Hydrodynamics of the IPS buoy wave energy converter including the effect of non-uniform acceleration tube cross section António F.O. Falcão a, * , José J. Cândido a , Paulo A.P. Justino b , João C.C. Henriques a a IDMEC, Instituto Superior Técnico, Technical University of Lisbon, 1049-001 Lisbon, Portugal b Laboratório Nacional de Energia e Geologia, Estrada Paço do Lumiar, 1649-038 Lisbon, Portugal article info Article history: Received 15 June 2011 Accepted 6 October 2011 Available online 6 November 2011 Keywords: Wave energy Wave power IPS buoy Oscillating body Hydrodynamics abstract An important class of floating wave energy converters (that includes the IPS buoy, the Wavebob and the PowerBuoy) comprehends devices in which the energy is converted from the relative (essentially heaving) motion between two bodies oscillating differently. The paper considers the case of the IPS buoy, consisting of a floater rigidly connected to a fully submerged vertical (acceleration) tube open at both ends. The tube contains a piston whose motion relative to the floater-tube system (motion originated by wave action on the floater and by the inertia of the water enclosed in the tube) drives a power take-off mechanism (PTO) (assumed to be a linear damper). To solve the problem of the end-stops, the central part of the tube, along which the piston slides, bells out at both ends to limit the stroke of the piston. The use of a hydraulic turbine inside the tube is examined as an alternative to the piston. A frequency domain analysis of the device in regular waves is developed, combined with a one-dimensional unsteady flow model inside the tube (whose cross section is in general non-uniform). Numerical results in regular and irregular waves are presented for a cylindrical buoy with a conical bottom, including the optimization of the acceleration tube geometry and PTO damping coefficient for several wave periods. Ó 2011 Elsevier Ltd. All rights reserved. 1. Introduction The concept of the point absorber for wave energy utilization was developed in the late 1970s and early 1980s, mostly in Scan- dinavia [1]. This is in general a wave energy converter of oscillating body type whose horizontal dimensions are small compared to the representative wavelength. In its simplest version, the body reacts against the bottom. In deep water (say 50 m or more), this may raise difficulties due to the distance between the floating body and the sea bottom. Multi-body systems may then be used instead, in which the energy is converted from the relative motion between two bodies oscillating differently. This is the case of several devices presently under development, like the Pelamis, the Wavebob and the PowerBuoy. Sometimes the relevant relative motion results from heaving oscillations. This paper considers the special situation when a floater reacts against the inertia of the water contained in a long vertical tube open at both ends, located underneath. This is the case of the spar-buoy OWC, possibly the simplest concept for a floating oscillating water column (OWC) device equipped with an air turbine, in which the upper end of the tube extends through the buoy above the sea water level. Masuda, in Japan, developed a navigation buoy based on the OWC spar-buoy concept [2,3]. The spar-buoy OWC will not be analysed in this paper. The IPS buoy is another type of spar-buoy and will be analysed here in detail. It was invented by Noren [4] and initially developed in Sweden by the company Interproject Service (IPS). The device consists of a buoy rigidly connected to a fully submerged vertical tube (the so-called acceleration tube) open at both ends (Fig. 1). The tube contains a piston whose motion relative to the floater-tube system (motion originated by wave action on the floater and by the inertia of the water enclosed in the tube) drives a power take- off (PTO) mechanism. The same inventor later introduced an improvement that significantly contributes to solve the problem of the end-stops: the central part of the tube, along which the piston slides, bells out at both ends to limit the stroke of the piston [5]. A half-scale prototype of the IPS buoy was tested in sea trials in Sweden, in the early 1980s [6]. The AquaBuOY is a wave energy converter, developed in the 2000s, that combines the IPS buoy concept with a pair of hose pumps to produce a flow of water at high pressure that drives a Pelton turbine [7,8]. A prototype of the AquaBuOY was deployed and tested in 2007 in the Pacific Ocean off the coast of Oregon. A variant of the initial IPS buoy concept, due to Stephen Salter, is the sloped IPS buoy: the natural frequency of the converter may be * Corresponding author. E-mail addresses: falcao@hidrol.ist.utl.pt, antonio.falcao@ist.utl.pt (A.F.O. Falcão). Contents lists available at SciVerse ScienceDirect Renewable Energy journal homepage: www.elsevier.com/locate/renene 0960-1481/$ e see front matter Ó 2011 Elsevier Ltd. All rights reserved. doi:10.1016/j.renene.2011.10.005 Renewable Energy 41 (2012) 105e114