This paper investigates two engine control strategies - constant rack (CR) and speed controller (SC) - for a coupled ship propulsion system in regular head waves. The study decomposes the efficiency chain into components to identify physical mechanisms behind performance differences. By integrating a mean value engine model with a time-domain ship simulator, we analyze transient interactions between hull, propeller, and engine under realistic seaway conditions. Results demonstrate that CR achieves superior fuel efficiency (up to 2.49% improvement), particularly in long-wavelength seas. This advantage stems from reduced turbo-lag effects and more stable air-fuel dynamics that minimize transient thermodynamic losses. However, CR induces significant engine speed fluctuations that may limit practical application. In contrast, SC provides better speed regulation but increases fuel consumption due to turbo-lag and unsteady air-fuel dynamics. Hydrodynamic effects contribute through control-strategy-induced variations in ship speed and wave resistance, though to a lesser extent. These findings highlight the importance of modeling both engine dynamics and nonlinear hydrodynamic effects when evaluating propulsion control strategies.

An alternative expression of the time domain free surface Green's function is proposed. Its source and image source contribution satisfies the homogeneous Neumann condition on the mean free surface, therefore it can be useful for the boundary element method based on the double-body flow linearization. Furthermore, it is proved that it is also the solution of Clement's 4th order Ordinary Differential Equation (Clement, 1998). The Frobenius method with time step movement proposed by Chuang et al. (2007) is adopted for accurate and efficient evaluation.

Wind propulsion is envisioned as one of the solutions for the decarbonisation of maritime transport, as it offers high efficiency in terms of primary energy comsumption. Many wind propulsion systems already exist at various development stages, but the uncertainties over their performance is a strong obstacle to their adoption by ship owners. This paper presents a general method for the assessment of steady and unsteady performances of wind- propelled ships with 6 degrees of freedom, as implemented in the open-source program xWASP_CN. Inspired by system-based modelling, the method consists in the independent modelling of the forces acting on the ship, as functions of the ship’s 6 degrees of freedom and environmental conditions. An original root-finding algorithm that leverages the specifics of the physical problem to find the steady equilibrium is presented. The method works either like a Power Prediction Program (PPP) or like a Velocity Prediction Program (VPP). As a PPP, the forward speed and course are fixed while the required propulsive power, leeway angle, heel, trim and sinkage are solved. As a VPP, only the course is fixed and the attained forward speed, leeway angle, heel, trim and sinkage are solved. This makes the method suitable for both hybrid propulsion and pure wind propulsion. The force models can be semi-empirical (usually requiring very little input data), based on preliminary experimental or numerical results (such as forward resistance curves, lift/drag coefficients and frequency-domain sea-keeping coefficients), or full-fledged flow solvers (e.g. potential theory, CFD). Thus the method is suitable for all design stages as each force can be modelled with several levels of accuracy depending on the input data available. Comparisons of an intermediate-level model with experiments on a 18-ft catamaran fitted with a Flettner rotor and a water turbine show good agreement for steady-state results.

This paper proposes an efficient potential and viscous flow decomposition method for wave-structure interaction simulation with single-phase wave models and two-phase Computational Fluid Dynamics (CFD) solvers. The potential part - represents the incident waves - is solved with spectral wave models; the viscous part - represents the complementary perturbation on the incident waves - is solved with the CFD solver. The decomposition strategy is called Spectral Wave Explicit Navier-Stokes Equations (SWENSE), originally proposed for single-phase CFD solvers ( Ferrant et al., 2003). Firstly, this paper presents a new two-phase SWENS Equations with interface capturing technique. To achieve this single-phase and two-phase decomposition, the incident fields are extended in the air with a density-weighted pressure. Secondly, an accurate and efficient interpolation method is proposed to transfer High Order Spectral (HOS) wave model's result on CFD mesh, which reduces drastically the divergence error of the interpolated velocity. Implemented within OpenFOAM, these methods are tested by three verification, validation, and application cases, considering incident wave propagation, high-order loads on a vertical cylinder in regular waves, and a Catenary Anchor Leg Mooring buoy in both regular and irregular waves. Speed-ups between 1.7 and 4.2 are achieved. The wave models and the interpolation method are released open-source to the public.

In this study, the added resistance and seakeeping performance of the KVLCC2 ship is investigated by using the spectral wave explicit Navier–Stokes equations (SWENSE) method. The SWENSE method is based on the decomposition of the total field into an incident part explicitly obtained by the wave potential flow theory and a complementary part solved with a modified Reynolds-averaged Navier–Stokes solver. Therefore, the computational efficiency can be achieved by using a relatively coarse mesh in the far field, retaining the accuracy of the incident waves. A parametric study is performed under regular wave conditions with 3Degree of Freedom (DOF) motions of the hull. The results are compared with the large literature available. An additional case is simulated to demonstrate the capability of the present method in simulating seakeeping problems in irregular sea states. Good agreement between the computed results with the reference data can be observed for the hull model, which indicates that the added resistance and seakeeping performances can be well predicted by the present method. Introduction In recent years, the Energy Efficiency Design Index (EEDI) has been introduced by the International Maritime Organization to restrict greenhouse gas emissions from ships. In the EEDI formula, the evaluation of the added resistance is required and defined as the increased resistance in the actual sea state due to waves, winds, etc. compared with the resistance in the calm sea condition. The resistance in actual sea states could be up to 30% greater than that in the calm water resistance (Lee et al. 2017). Therefore, prediction of the added resistance induced by waves is an important subject for ship design and is the focus of the present study.

In wave-structure interaction problems, the minimization of wave reflection at boundaries is important for achieving accurate results and limiting the disturbances on the air/water interface. The present study compares a set of existing wave outlet techniques which are commonly applied in free surface simulations using a viscous flow solver. These techniques are stretched mesh, linear damping source, increased viscosity, and relaxation schemes. The comparisons are performed for test conditions which include propagation of regular incident waves and damping of radiation waves.

Ce papier présente les derniers développements concernant le couplage de la méthode SWENSE (Spectral Waves Navier-Stokes Equations) et d'une méthode de résolution des équations RANS (Reynolds Averaged Navier-Stokes) avec capture d'interface de type Level Set. Ce couplage permet de combiner les avantages des deux méthodes, c'est-à-dire avoir une cinématique de houle de bonne qualité dans tout le domaine grâce à la méthode SWENSE et la prise en compte du déferlement via la fonction Level Set. Le catamaran Delft 372 est utilisé pour les validations avec des calculs sur mer calme et sur houle régulière à deux vitesses différentes.

This paper presents recent developments around the combination of the SWENSE (Spectral Waves Navier-Stokes Equations) method and a method solving RANS (Reynolds Averaged Navier-Stokes) equations with a free surface-capturing scheme. Such coupling allows us to use the best of both methods: high quality regular or irregular waves in the entire domain using a spectral potential flow solver with a small CPU cost for SWENSE and the possibility to modelize the wave breaking using a single-phase Level Set free surface capturing scheme. In this work, the Delft 372 catamaran is used for all validations in calm water and in regular waves for two different speeds.

Numerical wave tanks rely on specific models to generate realistic wave condition, propagate accurately the waves in the domain, and absorb the reflected waves at the boundaries. In this paper, three wave modeling methods for two-phase CFD solvers are compared, including the Internal Wave Generator method, the Relaxation Zone method, and the Spectral Wave Explicit Navier Stokes Equations (SWENSE) method. The first two methods consist in generating and absorbing the waves in specific regions of the domain, while the third achieves a potential/viscous coupling in the entire domain. These methods, implemented either in OpenFOAM or in ISIS-CFD are compared by simulating a fixed Catenary Anchor Leg Mooring (CALM) buoy in regular waves. The simulation results are compared with available experimental data obtained by a model test in the Ocean Engineering Tank of Ecole Centrale de Nantes. The comparison shows the efficiency and the accuracy of these waves modeling methods. A problem related to the turbulence modeling in two-phase flow is also remarked.

for 33rd IWWWFB, Brest, France, 2018 Preliminary study on coupling of viscous and potential flow using domain decomposition and relaxation zones Choi Y.M.1, Malenica Š.2, Bouscasse B.1, Seng S.2, Monroy C.2, Gentaz L.1, and Ferrant P.1 1Ecole Centrale de Nantes, Nantes, France CNRS UMR 6598 2Bureau Veritas, Paris, France Introduction The use of RANS based CFD methods has increased recently in naval and offshore engineering to overcome the limits of classical potential flow methods. The problem of seakeeping with forward speed causes many difficulties even for the linear potential flow methodolgy based on boundary integral equation (BIE) and enormous efforts are demanded when the wave steepness becomes higher, especially when wave breaking occurs. The computing resources becomes more powerful nowadays, and it encourages usage of CFD for naval applications, though it is still demanding. There are still many difficulties for practical application of CFD methods. Generation of meshes is one of those, the discretization of the whole fluid domain makes the modelling of the problem complex and expensive. It is usually concluded that the solution obtained from the finest mesh is chosen as the final value. The wave propagation is also an important difficulty specific to the naval and offshore field. The numerical schemes used in RANS based CFD methods induce numerical damping which added to the physical viscosity. As a result the waves generated by the wave-body interaction do not propagate properly up to far-field. On the other hand, the potential flow methods are quite suitable to propagate the waves up to far-field. However potential flow method becomes complex and difficult to solve when phenomena are highly nonlinear, as it ususally happens close to the body. Considering the characteristics of viscous CFD and potential flow methods, one idea is to combine these approaches to solve typical naval and offshore applications, as done by many researchers over the years [1, 2]. The present study focuses on the advantages and disadvantages of coupling those two methods by introducing two examples: pure wave propagation and a radiation problem (the swaying two dimensional Lewis form). For both problems, several types of outlet conditions of the CFD zone are tested. Those outlet consists of blending zones or mesh stretching and several schemes and target solutions are compared in terms of precision and computational cost. Description Finite volume method (FVM) based open-source library OpenFOAM is used in the present study. foamStar is developped by Bureau Veritas (BV) [3, 4] for naval and offshore purpose. foamStar is based on the standard multiphase solver of OpenFOAM (interDymFoam) and special modules are included for the generation of waves and floating body dynamics. Generation and absoprtion of waves in foamStar uses explicit blending (relaxation) scheme in a defined relaxation zone. The blending equations are given in (1) and (2) u = (1 − w)u + wu (1) α = (1 − w)α+ wα (2) where u, α and w is the fluids velocity, volume of fraction and weight function. Target denoted on superscript represents the target value to be blended. The pressure is not blended because of mass conservation. For the first problem of wave propagation, different outlets are considered: mesh stretching, blending to no waves, blending to incident waves and blending to modified waves (simple coupling). The schematic view of the different outlets is depicted in figure 1. Mesh stretched outlet, widely used in CFD fields, utilizes numerical damping arising from the stretched mesh, making waves damp out. The conditions blending to no waves and Abstract for 33rd IWWWFB, Brest, France, 2018for 33rd IWWWFB, Brest, France, 2018 blending to incident waves are given by setting the target values as zeroes and incident waves respectively in the blending equations (1) and (2). When propagating in the CFD domain, waves change slightly due to numerical effects. Therefore when entering outlet it does not match exactly with the incoming waves. The condition blending to modified waves assumes then in the target solution that the waves amplitude and phase change during the propagation in the CFD domain but that the wavelength and period stay constant. Consequently, the change of wave amplitude and phase are computed by Fourier transform over one wave period using the one point measurement located one wavelength before the outlet. The target solution used in the blending to modified waves uses the same expression as the one used in blending to incident waves but it has time varying wave amplitude and phase. (a) Mesh stretched outlet (b) Blending outlet with different target values Figure 1: Different outlet tested in the wave propagation case The second test case “swaying two dimensional Lewis form” is considered to remove incident waves and to see the coupling effect on perturbed waves. A schematic view on swaying Lewis form is depicted in figure 2. The considered outlet are in this case mesh streched outlet, blend to no waves and blending to potential flow solution. The potential flow solution is available thanks to Ursell-Tasai’s multipole expasion [5, 6]. Figure 2: Schematic view of the radiation problem with outlet Results and Discussion For the first test case, the velocity fields obtained using the different outlets are shown in figure 3. The instabilities are observed for all outlets. Relatively small instabilities are observed when blending to incident and blending to modified waves are applied compared with the results obtained with other outlets. The wave reflection coefficients are measured from 250 wave gauges located in the middle of the domain of interest and given in Table 1. All blending schemes give a smaller wave reflection compared with the one obtained with mesh stretched outlet. Comparing the various blending schemes, the smallest reflection is measured when the blending to modified waves is used. Comparing with blending to incident waves, only a small improvement is observed but it has to be noted that comparing with blending to no waves is more reasonable because it is more common and general in CFD methods. Abstract for 33rd IWWWFB, Brest, France, 2018for 33rd IWWWFB, Brest, France, 2018 (a) Mesh stretched outlet (b) Blend to no waves (c) Blend to incident waves (d) Blend to modified waves Figure 3: Velocity fields obtained with different outlets Table 1. Reflection coefficient obtained with different outlets Outlet Refelection Coef. Mesh stretched 0.207 Blend to no waves 0.077 Blend to incident waves 0.042 Blend to modified waves 0.039 In the second test case, the total computation domain is expected to be reduced when the target values blended are closer to the values of outgoing waves. The size of the relaxation and pure CFD zone (without blending) are varied and tested with different outlets. For all tests, the computation cells near to the body are always kept of similar size. The results show that having target values similar to the outgoing waves can help to reduce the size of both the relaxation and the CFD zone but it shows also that the computation domain cannot be reduced dramatically. In particular, the radiation forces are more sensitive to the size of the relaxation zone than to the size of the CFD zone. The results about the size of the computational domain will be presented in the workshop. The convergence of the radiation forces acting on Lewis form using the various outlet conditions are shown in figure 4. For the comparison, same size of pure CFD zone is used but the size of the relaxation zone is varied. The radiation forces with mesh stretched outlet start to diverge after some periods and it results from the pressure modulation in the outlet. Comparing the convergence of radiation forces, blending to potential flow is faster than blending to no waves. Simulation time to get converged values with blending to no waves requires three times of blending to potential flow. (a) Added mass (b) Radiation damping Figure 4: Convergence of radiation forces acting on Lewis form Abstract for 33rd IWWWFB, Brest, France, 2018for 33rd IWWWFB, Brest, France, 2018 The radiation coefficients are compared with the analytic values in Table 2. The smallest errors are obtained with blending to potential flow even if the smallest relaxation zone is used. However, the increase of accuracy is small comparing with the solution obtained with blending to no waves. The total computation time to get converged radiation forces are given in Table 3. The results obtained with mesh stretched outlet is excluded because it diverges and a long computation time is required comparing with what is needed with blending schemes. In view of simulation time, the blending to potential flow converges faster than blending to no waves but the computation time needed for each time step is 5 times longer than with blending to no waves. As a whole, the total computation time demanded by blending to potential flow is 3 times longer than what needed with blending to no waves. Table 2. Radiation coefficients and errors obtained with different outlets Coef. ω Analytic Mesh stretched Blend to no waves Blend to potential a22 2.4 1.304 1.298 (diverge) 1.283 1.316 4.2 0.136 0.148 0.129 0.141 7.0 0.365 0.390 0.380 0.392 b22 2.4 2.169 2.150 (diverge) 2.194 2.185 4.2 0.798 0.768 0.781 0.798 7.0 0.156 0.148 0.146 0.151 Error > 13.22 % 9.52 % 9.13 % Table 3. Total computation time to get converged radiation forces Cases ω=2.4 rad/s ω=4.2 rad/s ω=7.0 rad/s Blend to no waves 147,469 s 108,282 s 52,680 s Blend to potential flow 398,204 s 367,904 s 179,644 s Ratio of CPU time required 2.70 3.39 3.41 The results show that blending to outgoing waves gives a slightly better solution and has possiblity to reduce the computational domain. Many objections are recognized, mainly because the improvements are small and the extra computation time for potential flow makes the coupling unattractive. In

for 33rd IWWWFB, Brest, France, 2018 Challenges in developing a SWENSE two-phase CFD solver for complex wave conditions Zhaobin Li, Benjamin Bouscasse, Guillaume Ducrozet, Lionel Gentaz, and Pierre Ferrant LHEEA Lab, Ecole Centrale de Nantes, CNRS UMR 6598, Nantes, France Email: zhaobin.li@ec-nantes.fr Introduction Simulating wave-structure interaction with CFD tools is often computational resource demanding: large computational domains are used to prevent waves from being reflected at the boundary and fine meshes are always needed to avoid excessive numerical attenuation of incoming waves. To reduce the computational cost, the Spectral Wave Explicit Navier-Stokes Equations (SWENSE) method was proposed to couple the solutions from potential theory and Navier-Stokes (NS) equations[1]. In this method, the incident wave solution is evaluated by the wave models based on potential theory in the entire computational domain, leaving only the perturbation caused by the structure and the influence of viscosity to be solved with CFD. In its original single-phase formalism, it has been proved that coarse meshes can be used in the farfield for incident wave propagation while keeping a good accuracy[2]. The extension of the SWENSE method to two-phase solvers is not straightforward. Few attempts appeared recently[3, 4]. This paper presents this extension in the frame of Volume of Fluid (VOF) solvers. The two main challenges are: (a) developing numerically stable two-phase SWENSE equations; (b) mapping accurately the solution of potential wave models to the CFD calculation grids. The latter is not only the bottleneck of the development of the two-phase SWENSE method but also a common difficulty in coupling potential wave models and two-phase CFD solvers. The authors propose a solution to overcome these difficulties and develop a two-phase SWENSE solver with the open source CFD package OpenFOAM. Several test cases are proposed for validating the model, including 2D regular and irregular waves propagation and the computation of wave forces on a 3D cylinder. Challenge 1: SWENSE equations for two-phase VOF solvers The SWENSE method decomposes a wave structure-interaction problem χ into an incident part χI and a complementary part χC as shown in Eqn.(1). The incident part takes into account the propagation of the incident waves, whose solution is given by a dedicated wave model; the complementary part serves as a correction due to the disturbances caused by the viscosity and the presence of structures. χ = χI + χC (1) Complying with the idea of the SWENSE method for single-phase solver[1], the two-phase SWENSE governing equations should be obtained by subtracting the Euler equations from two-phase Navier-Stokes equations. The NS momentum equation for two-phase incompressible fluid, written with VOF is as follows, where w and a stand for the properties in the water and in the air respectively and the α field is the VOF field. ρ = αρ + (1− α)ρ (2) ∂α ∂t + u.∇α = 0 (3) ∂u ∂t + u.∇u = −∇p ρ + g + ν∇u (4) The perfect fluid Euler momentum equation behind potential wave models reads: ρI = ρ w (5) ∂uI ∂t + uI .∇uI = − ∇pI ρI + g (6) Abstract for 33rd IWWWFB, Brest, France, 2018for 33rd IWWWFB, Brest, France, 2018 To demonstrate the challenge, we subtract directly the two equations as in the single-phase SWENSE method[1]. The hypothesis done is that the solution from wave models can be extended in the air. The momentum equation obtained, written with the notation of uC = u− uI and pC = p− pI , reads: ∂uC ∂t + uC .∇uC + uC .∇uI + uI .∇uC = − ∇pC ρ + ∇pI ρI − ∇pI ρ + ν∇uC (7) The underlined terms are canceled out in the single-phase SWENSE momentum equation since ρ = ρI . However, these terms remain in two-phase flows, having non-zero values in the air phase. They behave as source terms and affect the numerical stability. To overcome this problem, we propose a mathematical reformulation for Eqn.(6). We introduce a modified incident pressure field pI defined by: pI = ρ pI ρI (8) Eqn.(6) written in its modified version using pI reads: ∂uI ∂t + uI .∇uI = − ∇pI ρ + pI ρI ∇ρ ρ + g (9) Subtracting Eqn.(9) from the two-phase Navier-Stokes equation Eqn.(4), and using the notion of pC = p− pI , the momentum equation written with the complementary variables is: ∂uC ∂t + uC .∇uC + uC .∇uI + uI .∇uC = − ∇pC ρ − pI ρI ∇ρ ρ + ν∇uC (10) The underlined term in Eqn.(10) is the only difference when comparing with the single-phase SWENSE momentum equation[1]. This term is similar to the dynamic pressure jump at the free surface in the conventional two-phase Navier-Stokes equation. The property of that dynamic pressure jump is that it equals to zero when the free surface matches the hydrostatic equilibrium position so that this hydrostatic equilibrium is maintained. In the case of the SWENSE method, the underlined term equals to zero when the free surface in the CFD matches the one from the wave models so that the incident wave solution is maintained. This formulation is tested with two cases. The first one concerns the propagation of non-linear regular waves in a periodic 2D wave tank. The second deals with the calculation of the wave forces on a cylinder in regular waves. The details of the two test cases can be found in a separated paper[5]. For the first test case, Fig. 1 shows the first and second harmonic amplitudes of the free surface elevation. Compared with OpenFOAM native two-phase solver interFoam, an improvement on both the accuracy and the stability is confirmed. 0 10 20 30 40 t/T 0.8 0.85 0.9 0.95 1 1.05 1.1 1 s t H a rm o n ic A m p lit u d e (n o n -d im .) R & F two-phase SWENSE ( / x = 100, T/ t = 400) interFoam ( / x = 200, T/ t = 800) (a) First harmonic amplitude 0 10 20 30 40 t/T 0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4 1.5 2 n d H a rm o n ic A m p lit u d e (n o n -d im .) R & F two-phase SWENSE ( / x = 100, T/ t = 400) interFoam ( / x = 200, T/ t = 800) (b) Second harmonic amplitude Figure 1: Harmonic analysis of wave elevation for the regular wave propagation test case For the second test case, Fig.2 shows the first and second harmonic amplitudes of the in-line wave force with different incident wave steepnesses. The results of the two-phase SWENSE solver have a good agreement with the single-phase SWENSE solver[6], and a smaller discrepancy from the experimental data for the first harmonic amplitude compared with a conventional two-phase VOF solver. Abstract for 33rd IWWWFB, Brest, France, 2018for 33rd IWWWFB, Brest, France, 2018 0 0,05 0,1 0,15 0,2 0,25 ka 6 6,2 6,4 6,6 6,8 |F 1 ’| single-phase SWENSE two-phase SWENSE two-phase VOF EXP (a) First harmonic amplitude 0 0,05 0,1 0,15 0,2 0,25 ka 0 0,1 0,2 0,3 0,4 0,5 0,6 |F 2 ’| single-phase SWENSE two-phase SWENSE two-phase VOF EXP (b) Second harmonic amplitude Figure 2: Harmonic analysis of wave force on a vertical cylinder Challenge 2: Mapping solutions from wave models to CFD grids The SWENSE method adopts spectral methods to efficiently model incident waves: the solution method of Rienecker-Fenton[7] is used for the regular waves and the High Order Spectral (HOS) method[8] is used for the irregular waves. The mapping of the solution from HOS solvers to the CFD grids is done with an open source wrapper program Grid2Grid[9]. However, an accurate mapping is a challenge. To model irregular waves, HOS solvers typically use less than 10 points per peak wavelength. Excessive points do not help capturing the physics of the waves and may generate stability problems due to the higher modes. However, the necessary cell number per wavelength is usually about 100 for two-phase VOF based solvers. Mapping the solution from wave models to the CFD cells is needed and done through interpolating from the neighbor HOS points. In a previous study[10], various interpolation techniques were compared from the simplest linear to the most sophisticated Lagrange method, but the interpolation errors are all too large to be accepted by the VOF based two-phase SWENSE method[4]. Recently, the authors come up with a solution for this problem. Instead of increasing the number of the HOS calculation points, ghost HOS points are added at the post-processing stage to provide more informations between two HOS calculation points and thus shorten the distance of the interpolation. This method avoids the time consuming point-by-point evaluation of the wave solution using the HOS modes; the value on each HOS ghost point is obtained directly through Fast Fourier Transforms (FFT). Fig.3 demonstrates a reduction of the interpolation errors on the divergence of velocity for an irregular wave case with Hs = 0.028m and Tp = 0.701s. The waves are modeled by the HOS solver with 64 points in a computational domain with 10 peak wave lengths. By adding ghost points, the maximum value of the divergence decreased from 0.86 to 0.0022, corresponding to approximately 0.25% of the interpolation error using the original method. (a) 64 HOS points max(∇.uI) = 0.86 (b) 64 HOS points + 448 ghost points max(∇.uI) = 0.0022 Figure 3: Interpolation errors for irregular waves with Hs = 0.028m and Tp = 0.701s Thanks to this improvement, the two-phase SWENSE solver is able to simulate irregular waves. Fig.4 shows an example of irregular waves propagating in a 2D wave tank simulated by the two-phase SWENSE method. The result of the two-phase VOF based SWENSE method and the HOS wave solution are in good agreement on the free surface elevation. More work including the simulation of structures in irregular waves is in progress Abstract for 33rd IWWWFB, Brest, France, 2018for 33rd IWWWFB, Brest, France, 2018 and will be presented at the workshop. 0 1 2 3 4 5 6 7 Time (s) -0,02 -0,01 0 0,01 0,02 F re e su rf ac e el ev at io n ( m ) HOS two-phase SWENSE Figure 4: Time history of free surface elevation for irregular waves with Hs = 0.028m and Tp = 0.701s Acknowledgements This work is done in the framework of the Chaire Hydrodynamique et Structure Marines CENTR

The capability of wave generation and absorption in a viscous flow solver becomes important for achieving realistic simulations in naval and offshore fields. This study presents an efficient generation of nonlinear wave fields in the viscous flow solver by using a nonlinear potential solver called higher-order spectral method (HOS). The advantages of using a fully nonlinear potential solver for the generation of irregular waves are discussed. In particular, it is shown that the proposed method allows the CFD simulation to start at the time and over the space of interest, retrieved from the potential flow solution. The viscous flow solver is based on the open source library OpenFOAM. The potential solvers used to generate waves are the open source solvers HOS-Ocean and HOS-NWT (Numerical Wave Tank). Several simulation parameters in the CFD solver are investigated in the present study. A HOS wrapper program is newly developed to regenerate wave fields in the viscous flow solver. The wrapper program is validated with OpenFOAM for 2D and 3D regular and irregular waves using relaxation zones. Finally, the extreme waves corresponding to the 1000 year return period condition in the Gulf of Mexico are simulated with the viscous flow solver and the wave elevation is compared with the experiments.

This paper presents the recent developments of the Spectral Wave Explicit Navier-Stokes Equations (SWENSE) method to extend its range of application to two-phase VOF solvers. The SWENSE method solves the wave-structure interaction problem by coupling potential theory and the Navier-Stokes (NS) equations. It evaluates the incident wave solution by wave models based on potential theory in the entire computational domain, leaving only the perturbation caused by the structure and the influence of the viscosity to be solved with CFD. The method was proven in previous studies to be accurate and efficient for wave structure interaction problems, but it was derived for single-phase NS solvers only. The present study extends the SWENSE method by proposing a novel formulation which is convenient to implement in two-phase NS solvers. A customized SWENSE solver is developed with the open source CFD package Open FOAM. An improvement in accuracy and stability is observed in wave simulations compared with conventional two-phase VOF solvers. The horizontal force on a vertical cylinder in regular waves is also calculated. First results show a good agreement with the experiment on the first harmonic component.

The ringing phenomenon is associated to the excitation of a structure at its natural frequency through higher harmonic components of the wave loading. Observations of this phenomenon on model tests were reported rst at the beginning of the 90's, before being observed at full scale during storm events in the North Sea. As the corresponding loading may induce a signi cant increase of the fatigue of the structure, the discovery of the phenomenon triggered strong research e orts for the understanding and prediction of higher harmonic wave loads on o shore structures. Using potential ow theory, Faltinsen et al (1995) developed a third order perturbation theory in the long wave regime. Malenica & Molin (M&M) (1995) proposed a complete third order quasi-analytical solution for the triple harmonic force component on a vertical cylinder in regular waves. Ferrant (1996) used a time domain fully nonlinear boundary element method and obtained results in good agreement with the M&M's theory. Huseby and Grue (1998) reported experiments on a bottom-mounted vertical cylinder in deep water conditions, focusing on the third harmonic force components, and con rming again the validity of M&M formulation. The confrontation of these experimental data to results of fully nonlinear potential ow simulations leads to favorable comparisons up to the seventh harmonic force components, published in Ferrant (1998) and Huseby & Grue (2000). In the present paper, we are revisiting this set of data, using the so-called SWENSE method in which the ow is decomposed into an incident wave system modelled by fully nonlinear potential ow theory, and a di racted/radiated ow solved using a modi ed version of Navier-Stokes equations in which incident ow components appear as forcing terms. The main nding is that the inclusion of viscous e ects leads to a slightly better agreement with experiments for the wave frequency component, compared to potential ow results. A rst analysis seems to indicate that the observed deviation between potential ow and viscous ow results is due to the in uence of a minor ow detachment on the pressure component of the load, while the frictional component have little in uence.

The state of the art tools to assess the efficiency of the wave energy converters comprise the boundary element method (BEM) codes which are based on the potential linear approach whereas computational fluid dynamics (CFD) is still considered to be relatively computationally expensive. An attempt to enlarge the scope of the state of the art computational tools for wave energy converter applications is made in order to account for the viscous effects. This is achieved via the viscous damping term of the Morison equation which relies on a coefficient C-d - to be estimated prior force calculation.The state of the art wave to wiremodel to gether with additional viscous term is termed as potential time domain viscous model and is employed for evaluation of the power efficiency of a generic surging type wave energy conversion system. Finally a comparison of CFD and the viscous time domain model is conducted which concludes that the Morison equations' drag term does offer an improvement. (C) 2015 Elsevier Ltd. All rights reserved.

The purpose of this paper is to present combination of the SWENSE (Spectral Wave Explicit Navier-Stokes Equations – [1]) method — an original method to treat fully nonlinear wave-body interactions — and a free surface RANSE (Reynolds Averaged Navier-Stokes Equations) solver using a single-phase Level Set method to capture the interface. The idea is to be able to simulate wave-body interactions under viscous flow theory with strong deformations of the interface (wave breaking in the vicinity of the body, green water on ship decks…), while keeping the advantages of the SWENSE scheme. The SWENSE approach is based on a physical decomposition by combining incident waves described by a nonlinear spectral scheme based on potential flow theory and an adapted Navier-Stokes solver where only the diffracted part of the flow is solved, incident flow parameters seen as forcing terms. In the single-phase Level Set method [2, 3], the air phase is neglected. Thus, only the liquid phase is solved considering a fluid with uniform properties. The location of the free surface is determined by a Level Set function initialised as the signed distance. The accuracy of simulation depends essentially on the pressure scheme used to impose free surface dynamic boundary condition. Comparisons of numerical results with experimental and numerical data for US navy combatant DTMB 5415 in calm water and in head waves are presented.