Experimental study on vortex-induced motions of a semi-submersible platform with four square columns, Part II: Effects of surface waves, external damping and draft condition Rodolfo T. Gonc - alves a,n , Guilherme F. Rosetti a , Andre ´ L.C. Fujarra a , Allan C. Oliveira b a TPN—Numerical Offshore Tank, Department of Naval Architecture and Ocean Engineering, Escola Polite´cnica—University of S ~ ao Paulo, Av. Professor Mello Moraes, 2231, Cidade Universita ´ria, S ~ ao Paulo, SP 05508-030, Brazil b CENPES—Research and Development Center, Petrobras, Rio de Janeiro, RJ, Brazil article info Article history: Received 3 July 2012 Accepted 7 January 2013 Available online 17 February 2013 Keywords: Vortex-induced motions (VIM) Semi-submersible Model tests 6 degrees-of-freedom (6 DOF) Wave incidence Damping level Draft condition abstract Aiming to complete the results presented before by Gonc - alves et al. (2012d. Ocean Eng. 54, 150–169) the present work brings new experimental results on VIM of a semi-submersible platform with four square columns, particularly concerning changes in three different aspects: simultaneous presence of current and surface waves in the same direction, external damping level, and draft conditions. The VIM tests were performed in the presence of regular and irregular waves, both conditions with simultaneous current presence, to understand the wave effects. Considerable differences between the presences of regular and irregular waves were observed. The motion amplitudes in the transverse direction, in the tests with regular waves, were markedly lower than those with irregular waves, and the VIM behavior was not observed. In the sea state tests, the amplitudes are lower than current-only ones, yet a periodic motion characterized by VIM was observed. Furthermore, the effects of the lower draft condition and damping level were addressed, showing they are important for model tests because they contribute to decreasing VIM amplitudes. & 2013 Elsevier Ltd. All rights reserved. 1. Introduction As opposed to what happens with cylindrical platforms such as monocolumns and spars, the study on vortex-induced motions (VIM) phenomenon of semi-submersibles is quite more recent and, therefore, much less can be found about it, which probably happens because this phenomenon was only noticed after the increase in size of the new semi-submersibles, mainly the dimension of their columns. Nevertheless, important works can be cited, among which Rijken et al. (2004, 2011), Waals et al. (2007), Rijken and Leverette (2008), Hong et al. (2008), Hussain et al. (2009), Magee et al. (2011), Tahar and Finn (2011), Martin and Rijken (2012) and Xu et al. (2012). In a previous work, Gonc - alves et al. (2012d) performed a series of tests to verify the influence of the incidence angle of current and the hull appen- dages on VIM of a semi-submersible with four square columns. The main results showed that VIM in the transverse direction occurred in a range of 4.0 rV r r14.0 with amplitude peaks around 7.0 rV r r8.0. The largest amplitudes obtained were around 40% of the column width for 30 and 45-degree incidences. Another important result observed was a considerable yaw motion oscillation, also denominated vortex-induced yaw (VIY), in which a synchronization region could be identified as a resonance phenomenon. The largest yaw motions were verified for the 0 and 180-degree incidences and the maxima angular amplitudes around 4.5 1. There are a number of other aspects that are relevant on VIM of floating platforms, as discussed in Gonc - alves et al. (2012c) and Fujarra et al. (2012), and the following can be mentioned: current incidence angle; hull appendages; simultaneous presence of sur- face waves and current incidence; draft conditions and external damping caused, for instance, by risers and mooring lines. Under this context and aiming to complete the results pre- sented before, the present work brings new experimental results on VIM of the same semi-submersible platform, illustrated in Fig. 1, concerning the three important remaining aspects: simultaneous presence of current and surface waves in the same direction, external damping level, and draft conditions. Section 2 presents a background of the effects of surface waves, damping level and draft condition on the VIM phenom- enon, as well as a background of fundamental studies in the same Contents lists available at SciVerse ScienceDirect journal homepage: www.elsevier.com/locate/oceaneng Ocean Engineering 0029-8018/$ - see front matter & 2013 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.oceaneng.2013.01.019 n Corresponding author. Tel./fax: þ55 11 30911727. E-mail addresses: rodolfo_tg@tpn.usp.br (R.T. Gonc - alves), guilherme.feitosa@tpn.usp.br (G.F. Rosetti), afujarra@usp.br (A.L.C. Fujarra), allan_carre@petrobras.com.br (A.C. Oliveira). Ocean Engineering 62 (2013) 10–24