In the present paper, a new fully coupled simulator based on DeepLines™ software is described in order to address floating wind turbines dynamic simulation. It allows its user to take into account either separately or together the hydrodynamic and aerodynamic effects on one or several floating wind turbines. This simulator includes a non linear beam finite elements formulation to model the structural components — blades, tower, drivetrain, mooring lines and umbilicals — for both HAWT and VAWT layouts and advanced hydrodynamic capabilities to define all kinds of floating units and complex environmental loadings. The floating supports are defined with complete hydrodynamic databases computed with a seakeeping program. The aerodynamic loads acting on the turbine rotor are dynamically computed by an external aerodynamic library, which first release includes BEM (blade element moment for HAWTs) and SSM (single streamtube method for VAWTs) methods. The integration in time is performed with an implicit Newmark integration scheme.

Frequency-domain analysis can be used to evaluate the motions of the FPSO with its mooring and riser. The main assumption of the frequency-domain analysis is that the coupling is essentially linear. Calculations are performed taking into account first order wave loads on the floating structure. Added mass and radiation damping terms are frequency dependent, and can be easily considered in this formulation. The major non-linearity comes from the drag force both on lines and the floating structure. Linearization of the non-linear drag force acting on the lines is applied. The calculations can be extended to derive the low frequency motion of the floating structure. Second order low frequency quadratic transfer function is computed with a diffraction/radiation method. Given a wave spectrum, the second order force spectrum can then be derived. At the same time frequency-domain analysis is used to derive the low frequency motion and wave frequency motion of the floating system. As an example case, an FPSO is employed. Comparison is performed with time domain simulation to show the robustness of the frequency-domain analysis. Some calculations are also performed with either low frequency terms only or wave frequency terms only in order to check the effect of modeling low and wave frequency terms, separately. In the case study it is found that the low frequency motion is reduced by the wave frequency motion while the wave frequency motion is not affected by the low frequency motion.

The present paper describes the validation and the modeling capabilities of a new fully coupled floating wind turbine simulator based on DeepLines™ software. A first validation, based on code comparison with NREL-FAST software, is presented and shows very good correlation on a rigidly founded 5MW wind turbine in various wind conditions despite the different modeling techniques and assumptions of the two softwares. This benchmark, in addition to the extensive validation on various offshore projects, makes us confident on DeepLines capabilities to assess founded and floating wind turbine behaviour in a complex offshore environment. Furthermore, some simulation results on jacket and floating founded wind turbines, defined in the frame of IEA OC4 project, are presented and highlight the versatility of our simulator to perform offshore and floating wind turbine optimal design.

In the offshore industry, modeling pipe vibrations due to current is important to predict structural fatigue life. In the case of Wake Induced Oscillations (WIO), clashing is also an issue during the design phase to be able to define enough clearance to prevent clashing. If not possible, it is then needed to estimate contact energy between pipes and ensure that clashing is acceptable. Wake induced oscillations are difficult to predict, involving Vortex-Induced Vibrations (VIV) at relatively high frequency and small displacement together with larger motion at lower frequency leading to potential contact. A hydrodynamic model is proposed to predict WIO of a flexible pipe in the wake of an upstream pipe. The structural displacement of the two pipes is computed with a classical finite element model. The pipes are linked thru two dimensional strips where the hydrodynamic loads are computed based on the pipe distance in the strip. Since both pipes are flexible, the upstream pipe is subjected to VIV while the downstream pipe is subjected to the mean wake created by the pipe, to VIV as well as WIO. Each effect is represented by a simplified model. A Blevins model is used to represent the quasi-static drag and lift forces on the downstream riser. The VIV on the upstream riser is computed with a Van der Pol oscillator model, and a similar model is used for the downstream riser with an added term to account for the upstream riser presence. Experimental results on two tandem jumpers are used to validate the approach in steady current and in current plus wave. The database has a large number of model tests with different initial gaps between the two jumpers. Dynamic response of the two pipes is measured thru accelerometers and tension sensors. Some of the configurations exhibit clashing and/or overlapping of the jumpers. Amplitude and spectra of vibrations are compared to the proposed model; the general characteristics of the interaction (contact, overlapping) are also addressed.

Introduction This paper is devoted to the mechanical analysis of contact friction problems met by slender offshore structures such as mooring lines, risers and pipes. Several types of interactions are considered since contact-friction arises either between multiple risers (internal and external contact) or between a single riser and a rigid surface. The later can either be fixed, or move freely under the influence of external forces. Non linear time domain simulations of the mechanical behavior of these structures undergoing large displacements and finite strains are presented based on the finite element method (FEM). To solve efficiently the geometrical nonlinearity associated with contact friction interactions, specific algorithms have been developed to localize automatically contact elements. The convergence of the iterative algorithms is sped-up through the use of a regularized Coulomb's law, which insure fast and reliable results even for complex systems, as demonstrated here. To illustrate the capabilities of the DeepLines?software, detailed modeling of realistic systems derived from industrial applications are presented, such as the layout of a riser on a sea floor arbitrarily shaped, the wave induced motion of a riser laying onto a freely moving sub-sea arch, a riser rubbing onto the moonpool or maintained within a bellmouth connected to an FPSO. Pipe in pipe configurations will also be considered, through applications linked to SCR. Finally, some results concerning the strains along the pipes or risers are given, demonstrating the necessity to model accurately these phenomena which can lead to high curvatures locally. General Theoretical Framework For the sake of completeness, we present here the basic theory sustaining the solution procedure used in the FEM code DeepLines?, following Fargues (1995) and Durville (1998a,b, 1999). More specific details can also be found in DeepLines? (2002,a,b). Sea-bottom to surface links (mooring lines, risers...) are considered as slender structures. The structural problem for their dynamics is formulated as a principle of virtual work of interaction and can be stated as follow: find the cinematically admissible solution u, which verifies (Mathematical Equation-Available in full paper) for any cinematically admissible displacement field v. Here, S(u) is the second Piola-Kirchhoff stress tensor and E(u) is the non-linear Green Lagrange strain tensor. The first term corresponds to the virtual work of internal loads, the second and third terms represent the virtual work associated with contact-friction interactions, and the RHS corresponds to the virtual work of both volume and surface external loads which are respectively applied on the structure ? and part of its border ?F. ?C refers to the surface where contacts between structures effectively take place, with reaction forces R as defined in figure 1. Figure 1: Definitions of contact-friction reaction force between a slender structure (?) and a rigid surface (obstacle). The main difficulty in this formulation is to derive a precise expression for the virtual work Winteract of these contactfriction forces. Indeed, the location ?C where contacts between structures occur is a priori not known, therefore introducing a geometrical nonlinearity.