Semi-analytical and CFD formulations of a spherical floater
Authors: Spyridon Mavrakos  , Spyridon Zafeiris  , Georgios Papadakis  , Konispoliatis Dimitrios 
Published: September 2023

Today, humanity is facing the great pressure of fossil fuels exhaustion and environmental pollution. This obliges governments and industries to make accelerated efforts on producing green energy. The focus is spotted on marine environment which is a vast source of renewable energy. Among several classes of designs proposed for wave energy conversion, spherical Wave EnergyConverters (WECs) have received considerable attention. The problems of water wave diffraction and radiation by a sphere has been examined by a substantial amount of literature, i.e., [1]–[4], whereas in [5]–[8] linear hydrodynamic effects on a spherical WEC have been examined. All these research works are based on potential flow methodologies. Nevertheless, overthe last decade there has been a significant interest on Computational Fluid Dynamics CFD modelling due to its detailed results, focusing also to spherical WECs [9]–[10].In the present work a semi-analytical model is applied to solve the wave radiation problem around a spherical WEC (Figure 1), in the context of linear potential theory. The outcomes of the theoretical analysis are supplemented and compared with high fidelity CFD simulations (Figure 2 for a semi-submerged sphere). Furthermore, the two methodologies are compared with a theoretical approach for the hydrodynamic analysis of floating bodies with vertical axis as being presented in [11]. The method is based on the discretization of the flow field around the body using coaxial ring elements, which are generated from the approximation of the sphere’s meridian line by a stepped curve.Numerical results are given from the comparison of the three formulations, and some interesting phenomena are discussed concerning the viscous effects on the floater.
[1] Havelock, T. H. 1955. Wave due to a floating sphere making periodic heaving oscillations. R. Soc. London,A231, 1-7.[2] Hulme, A. 1982. The wave forces acting on a floating hemisphere undergoing force periodic oscillation. J. FluidMech., 121, 443-463.[3] Wang, S. 1986. Motions of a spherical submarine in waves. Ocean Engng., 13, 249-271.[4] Wu, G.X. 1995. The interaction of water waves with a group of submerged spheres. Appl. Ocean. Res., 17, 165-184.[5] Srokosz, M.A. 1979. The submerged sphere as an absorber of wave power. J. Fluid Mech., 95, 717-741.[6] Thomas, G.P., Evans, D.V. 1981. Arrays of three-dimensional wave energy absorbers. J. Fluid Mech., 108, 67-88.[7] Linton, C.M. 1991. Radiation and diffraction of water waves by a submerged sphere in finite depth. Ocean Engng.,18, 61-74.[8] Meng, F., et al. Modal analysis of a submerged spherical point absorber with asymmetric mass distribution.Renew. Energy 130, 223-237.[9] Shami, E.A., et al. 2021. Non-linear dynamic simulations of two-body wave energy converters via identificationof viscous drag coefficients of different shapes of the submerged body based on numerical wave tank CFD simulation.Renew. Energy, 179, 983-997.[10] Katsidoniotaki, E., et al. 2023. Validation of a CFD model for wave energy system dynamics in extreme waves.Ocean Engng., 268, 113320.[11] Kokkinowrachos, K., et al. 1986. Behaviour of vertical bodies of revolution in waves. Ocean Engng., 13, 505-538