Krish Thiagarajan

An Investigation Into the Hydrodynamic Efficiency of an Oscillating Water Column

An oscillating water column device enables the conversion of wave energy into electrical energy via wave interaction with a semi-submerged chamber coupled with a turbine for power take off. This present work concentrates on the wave interaction with the semi-submerged chamber, whereby a shore based oscillating water column (OWC) is studied experimentally to examine energy efficiencies for power take-off. The wave environment considered comprises plane progressive waves of steepnesses ranging from kA=0.01 to 0.22 and water depth ratios varying from kh=0.30 to 3.72, where k, A, and h denote the wave number, wave amplitude, and water depth, respectively. The key feature of this experimental campaign is a focus on the influence of front wall geometry on the OWC’s performance. More specifically, this focus includes: front wall draught, thickness, and aperture shape of the submerged front wall. We make use of a two-dimensional inviscid theory for an OWC for comparative purposes and to explain trends noted in the experimental measurements. The work undertaken here has revealed a broad banded efficiency centered about the natural frequency of the OWC. The magnitude and shape of the efficiency curves are influenced by the geometry of the front wall. Typical peak magnitude resonant efficiencies are in the order of 70%.

Low KC flow regimes of oscillating sharp edges I. Vortex shedding observation

Abstract Viscous flow around an oscillating vertical cylinder with a disk attached at keel is studied in detail by direct numerical simulation based on finite difference method. Over the range of flow parameters investigated, viz. Keulegan–Carpenter number (KC) from 7.5×10 −4 to 0.75 and β =1.585×10 5 , three shedding modes were observed. These modes, named independent, interactive and uni-directional, are found to be governed by both flow parameters (KC, β ) and the geometry of the disk, such as aspect ratio, t d / D d . The mechanism for the initial condition dependence of the asymmetric uni-directional vortex shedding is analyzed. The effects of KC number and aspect ratio of the disk on the vortex shedding angle are also presented.

Low KC flow regimes of oscillating sharp edges. II. Hydrodynamic forces

Abstract Three vortex shedding modes, i.e. independent vortex shedding, interactive vortex shedding and uni-directional vortex shedding, for flow induced by oscillatory vertical cylinder witha disk attached at its keel were presented in Part I. The occurrence of these modes were shown to depend on the Keulegan–Carpenter ( KC ) number and disk thickness–diameter ratio. Associated with these distinct changes of vortex shedding patterns are distinct increases in the hydrodynamic damping. A quantitative method of identifying the vortex shedding flow regimes is proposed, and the scaling laws for heave damping estimation of cylinder+disk configuration are presented. A sample calculation on a classic Spar platform show that addition of a heave plate increased the heave damping fourfold.

Heave Response of Classic Spar With Variable Geometry

Spar platforms with cylindrical shape and constant cross-section area may experience resonant heave motions in sea states with long peak periods, which are probably excessive for riser integrity due to its low damping and relatively low natural heave period. Changes to hull shape and cross-section that produce more benign heave behavior were discussed by some researchers in the past. In this study, the viscous damping of spar structures is explicitly calculated, and incorporated to the potential solution. It is concluded that the heave resonant response can be considerably reduced by alternative hull shapes via increased damping mechanism and the natural heave period being kept outside the range of the wave energy.

Benchmarking of Truss Spar Vortex Induced Motions Derived From CFD With Experiments

Floating spar platforms are widely used in the Gulf of Mexico for oil production. The spar is a bluff, vertical cylinder which is subject to Vortex Induced Motions (VIM) when current velocities exceed a few knots. All spars to date have been constructed with helical strakes to mitigate VIM in order to reduce the loads on the risers and moorings. Model tests have indicated that the effectiveness of these strakes is influenced greatly by details of their design, by appurtenances placed on the outside of the hull and by current direction. At this time there is limited full scale data to validate the model test results and little understanding of the mechanisms at work in strake performance. The authors have been investigating the use of CFD as a means for predicting full scale VIM performance and for facilitating the design of spars for reduced VIM. This paper reports on the results of a study to benchmark the CFD results for a truss spar with a set of model experiments carried out in a towing tank. The focus is on the effect of current direction, reduced velocity and strake pitch on the VIM response. The tests were carried out on a 1:40 scale model of an actual truss spar design, and all computations were carried out at model scale. Future study will consider the effect of external appurtenances on the hull and scale-up to full scale Reynolds’ numbers on the results.Copyright

Influence of Heave Plate Geometry on the Heave Response of Classic Spars

A production spar designed for West African (WA) offshore conditions must consider possible resonance with long period swell, which might result in large amplitude heave oscillations. Preliminary study of a classic spar with diameter of 39 m (128 ft) and draft 198 m (650 ft) for a WA application led the authors to believe that excessive heave response of 5.2 m (17 ft) may occur at the natural period of 28 seconds. This led the team to investigate the possibility of adding a heave plate (circular disk) at the base of the spar to control the response to within 3.1 m (10 ft), which is the limit set by a typical compensation system. Important design issues arose with regards to the geometry of the plate, i.e. diameter and thickness. Numerical simulations and model testing were used to identify the influence of a heave plate on the heave response of the spar. Heave response for various diameters and thickness were investigated. Comparison of added mass and damping values were found to be in reasonable agreement. Issues such as effect of a centerwell and moorings, plate cutouts for ease of transportation were also investigated. Discussion of the experimental results and comparison with numerical simulations are presented in this paper, and some recommendations are made on optimum heave plate geometry.© 2002 ASME

On the parametric dependence of springing damping of TLP and Spar columns

Abstract The non-linear viscous damping forces on a Tension Leg Platform (TLP) column experiencing “springing” vibration are calculated by directly solving the Navier–Stokes equations. Different characteristics of heave damping have been found in two different regimes in the ranges of Keulegan–Carpenter (KC) from 0.001 to 1.0 and β from 89 236 to 435 298. At very low KC, the heave damping force tends to be approximately linear with the velocity, whereas a definite non-linear dependence on the velocity has been found as KC increases. It is found that the laminar boundary layer theory based on the infinite length circular cylinder assumption is still suitable to the friction drag estimation at very low KC, but the leading edge effect is not negligible as KC approaches 2π/(D/Td) (D=diameter of the cylinder, and Td=the draft of the cylinder). From the present numerical estimation, one can conclude that a uniform scaling law cannot be applied, and the scaling laws for the heave damping estimation of a TLP column in two different regimes have been presented.

Performance Specifications for Real-Time Hybrid Testing of 1:50-Scale Floating Wind Turbine Models

This paper presents performance requirements for a real-time hybrid testing system to be suitable for scale-model floating wind turbine experiments. In the wave basin, real-time hybrid testing could be used to replace the model wind turbine with an actuation mechanism, driven by a wind turbine simulation running in parallel with, and reacting to, the experiment. The actuation mechanism, attached to the floating platform, would provide the full range of forces normally provided by the model wind turbine. This arrangement could resolve scaling incompatibilities that currently challenge scale-model floating wind turbine experiments.In this paper, published experimental results and a collection of full-scale simulations are used to determine what performance specifications such a system would need to meet. First, an analysis of full-scale numerical simulations and published 1:50-scale experimental results is presented. This analysis indicates the required operating envelope of the actuation system in terms of displacements, velocities, accelerations, and forces. Next, a sensitivity study using a customization of the floating wind turbine simulator FAST is described. Errors in the coupling between the wind turbine and the floating platform are used to represent the various inaccuracies and delays that could be introduced by a real-time hybrid testing system. Results of this sensitivity study indicate the requirements — in terms of motion-tracking accuracy, force actuation accuracy, and system latency — for maintaining an acceptable level of accuracy in 1:50-scale floating wind turbine experiments using real-time hybrid testing.Copyright

Influence of Bilge Keel Width on the Roll Damping of FPSO

Current industry practice to control roll motions in floating production storage and offloading (FPSO) vessels is based on using large-width bilge keels. This paper details an experimental study involving a range of bilge keel widths from 0% to 20% of half beam of a FPSO with rectangular geometry. Both free decay and forced oscillation tests were conducted on the range of geometries at different amplitudes and frequencies. The results show that, for given amplitude of roll motion, the damping coefficient increases with increasing bilge keel size up to a certain point and then declines. Numerical simulations using the free surface random vortex method were performed on rectangular cross sections with bilge keels, which show good agreement with the experimental results. Simulations extended up to even larger keel widths indicate that the same trend for damping coefficient as a function of keel size is found. An examination of the simulation results suggests a likely explanation for this behavior. A simplified formulation for damping coefficient is developed as a function of bilge keel width and roll amplitude.

Variation of Heave Added Mass and Damping Near Seabed

During installation of subsea structures such as mud mats, the tension in crane wires can experience spikes when the structure is near the seabed. It is hypothesized that such spikes may be caused by the structure undergoing resonant oscillations, which in turn may be due to changes in added mass and damping near the seabed. Such motions can cause hardship for operators as they interfere with precise positioning during installation. With increasing exploration and production in deep and remote fields, the size and weight of subsea equipments are continuously increasing. Installation operations such as lifting and lowering, positioning of the object require good knowledge of the hydrodynamic coefficients. Following on ideas used in Norwegian offshore, the mud mat is modeled as a circular disk. Experiments are conducted on an oscillating solid disk of diameter and thickness 200 mm and 2 mm respectively. The heave oscillations are forced by a programmable actuator, at amplitudes varying from 1–56 mm and frequencies from 1.0–1.8 Hz. The elevation ‘h’ of the disk from the mean seabed is varied from 0.2–2 times the disk radius. The forces on the disk are measured using a submersible high-sensitivity load cell. The motions of the disk are restricted to axial (heave) direction, and are measured with a displacement transducer. The measured forces and displacement are analyzed using a Fourier Transform algorithm to separate the added mass and damping effects. The authors have found similar trends in the hydrodynamic behavior of a disk approaching the seabed to what was found when the disk approached the free surface in Wadhwa & Thiagarajan [1]. The added mass and damping coefficients were found to increase with increasing KC, as well as with increasing proximity to the seabed. Another noticeable feature of the experiments was the cavity formation underneath the oscillating structure. The width of the cavity was about 3–4 times the radius of the disk and depth was about one third/fourth of the radius of the disk. The size of the cavity and the increase in hydrodynamic forces near the seabed suggest the importance of knowledge of hydrodynamic behavior near the seabed.Copyright