This paper presents a numerical study of a simplified wave energy converter (WEC) with and without a moon-pool under focused wave conditions and the work presented corresponds to a contribution to the CCP-WSI Blind Test Series 3. The numerical model applies the overset mesh technique in order to deal with large amplitude motions induced by the focused wave groups. The generation of the incident wave group is first examined through a mesh convergence test and by comparing with the experimental data. Simulations are then carried out with the presence of the WEC. In total three wave conditions are considered, each with the same wave period but different wave height. Non-linear effects on the WEC motion are clearly shown when the wave steepness increases and wave over-topping occurs. Furthermore, the effects of the moon pool on the dynamics and kinematics of the WEC including the damping effects on pitch response are also discussed, where the WEC motion is compared for the case with and without a moon-pool under the same wave conditions

Bai, Wei

Chen, Hao

Lin, Zaibin

Ma, Zhihua

Qian, Ling

This paper presents a numerical study of a simplified wave energy converter (WEC) with and without a moon-pool under focused wave conditions and the work presented corresponds to a contribution to the CCPWSI Blind Test Series 3. The numerical model applies the overset mesh

technique in order to deal with large amplitude motions induced by the

focused wave groups. The generation of the incident wave group is first

examined through a mesh convergence test and by comparing with the

experimental data. Simulations are then carried out with the presence of

the WEC. In total three wave conditions are considered, each with the

same wave period but different wave height. Non-linear effects on the

WEC motion are clearly shown when the wave steepness increases and

wave over-topping occurs. Furthermore, the effects of the moon pool on

the dynamics and kinematics of the WEC including the damping effects

on pitch response are also discussed, where the WEC motion is compared for the case with and without a moon-pool under the same wave

conditions

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CCP-WSI Blind Test Series 3: OpenFOAM Simulation of Focused Wave Interaction

with a Simplified Wave Energy Converter

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Chen, Hao and Qian, Ling and Ma, Zhihua and Bai, Wei and Lin, Zaibin(2019) CCP-WSI Blind Test Series 3: OpenFOAM Simulation of FocusedWave Interaction with a Simplified Wave Energy Converter. In: Proceedingsof The 29th International Ocean and Polar Engineering Conference (ISOPE2019), 16 June 2019 - 21 June 2019, Honolulu, Hawaii, USA.Downloaded from: http://e-space.mmu.ac.uk/625352/Publisher: International Society of Ocean and Polar Engineers (ISOPE)Please cite the published versionhttps://e-space.mmu.ac.ukCCP-WSI Blind Test Series 3: OpenFOAM Simulation of Focused Wave Interactionwith a Simplified Wave Energy ConverterHao Chen, Ling Qian, Zhihua Ma, Wei Bai and Zaibin LinCentre for Mathematical Modelling and Flow Analysis, School of Computing, Mathematics and Digital TechnologyManchester Metropolitan University, Manchester, United KingdomABSTRACTThis paper presents a numerical study of a simplified wave energy con-verter (WEC) with and without a moon-pool under focused wave condi-tions and the work presented corresponds to a contribution to the CCP-WSI Blind Test Series 3. The numerical model applies the overset meshtechnique in order to deal with large amplitude motions induced by thefocused wave groups. The generation of the incident wave group is firstexamined through a mesh convergence test and by comparing with theexperimental data. Simulations are then carried out with the presence ofthe WEC. In total three wave conditions are considered, each with thesame wave period but di↵erent wave height. Non-linear e↵ects on theWEC motion are clearly shown when the wave steepness increases andwave over-topping occurs. Furthermore, the e↵ects of the moon pool onthe dynamics and kinematics of the WEC including the damping e↵ectson pitch response are also discussed, where the WEC motion is com-pared for the case with and without a moon-pool under the same waveconditions.KEY WORDS: Wave energy converter; Overset mesh; Floating body;Focused wave groups, CCP-WSI Blind Test Series 3.INTRODUCTIONIn recent years, the possibility of harnessing energy from ocean waveshas gained great interests, where di↵erent design concepts of waveenergy converters (WECs) have been proposed, such as oscillating watercolumns, bottom-hinged pitching devices, floating pitching devices,over-topping devices, and point absorbers.Point absorbers are one of the simplest WECs. Their characteristiclength is generally shorter than typical wave length at the peak wave fre-quency and they are typically subjected to large amplitude motions closeto resonance. Under such conditions, highly nonlinear wave-structureinteraction will normally occur, which cannot be predicted accuratelyby simple models based on linear or second order potential flow theory.Hereby the fully nonlinear numerical models such as those base on thesolutions of the full Navier-Stokes equations are needed. Examples offully nonlinear CFD simulations on the point absorbers and other typesof WECs have been presented in Yu and Li (2013), Palm et al. (2016),Hu et al. (2011), Qian et al. (2005) and Ransley (2017).Marine operations from ships and o↵shore platforms often use moon-pools to lower or lift devices such as subsea modules and remoteoperated underwater vehicles. Piston-mode resonance can be excitedby the relative vertical motions in the neighbourhood of the moon-pool,which causes strong amplification of the dynamic wave elevation inthe moon-pool. This has been studied in e.g. Fredriksen et al. (2014),Fredriksen et al. (2015) and Faltinsen et al. (2007).In the present work, the motion responses of a point absorber under fo-cused wave groups are numerically simulated. Two geometries of thesimplified WEC are considered, namely a hemispherical-bottom cylin-der and a hollow cylinder with moon-pool. The motion responses ofthe WEC under di↵erent wave conditions are compared with the e↵ectsof moon-pool investigated. The test cases, which are proposed by theCCP-WSI Blind Test Series (Ransley et al 2019) in conjunction with theAnnual ISOPE Conferences, are designed to provide an understandingof the required model fidelity for modelling the behaviour of floatingstructures, for which this work provides a reasonably high fidelity con-tribution.NUMERICAL MODELFlow SolverThe incompressible Navier-Stokes equations are solved in the open-source toolbox OpenFOAM for a two-phase system, where volume offluid method is employed to capture the free surface. The governingequations for this system are given as:r · u = 0 (1)@⇢u@t+ r · (⇢uu)   r · µru =  rp⇤   (g · x)r⇢ (2)@↵@t+ r · (u↵) + r · (ur↵(1   ↵)) = 0 (3)where x = (x, y, z) is the Cartesian coordinate system, u is the velocity,g is the gravitation, ⇢ is the density, µ is the dynamic viscosity and p⇤is the pseudo-dynamic pressure, where the hydrostatic pressure has beensubtracted. ur here is referred as the compressive velocity (Berberovic etal., 2009), which aids in retaining a sharp interface. The term ↵(1   ↵)vanishes everywhere except at the interface.Rigid body motion solverThe standard OpenFOAM sixDoFRigidBodySolver is used to solve thesix degrees of freedom motion solver, where the mooring system is mod-elled as a linear spring. Linear and angular momentum conservationequation is solved to obtain the accelerations. The acceleration is under-relaxed with a fixed factor of 0.4 to maintain the stability of the solver.Then Newmark scheme is used to numerically integrate the accelerationin order to calculate the displacement and the velocity.Overset meshThe overset mesh functionality released in OpenFOAM v1706 (ESI ver-sion) is applied to properly resolve the moving mesh issues. Under ex-treme sea conditions, the motion of the floating structures can be eventu-ally very large, which is not straightforward to model using the dynamicmesh approach. The overset mesh can e↵ectively resolve this issue sinceit adopts a composite mesh structure. We shall use two layers of mesh,namely the background mesh and the body fitted mesh. The backgroundmesh is fixed, while the body-fitted mesh follows the motion of the float-ing structure without any deformation. Data are exchanged at every timestep between these two layers of mesh.Numerical wave generationThe extreme wave conditions are described by NewWave type focusedwave groups. The wave generation toolbox IHFOAM, developed byHiguera et al. (2013), is employed to numerically generate the focusedwave groups. Unlike the moving paddles or flaps used in physical mod-elling in wave tanks, the surface elevation and the particle velocity pro-files at the fixed wave generation boundary are calculated based on thesecond order irregular wave theory, which have been given in e.g. Hu etal. (2016).RESULTS AND DISCUSSIONExperimentsThe experiments, as part of the CCP-WSI project for the CCP-WSI BlindTest Series 3, were performed in the COAST Laboratory Ocean Basinat Plymouth University, UK. The basin is 35 m long and 15.5 m wide.The depth of the basin was set to 3 m in this set of experiments. Twotypes of wave energy converters were considered in the experiments,namely the simple hemispherical-bottomed cylinder and a cylinderwith a moon-pool, as shown in Fig. 1 and Fig. 2, respectively. Theirmass properties are given in Table 1. The WECs were moored by alinear spring vertically which connects to the basin bottom. The springsti↵ness was 67 N/m and the pretension force on the mooring lines were32.07 N and 31.55 N for the two cases.Table 1 Mass properties for the WECs. M is the mass, I is the mo-ment of inertia. ID is the case ID number. Case 1 is forthe hemispherical-bottom cylinder in focused wave groupsand Case 2 is the hollow cylinder with moon-pool in fo-cused wave groups.ID M [kg] Ixx [kgm2] Iyy [kgm2] Izz [kgm2]1 43.674 2.219 2.219 1.1432 61.459 1.790 1.790 3.298Fig. 1 The geometry and the dimensions for the hemispherical-bottom cylinder. CoM is the centre of mass. (Reproducedfrom the CCP-WSI Blind Test Series 3 description)Fig. 2 The geometry and the dimensions for the hollow cylinderwith a moon-pool. CoM is the centre of mass. (Repro-duced from the CCP-WSI Blind Test Series 3 description)The wave parameters for the incident wave groups are given in Table 2.All the wave groups were crest-focused with the same peak frequencybut increasing wave steepness. Each wave was created using linear su-perposition of 244 wave fronts with frequencies evenly spaced between0.10 Hz and 2 Hz. For all cases, 13 wave gauges were placed in the wavebasin as illustrated in Fig. 3. Gauge 5 was placed at the rest positionof the buoy(s) (with the structure in place this wave gauge was removedbut the same number system maintained), which also corresponds to thefocal position of the wave group.Table 2 The test conditions for the incident wave groups. All thewaves were generated based on the PM spectrum. A isthe focal crest height, Tp is the wave period for the wavecomponent at peak frequency, Hs is the significant waveheight and kp is the wave number for the wave componentat the peak frequency.Case A [m] Tp [s] Hs [m] h [m] kpA [-]1 0.20 2.5 0.274 3.00 0.12872 0.30 2.5 0.274 3.00 0.19313 0.32 2.5 0.274 3.00 0.2060Fig. 3 The positions of the wave gauges around the WECs. (Re-produced from the CCP-WSI Blind Test Series 3 descrip-tion)Computational domain and meshA domain size of 20 m long and 6 m wide is used throughout the sim-ulations, where the domain length corresponds to 1.9 p where  p is thewave length at the peak wave frequency, and the domain width is equalto about 12D1 and 10D2 where D1 and D2 are the diameter of the WECwithout and with moon pool, respectively. The depth of the wave tank isset to the same as in the experiments, i.e. 3 m, while the height above thewater surface is 1 m to allow the two-phase flow simulation. The wavegroups are focused at 12 m from the wave-maker side at 12 s. As theoverset mesh is applied in the numerical model, two layers of mesh areused. Hexahedra cells are applied in the background mesh, which arestatic throughout the simulation. The cells are stretched vertically fromthe bottom and the atmosphere boundary to the free surface area betweenz =  0.3 and z = 0.3 (z = 0 corresponds to the still water level) and theyare uniformly distributed in this area. In x and y direction, the mesh cellsare also stretched smoothly to the focal position. Regarding the body-fitted mesh layer, the utility snappyHexMesh is used to cut the regularhexahedra cells into tetrahedron. Moreover, the mesh is further refinednear the WEC body surface. An example of the overset mesh near theWEC is presented in Fig. 4.Incident wave groupsConvergence testsConvergence study is carried out to examine the sensitivity of mesh res-olution on the generated incident wave groups. The domain size is thesame as the background mesh introduced above. Only the wave casewith the lowest crest height (case 1) was tested here as a finer mesh isrequired to resolve the free surface for smaller waves. Three mesh reso-lutions are used in the study, of which the parameters are shown in Table3. The CPU time shown in the table is the wall clock time of runningthe test case on two Intel Xeon E5-2600 CPUs with 32 cores. The sur-face elevation at the focal position (Gauge 5) is plotted in Fig. 5 usingthese mesh resolutions. It is observed that the time series of the surfaceelevations are almost identical, which perfectly collapse into one line.This demonstrates that the mesh resolutions are su ciently fine and thenumerical solutions are convergent. Grid 2 will be used in the followingsimulations.Comparison of surface elevationWe present comparison of the surface elevation at several wave gaugesfor Case 1 and Case 3 in Fig. 6 and Fig. 7. The selected wave gauges arealong the centre line from the front to the back part. It is observed thatthe numerical results agree well with the experimental data for Case 1,corresponding to the relatively mild wave conditions. However, when theFig. 4 An example of the overset mesh near the WEC for the casewithout moon pool (upper) and with moon pool (lower).Table 3 The grid parameters in the convergence study.  x,  y and z are the averaged cell length in x, y and z directions inthe refined free surface area.ID  x [m]  y [m]  z [m] NO. [-] CPU time [hour]1 0.076 0.077 0.025 1.64 m 4.672 0.060 0.061 0.020 3.22 m 11.433 0.050 0.051 0.017 5.56 m 16.08-20 -15 -10 -5 0 5 10 15 20-1-0.500.51 Grid 1Grid 2Grid 3Fig. 5 The surface elevation at WG 05 using di↵erent mesh reso-lutions.wave steepness is increasing, the deviation is likely to increase. At thefocal position (WG05), the wave crest is underpredicted by the numericalmodel for about 26%.E↵ects of wave height on the WEC motionThe surge, heave and pitch motion of the wave energy converter withmoon pool are presented in Fig. 8 under three di↵erent wave conditions.We only plot the numerical results, since the experimental data are notavailable yet. Several comments are given here for the numerical results.Regarding the surge motion, strong drift motion is found for the caseswith wave conditions 2 and 3. The maximum surge motion is more than-20 -15 -10 -5 0 5 10 15 20-1-0.500.51Gauge1ExperimentsOpenFOAM-20 -15 -10 -5 0 5 10 15 20-1-0.500.51Gauge3ExperimentsOpenFOAM-20 -15 -10 -5 0 5 10 15 20-1-0.500.51Gauge5ExperimentsOpenFOAM-20 -15 -10 -5 0 5 10 15 20-1-0.500.51Gauge8ExperimentsOpenFOAMFig. 6 Comparison of surface elevation at the selected wavegauges for Case 1.five times the wave crest. This may be partially due to the mooring sys-tem. A single point mooring line may not provide su cient restoringforce. Under relatively large wave steepness, it takes particularly longtime to restore to the original position. Meanwhile, it is also possiblethat the numerical model is not stable enough, leading to the drift mo-tion.Regarding the heave motion, the nondimensional crest is quite similarfor all the cases, i.e. smaller than 1. But a second peak is observed forCase 2 and 3. This is due to the strong nonlinear free surface motion,-20 -15 -10 -5 0 5 10 15 20-1-0.500.51Gauge1ExperimentsOpenFOAM-20 -15 -10 -5 0 5 10 15 20-1-0.500.51Gauge3ExperimentsOpenFOAM-20 -15 -10 -5 0 5 10 15 20-1-0.500.51Gauge5ExperimentsOpenFOAM-20 -15 -10 -5 0 5 10 15 20-1-0.500.51Gauge8ExperimentsOpenFOAMFig. 7 Comparison of surface elevation at the selected wavegauges for Case 3.where violent overtopping occurs. A snapshot of the free surface motionat di↵erent time instants near the focal time is presented in Fig. 9. Thenear field waves are clearly di↵racted and radiated due to the presence ofthe WEC. Clear overtopping of incident waves are generated at t = 12.80and t = 13.00 s.E↵ects of moon-pool on the WEC motionThe three motion modes of the WEC with and without moon-pool isplotted in Fig. 10 for wave condition 1. A strong dissipation e↵ect isFig. 8 The surge, heave and pitch motion of the WEC under threewave conditions for the case with moon-pool.Fig. 9 The free surface motion near the WEC with moon-pool un-der wave condition 3.Fig. 10 The surge, heave and pitch motion of the WEC with andwithout moon pool under wave condition 1.found when the WEC is equipped with moon pool, due to the internalfluid motion inside the moon-pool. This is particularly obvious for thepitch motion. When the WEC is equipped with moon pool, the crestvalue of the pitch motion is smaller than the case without moon-pool.Furthermore, the pitch motion is soon damped in the defocusing processfor the case with moon-pool, while it keeps oscillating for the other case.Similar phenomenon is found for the surge motion in the de-focusingprocess. But the crest value is the same for both cases. Moreover, forheave motion, the moon-pool e↵ect is rather small, and the heave motionexhibits similar characteristics for both cases. This is reasonable sincethe dissipation of the moon-pool is likely due to the viscous e↵ects, whilethe heave motion is primarily dominated by the potential energy of thewaves.CONCLUSIONSThis paper presents the numerical modelling of a simplified WEC withand without a moon-pool under focused wave groups as a contribution tothe CCP-WSI Blind Test Series 3. The numerical model applies an over-set mesh method in order to consider the large amplitudes motions in-duced by the waves. Three wave conditions with increasing wave steep-ness are tested and from the simulation results, it is clear that the motionof the WEC becomes strongly nonlinear when the non-dimensional wavesteepness kpA reaches 0.2. When comparing the WEC motion with andwithout moon-pool under the same wave condition, it is found that themoon-pool actually introduces dissipations due to the internal fluid mo-tion inside and near the moon-pool. This dissipation reduces the crestvalue of the pitch motion and damped the motion in the de-focusing pro-cess. But it has negligible e↵ect on the heave motion, which is dominatedby potential e↵ects.ACKNOWLEDGEMENTThis research was supported by the Engineering and Physical SciencesResearch Council (EPSRC), U.K. Project: A Zonal CFD Approach forFully Nonlinear Simulations of Two Vessels in Launch and RecoveryOperations, under Grant No. EP/N008839/1.REFERENCESBerberovic, E, Hinsberg N V, Jakirlic, S, Roisman, I, and Tropea, C.(2009). “Drop impact onto a liquid layer of finite thickness: Dynam-ics of the cavity evolution ”, Physical Review E, Vol. 79.Faltinsen, O M, Rognebakke, O F and Timokha, A N. (2007). “Two-dimensional resonant piston-like sloshing in a moonpool ”, Journalof Fluid Mechanics, Vol. 575, pp. 359–397.Fredriksen, A G, Kristiansen, T and Faltinsen, O M. (2014). “Experi-mental and numerical investigation of wave resonance in moonpoolsat low forward speed.”, Applied Ocean Research, Vol. 47, pp. 28–46.Fredriksen, A G, Kristiansen, T and Faltinsen, O M. (2015). “Wave-induced response of a floating two-dimensional body with a moon-pool ”, Philosophical Transactions of the royal society A, Vol. 373.Higuera, P, Lara, J L and Losada, I J. (2013). “Realistic wave generationand active wave absorption for Navier-Stokes models. Applicationto OpenFOAM. ”, Coastal Engineering, Vol. 71, pp. 102–118.Hu, Z Z, Causon, D M, Mingham, C G and Qian, L. (2011). “Numer-ical simulation of floating bodies in extreme free surface waves. ”,Natural Hazards and Earth System Sciences, Vol. 11, pp. 519–527.Hu, Z Z, Greaves, D and Raby, A. (2016). “Numerical wave tank studyof extreme waves and wave-structure interaction using OpenFoam.”, Ocean Engineering, Vol. 126, pp. 329–342.Palm, J, Eskilsson, C, Paredes, G M and Bergdahl, L. (2016). “Coupledmooring analysis of floating wave energy converters using CFD ”,International Journal of Marine Energy, Vol. 16, pp. 83–99.Qian, L, Mingham, C, Causon, D, Ingram, D, Folley, M and Whittaker,T. (2005). “Numerical simulation of wave power devices using atwo-fluid free surface solver. ”, Modern Physics Letters B, Vol. 19,pp. 1479–1482.Ransley, E, Greaves, D, Raby, A, Simmonds, D and Hann, M (2017).“Survivability of wave energy converters using CFD ”, RenewableEnergy, Vol. 109, pp. 235–247.Ransley, E., Yan, S., Brown, S., Mai, T., Graham, D., Ma, Q., Musiedlak,P.-H., Engsig-Karup, A. P., Eskilsson, C., Li, Q., Wang, J., Xie, Z.,Sriram, V., Stoesser, T., Zhuang, Y., Li, Q., Wan, D., Chen, G., Chen,H., Qian, L., Ma, Z., Mingham, C., Causon, D., Gatin, I., Jasak,H., Vukevi, V., Downie, S., Higuera, P., Buldakov, E., Stagonas, D.,Chen, Q., Zang, J., Greaves, D. (2019). “A blind comparative studyof focused wave interactions with a fixed FPSO-like structure (CCP-WSI Blind Test Series 1) ”, International Journal of O↵shore andPolar Engineering, in press.Yu, Y H and Li, Y. (2013). “Reynolds-Averaged Navier-Stokes simula-tion of the heave performance of a two-body floating-point absorberwave energy system. ”, Computers and Fluids, Vol. 73, pp. 104–114.

CCP-WSI Blind Test Series 3: OpenFOAM Simulation of Focused Wave Interaction with a Simplified Wave Energy Converter

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CCP-WSI Blind Test Series 3: OpenFOAM Simulation of Focused Wave Interaction with a Simplified Wave Energy Converter

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