Comparing nonlinear hydrodynamic forces in heaving point absorbers and oscillating wave surge converters

Giorgi, Giuseppe; Ringwood, John V.

doi:10.1007/s40722-017-0098-2

Cited by 33 publications

(41 citation statements)

References 11 publications

(7 reference statements)

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“…The two main nonlinearities affecting PAWECs in the resonance region are drag forces and nonlinear Froude-Krylov (FK) forcing. The nonlinear FK force can be well accounted for in quasi-linear radiation-diffraction (wave-to-wire) codes as it is a purely geometric effect [14]. Drag forces are also commonly included in parametrised form as in the Morison equation [15], but this requires calibration of drag coefficients.…”

Section: Introductionmentioning

confidence: 99%

“…They also highlight the difference in flow pattern surrounding the WEC for the different body shapes and put forward viscous correction factors, which are deduced from the deviation of the WEC decay motion from potential theory. In a recent series of papers Giorgi and co-authors [14,21,22] discuss a case study of a spherical floater in heave. They show that weakly non-linear potential flow simulations with calibrated parametrised drag force give results much closer to CFD prediction than simulations using only nonlinear FK corrections.…”

Section: Introductionmentioning

confidence: 99%

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Assessment of Scale Effects, Viscous Forces and Induced Drag on a Point-Absorbing Wave Energy Converter by CFD Simulations

Palm

Eskilsson

Bergdahl

et al. 2018

JMSE

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This paper analyses the nonlinear forces on a moored point-absorbing wave energy converter (WEC) in resonance at prototype scale (1:1) and at model scale (1:16). Three simulation types were used: Reynolds Averaged Navier-Stokes (RANS), Euler and the linear radiation-diffraction method (linear). Results show that when the wave steepness is doubled, the response reduction is: (i) 3% due to the nonlinear mooring response and the Froude-Krylov force; (ii) 1-4% due to viscous forces; and (iii) 18-19% due to induced drag and non-linear added mass and radiation forces. The effect of the induced drag is shown to be largely scale-independent. It is caused by local pressure variations due to vortex generation below the body, which reduce the total pressure force on the hull. Euler simulations are shown to be scale-independent and the scale effects of the WEC are limited by the purely viscous contribution (1-4%) for the two waves studied. We recommend that experimental model scale test campaigns of WECs should be accompanied by RANS simulations, and the analysis complemented by scale-independent Euler simulations to quantify the scale-dependent part of the nonlinear effects.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Assessment of Scale Effects, Viscous Forces and Induced Drag on a Point-Absorbing Wave Energy Converter by CFD Simulations

Palm

Eskilsson

Bergdahl

et al. 2018

JMSE

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show abstract

“…We must remark here that for the OSWEC case, for both the single WEC and the array, our linear PTO model can exaggerate the performance of the OSWEC since we are not taking into account the strong non-linearities inherent in the dynamics of this WEC type. This has been pointed out in [8,45] among others. Therefore, if we were to choose a more sophisticated model for the OSWEC, the relative 'underperformance' of the hydraulic PTO system might disappear.…”

Section: Discussionmentioning

confidence: 62%

Analyzing the Near-Field Effects and the Power Production of an Array of Heaving Cylindrical WECs and OSWECs Using a Coupled Hydrodynamic-PTO Model

et al. 2018

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The Power Take-Off (PTO) system is the key component of a Wave Energy Converter (WEC) that distinguishes it from a simple floating body because the uptake of the energy by the PTO system modifies the wave field surrounding the WEC. Consequently, the choice of a proper PTO model of a WEC is a key factor in the accuracy of a numerical model that serves to validate the economic impact of a wave energy project. Simultaneously, the given numerical model needs to simulate many WEC units operating in close proximity in a WEC farm, as such conglomerations are seen by the wave energy industry as the path to economic viability. A balance must therefore be struck between an accurate PTO model and the numerical cost of running it for various WEC farm configurations to test the viability of any given WEC farm project. Because hydrodynamic interaction between the WECs in a farm modifies the incoming wave field, both the power output of a WEC farm and the surface elevations in the ‘near field’ area will be affected. For certain types of WECs, namely heaving cylindrical WECs, the PTO system strongly modifies the motion of the WECs. Consequently, the choice of a PTO system affects both the power production and the surface elevations in the ‘near field’ of a WEC farm. In this paper, we investigate the effect of a PTO system for a small wave farm that we term ‘WEC array’ of 5 WECs of two types: a heaving cylindrical WEC and an Oscillating Surge Wave Energy Converter (OSWEC). These WECs are positioned in a staggered array configuration designed to extract the maximum power from the incident waves. The PTO system is modelled in WEC-Sim, a purpose-built WEC dynamics simulator. The PTO system is coupled to the open-source wave structure interaction solver NEMOH to calculate the average wave field η in the ‘near-field’. Using a WEC-specific novel PTO system model, the effect of a hydraulic PTO system on the WEC array power production and the near-field is compared to that of a linear PTO system. Results are given for a series of regular wave conditions for a single WEC and subsequently extended to a 5-WEC array. We demonstrate the quantitative and qualitative differences in the power and the ‘near-field’ effects between a 5-heaving cylindrical WEC array and a 5-OSWEC array. Furthermore, we show that modeling a hydraulic PTO system as a linear PTO system in the case of a heaving cylindrical WEC leads to considerable inaccuracies in the calculation of average absorbed power, but not in the near-field surface elevations. Yet, in the case of an OSWEC, a hydraulic PTO system cannot be reduced to a linear PTO coefficient without introducing substantial inaccuracies into both the array power output and the near-field effects. We discuss the implications of our results compared to previous research on WEC arrays which used simplified linear coefficients as a proxy for PTO systems.

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“…It is worth to remark that the computational convenience of the proposed method is the analytical representation of the integral, which is needless of a numerical mesh-based computation of the wetted surface. Indeed, the mesh-based nonlinear FK software LAMSWEC (Gilloteaux, 2007), for example, although coded in Fortran, is about one order of magnitude slower than the method proposed in this paper (Giorgi and Ringwood, 2017a,2017b,2017cGilloteaux, 2007).…”

Section: Tablementioning

confidence: 88%

“…The inclusion of nonlinear terms in the equation of motion generally improves the accuracy of the model, but with additional complexity and computational burden. In particular, it has been shown, in the literature, that nonlinear Froude-Krylov (FK) forces, which represent the integral of the static and dynamic pressure over the wetted surface of the device, are especially important for point absorbers (Giorgi and Ringwood, 2017a). Furthermore, nonlinear FK forces are responsible for purely-nonlinear phenomena, such as pitching instability or parametric roll (Tarrant, 2015).…”

Section: Introductionmentioning

confidence: 99%

Analytical representation of nonlinear Froude-Krylov forces for 3-DoF point absorbing wave energy devices

Giorgi

Ringwood

2018

Ocean Engineering

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Accurate and computationally efficient mathematical models are fundamental for designing, optimizing, and controlling wave energy converters. Many wave energy devices exhibit significant nonlinear behaviour over their full operational envelope, so nonlinear models may become indispensable. Froude-Krylov nonlinearities are of great importance in point absorbers but, in general, their calculation requires an often unacceptable increase in model complexity/computational time. However, for axisymmetric bodies, it is possible to describe the whole geometry analytically, thereby allowing faster calculation of nonlinear Froude-Krylov forces. In this paper, a convenient parametrization of axisymmetric body geometries is proposed, applicable to devices moving in surge, heave, and pitch. While, in general, Froude-Krylov integrals must be solved numerically, by assuming small pitch angles, it is possible to simplify the problem, and achieve a considerably faster algebraic solution. However, both nonlinear models compute in real-time. The framework presented in the paper offers flexibility in terms of computational and fidelity levels, while still representing important nonlinear phenomena such as parametric pitch instability. Models with lower computational requirements may be more suitable for repetitive calculations, such as real-time control, or longterm power production assessment, while higher fidelity models may be more appropriate for maximum load estimation, or short-term power production capability assessment.

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Comparing nonlinear hydrodynamic forces in heaving point absorbers and oscillating wave surge converters

Cited by 33 publications

References 11 publications

Assessment of Scale Effects, Viscous Forces and Induced Drag on a Point-Absorbing Wave Energy Converter by CFD Simulations

Assessment of Scale Effects, Viscous Forces and Induced Drag on a Point-Absorbing Wave Energy Converter by CFD Simulations

Analyzing the Near-Field Effects and the Power Production of an Array of Heaving Cylindrical WECs and OSWECs Using a Coupled Hydrodynamic-PTO Model

Analytical representation of nonlinear Froude-Krylov forces for 3-DoF point absorbing wave energy devices

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