydrodynamic lift forces and their time variations are approximated by two diffe rent semiempirical wake oscillator models based on the van d er Pol and Rayleigh equations. These nonlinear wake oscillator s are coupled with linear structural oscillators through the acceleration and velocity coupling terms, respectiv ely. A direct numerical time integration approach is used to pred ict the response amplitude behaviors and parametrically inv estigate the vortex- and wake-induced vibration transverse r esponse of the two interfering upstream and downstream cylinders. Some empirical coefficients are calibrated against avail able, although very limited, computational fluid dynamics results. Preliminary parametric studies are conducted with the case of v arying reduced flow velocity, and some insightful aspects on the effect of mass and damping ratio are highlighted. Dependin g on system parameters, numerical prediction results bas ed on the van der Pol and Rayleigh equations are compared, and a combination of the two wake oscillators is suggeste d as a new model for predicting the vortex and wake-induced of the two interfering cylinders.

Cabling to connect offshore wind turbines to onshore facilities

This chapter presents a review of general aspects and practical challenges of subsea power cables for offshore wind farm applications. Interarray, interplatform and export cables are key components which require careful analysis and design in view of their mechanical properties, electrical voltages and installation methodologies. Some lifecycle cost savings related to offshore cables are discussed, including the use of higher-voltage cables, the layout optimization of interarray cables, the post-lay burial activities, the cable burial depth identifications and the J-tubeless interfaces. For offshore floating wind turbines and substations in deeper waters, the dynamic cable concepts are proposed along with discussion of some environmental impacts due to waves, currents and on-bottom dynamic stability. The outlook for offshore wind farm cables is provided, with a list of potential innovative cabling technologies of current industrial interest.

Dynamic response analysis of spar-type floating wind turbines and mooring lines with uncoupled vs coupled models

Offshore floating wind turbines (OFWT) are supported by the flexible mooring systems subjected to nonlinear hydrodynamic wave and current forces. Depending on the floater type and environmental condition, the mooring responses can have a significant impact on the overall dynamic performance of OFWT. To evaluate the dynamic responses of OFWT, both uncoupled (quasi-static) and coupled (dynamic) mooring models have been proposed in the literature and in practice based on the use of the well-known FAST software and the FAST-Orcaflex package, respectively. This paper will investigate and compare the dynamics of the OFWT and the mooring lines using uncoupled vs coupled models, based on the OC3-Hywind Spar platform supporting the 5MW wind turbines developed by the National Renewable Energy Laboratory. Preliminary numerical studies in several load cases reveal substantial differences in the OFWT and mooring dynamics obtained by the two approaches, e.g. under regular and irregular waves. The levels of differences are reported, and the comparisons with available experimental results are also made to validate the model analyses and outcomes. The importance of mooring line dynamics and their contributions to the overall 6-DOF responses of OFWT are highlighted which should be recognised in the analysis and optimization design.

Coupled Axial/Lateral VIV of Marine Risers in Sheared Currents

Modelling and prediction of vortex-induced vibrations (VIV) of marine risers is a challenging task due to the associated multi degrees of freedom in both cross-flow/in-line directions and the multi-mode fluid-structure interactions. In addition, the axial motion and its geometrically nonlinear coupling with lateral responses can be significant, especially at higher-order modes. Nevertheless, several papers in the literature dealing with VIV predictions have often overlooked such aspects. Therefore, this study aims to investigate and understand the effect of axial or longitudinal motion through a theoretical model and numerical approach in time domain. Attention is paid to VIV of vertical risers subjected to linearly sheared currents. To capture a three-dimensional aspect of the flexible cylinder experiencing VIV, a semiempirical model is developed consisting of nonlinear equations of cross-flow, in-line and axial structural oscillations which are coupled with the distributed van der Pol-type wakeoscillators modelling the fluctuating fluid lift/drag forces. The mean drag force is also taken into account. These model equations are numerically solved via a space-time finite difference scheme, and the obtained numerical results highlight several aspects of VIV of elastic cylinders along with the axial motion effects. Apart from the validation of the numerical model with published experimental results, this study reveals how the effect of axial motion and its nonlinear coupling with the two lateral cross-flow/in-line motions can be very important. These depend on the flow velocity, the fluid-structure parameters, the single or multi-mode lock-in condition, and the standing-wave or travelling-wave feature. We recommend that the axial response should be accounted for in VIV analysis and prediction model.

VORTEX INDUCED VIBRATION OF CIRCULAR CYLINDER WITH TWO DEGREES OF FREEDOM: COMPUTATIONAL FLUID DYNAMICS VS. REDUCED-ORDER MODELS

Computational fluid dynamics (CFD) studies capturing vortex-induced vibration (VIV) phenomena in a wide range of both the hydrodynamics and the structural parameters are important, because the analysis outcomes can be applied to numerical prediction codes, complement experimental measurement results and suggest a modification of some practical design guidelines. Nevertheless, in spite of many published studies on VIV, CFD studies for two dimensional coupled cross-flow/in-line VIV even with two degrees of freedom (2-DoF), are still quite limited. More CFD studies which can control the equivalence of system fluid-structure parameters in different directions with reduced uncertainty are needed to improve the numerical model empirical coefficients and capability to effectively match numerical predictions and experimental outcomes.This paper presents a CFD study on the 2-DoF VIV of elastically mounted circular cylinder with a low mass ratio (m* = 2.55). The Reynolds number is fixed to be 150 and the reduced flow velocity parameter is varied by changing the cross-flow natural frequency. To model the problem, two-dimensional Navier-Stokes equations coupled with linear structural equations in the in-line and cross-flow directions are solved. Particular attention is paid to the determination of maximum attainable amplitudes and the associated instantaneous lift and drag forces and hydrodynamic coefficients. These results are compared with the obtained results from alternative numerical prediction outcomes using new reduced-order models with four nonlinearly coupled wake-structure oscillators (Srinil and Zanganeh, 2012). Some qualitative and quantitative aspects are discussed. Overall, the important VIV characteristics are captured including the dual-resonance and figure-of-eight trajectories. Through the flow visualization study, it is found that as the dual-resonance is excited, a P+S wake pattern appears.Copyright

Resonant Non-Linear Dynamic Responses of Horizontal Cables via Kinematically Non-Condensed/Condensed Modeling

This paper focuses on a comparison of cable non-linear dynamic responses obtained with the kinematically non-condensed and condensed modeling. Planar non-linear interactions involving simultaneous primary external and internal resonance in horizontal suspended cables are analytically investigated. 1:1 or 2:1 internal resonance is considered. The governing partial-differential non-linear equations of motion of the non-condensed cable model account for the effects of dynamic extensibility, i.e., dynamic tension spatio-temporal variation, and capture the non-linear coupling and contributions of longitudinal/transversal modal displacements. On the contrary, in the condensed cable model, a single integro-partial-differential equation of motion is obtained by neglecting the longitudinal inertia according to a quasi-static stretching assumption of cable in motion. This entails linking the longitudinal displacement to the transversal one and considering a space-independent dynamic tension. This simplified model is typically considered in the literature involving cable nonlinear dynamics. Based on a multi-dimensional Galerkin-based discretization and a second-order multiple scales approach accounting for higher-order non-linear effects and resonant/non-resonant modal contributions, the ensuing dynamic responses and their stability are evaluated by means of force- and frequency-response diagrams with stability analyses. Moreover, the corresponding spacetime non-linear coupled configurations and dynamic tension distributions are analyzed. The numerical explorations highlight that, depending on cable elasto-geometric properties, internal resonance condition and system control parameters, the condensed model may lead to quantitative and/or qualitative discrepancies in the non-linear dynamic responses, with respect to the non-condensed model. The results allow us to point out such meaningful effects of disregarding the system longitudinal dynamics via the kinematic condensation procedure, and to identify cases where the parametric investigation has to be pursued with the more accurate non-condensed model.

Internally resonant nonlinear free vibrations of horizontal/inclined sagged cables

Internally resonant dynamics in the nonlinear free vibrations of suspended cables are analytically investigated by means of a multi-mode Galerkin-based discretization and second-order multiple scales. Emphasis is placed on planar 2:1 internal resonances. The equations of motion of a general inclined cable model, which account for the dynamic extensibility effects and the system asymmetry due to inclined equilibrium, are considered. By considering higher-order effects due to quadratic nonlinearities, approximate closed-form solutions of nonlinear amplitudes, frequencies and dynamic configurations associated with the resonant nonlinear normal modes reveal the dependence of cable nonlinear response on different resonant and non-resonant modes. Based on the modal convergence properties performed on the resonantly activated cables, the illustrative results provide hints for proper reduced-order model selections from the asymptotic solution. The underlying effects of cable inclination and cable sag are presented. The theoretical predictions are validated by finite difference numerical time laws of the original system equations of motion.Copyright