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Contract No. DE-AC36-08GO28308

Preliminary Results of a RANS 

Simulation for a Floating Point 

Absorber Wave Energy System 

Under Extreme Wave Conditions

Y. Yu and Y. Li

Presented at the 30th International Conference on Ocean, Offshore, 

and Arctic Engineering

Rotterdam, The Netherlands

June 19 – 24, 2011

Conference Paper

NREL/CP-5000-50967

October 2011
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1

Proceedings of the ASME 30th International Conference on Ocean, Offshore and Arctic Engineering

OMAE2011

June 19-24, 20111, Rotterdam, The Netherlands

PRELIMINARY RESULTS OF A RANS SIMULATION FOR A FLOATING POINT 

ABSORBER WAVE ENERGY SYSTEM UNDER EXTREME WAVE CONDITIONS

Yi-Hsiang Yu

National Renewable Energy Laboratory (NREL)

National Wind Technology Center

Golden, CO 80041

Email: yi-hsiang.yu@nrel.gov

Ye Li

National Renewable Energy Laboratory (NREL)

National Wind Technology Center

Golden, CO 80041

Email: ye.li@nrel.gov

ABSTRACT

This paper presents the results of a preliminary study on the 

hydrodynamics of a moored floating-point absorber (FPA) 

wave energy system under extreme wave conditions. For this 

study, we assumed that the FPA is locked in harsh weather 

conditions, and the whole device moves as a single rigid body. 

The prediction of the hydrodynamic response of the system and 

the corresponding wave impact loads on the FPA are important 

to the structural design of the system and its survivability in

extreme wave conditions.

After describing the working principle and the design 

specification of the floating-point absorber, we present the 

Reynolds-Averaged Navier-Stokes (RANS) method used in the 

study. We apply this method to analyze the hydrodynamic 

response of the FPA in regular as well as irregular waves. In 

addition, we evaluate the feasibility of using a Morison’s

Equation method for modeling the FPA system. Overall, the 

study shows that the nonlinear interaction between waves and 

the moored absorber has significant influences on the absorber

response under extreme wave conditions.

KEYWORDS

Wave energy conversion (WEC); Reynolds-Averaged NavierStokes (RANS) equation; degree of freedom (DOF); volume of 

fluid (VOF); free surface; floating-point absorber (FPA)

INTRODUCTION

Ocean waves contain a significant amount of renewable 

energy [1]. A wide variety of wave energy conversion devices 

have been developed based on various technologies and 

theories to capture the energy. These devices include oscillating 

water columns, overtopping devices, floating pitching devices, 

bottom-hinge devices, and FPAs. Comprehensive reviews on 

the fundamental designs and operating principles of wave 

energy systems can be found in [2,3]. The FPA is one of the 

simplest and one of the most promising WEC devices among 

numerous designs. This paper focuses on the study of a FPA 

system.

The FPA is typically a single buoy that either reacts against 

the seabed or a two-body system that generates energy from the

relative motion between the two bodies. An example of the 

two-body FPA system is Ocean Power Technology’s (OPT’s) 

40-kW utility-scale PowerBuoy. OPT deployed two of these 

systems, one in Santona Spain in 2008 and the other in Ohau 

Hawaii in 2009 (Fig. 1).

FIGURE 1. A PROTOTYPE OF OPT’S POWERBUOY WAVE 

ENERGY GENERATION SYSTEM (NREL PIX 17114)
2 

In 1970s, FPA research focused on understanding the 

complex hydrodynamics of FPA devices and on the prediction 

of the maximum wave power absorption [4,5,6,7]. These 

theoretical studies were reviewed by Falnes in [8,9]. More 

recent studies have focused on improving wave extraction 

efficiency under various wave conditions, using hydraulic 

power take off (PTO) mechanisms and latching control [10]. 

The studies have also examined optimal control strategies for 

irregular sea waves [11] and the use of array systems [12,13]. 

Most of the numerical analyses on wave energy system 

efficiency were performed using frequency domain potential 

flow methods for calculating the hydrodynamic excitation 

forces (e.g. [11,13,14,15,16]). However, the non-linear 

interaction between waves and a WEC device was assumed to 

be small in those studies, thus the wave breaking and 

overtopping effects were not considered. A more 

comprehensive understanding of the FPA system may require 

the use of more advanced numerical methods such as the 

RANS method. An example of the RANS analysis is presented 

in [17], in which the hydrodynamics of cylinder type buoys and 

the power capture efficiency were analyzed. In our related 

work, we performed a series of analyses using the RANS 

method to understand a practical FPA system. We investigated 

the hydrodynamics of a two-body FPA system and its power 

absorption efficiency under given conditions [18]. 

The objective of this research is to analyze the 

hydrodynamics of a FPA wave energy system in extreme wave 

conditions. First we present the working principle and the 

design specification. We modeled the baseline mooring 

configuration and the hydrodynamic response of the FPA using 

a Morison’s type method (OrcaFlex). We then investigated the 

flow field around the moored FPA and its hydrodynamic 

response in regular and irregular waves as well as the wave 

loads on the FPA body using the RANS method. 

POINT WAVE ABSORBER MODEL 

The point wave absorber model contains a float and a 

reaction part that includes a central column and a reaction plate. 

For extreme wave conditions, we assumed the absorber to be 

locked, and we performed the numerical study assuming all the 

parts are moving together as a single rigid body. 

We first designed the model using SolidWork, and then 

further modified the geometry in the numerical modeling by 

keeping the center of buoyancy, B, as close as to the original 

SolidWork design. The model properties and the dimensions are 

shown in Tab. 1 and Fig. 2, respectively, where G is the center 

of gravity, and the metacentric M is calculated by following 

OBOGGM BM,

BM ,/

+−=

I ∀= (1) 

where O is located at the intersection of the mean free surface 

and the longitudinal axis of the FPA, I is the area of inertia, and 

∀ is the displacement of the model. 

TABLE 1. POINT WAVE ABSORBER MODEL PROPERTIES 

Model properties Values (unit) 

Center of gravity G 22.4 (m) below the 

mean free surface 

Center of Buoyancy B 1.17 (m) above G 

Moment of inertia for pitch 69300 (kg m2) 

Metacentric M 4.12 (m) above G 

Weight 250 (metric tons) 

FIGURE 2. FPA GEOMETRY AND DIMENSIONS 

MODELING 

RANS method 

We applied a finite volume method-based RANS model 

(StarCCM+) for solving the details of the unsteady 

incompressible flow field around the FPA. The continuity 

equation and the Navier-Stokes equations are given as 

UUU TF

U

=∇⋅+ −∇ ⋅∇++

=⋅∇

t b ( ) p

,0

ρ

 (2) 

where ρ is the water density, U is the flow velocity vector , and 

Ut is its time derivative, Fb is the body force vector (e.g., 

gravity), and T is the stress tensor. 

The governing equations are discretized over the 

computational domain and are solved using a transient SIMPLE 

for the pressure–velocity coupling. The set of linear equations 

is solved through the use of an algebraic multigrid method. A kω SST turbulence model is applied with a two-layer all y+ wall 

treatment model, and the unsteady simulation is performed 

using a second order implicit scheme for time marching. The 

water free surface is captured using a volume of fluid (VOF) 

method, and a morphing model is adopted to move the mesh, 

where the cell movement and its deformation are taken into 

account in the momentum equation using an arbitrary 

Lagrangian-Eulerian method. 
3 

Absorber response calculation 

The translation and rotation of the body of the body (Fig. 3) 

is calculated by solving the equation of motion after the 

excitation force is obtained, and the equation of motion 

calculation is coupled with the RANS simulation. The 

translation and the rotation of the body at the center of gravity 

are solved following 

,

,

aIM Ω I Ω

aF

g g

m tb

×+=

=

Ω

 (3) 

where mb is the mass of the body, at is the acceleration vector 

for the translation, Ω and aΩ are the angular velocity and 

acceleration vectors, Ig is the moment of inertia tensor at the 

center of gravity, F and M are the resulting force and moment 

acting on the body, including the buoyancy force, wave load 

and the weight of the body. The corresponding translational and 

rotational motions are calculated by integrating the 

accelerations over time, and the equation of motion is coupled 

with the RANS method through iterations. 

FIGURE 3. THE TRANSLATION AND ROTATION OF THE 

BODY (6 DEGREES OF FREEDOM) 

Numerical wave tank settings 

The domain and the domain boundaries of the numerical 

wave tank are plotted in Fig. 4, where the water depth is 70 m. 

To reduce the size of the problem, a symmetric boundary is 

applied along the x-y plane. The given computational domain is 

100 m wide (0m≤y≤100m); 170 m high (-70m≤z≤100m); 7 

wavelengths long (-2λ≤x≤5λ) in the regular wave analysis and 

9 wavelengths long (-2λ≤x≤8λ) in the irregular wave analysis. 

The wall width to FPA diameter radius is around 19. The effect 

of wave reflection from the side wall is assumed to be small in 

this study. However, more studies need to be performed to 

quantify the impacts. The incident wave condition is specified 

at the inflow boundary, and a sponge-layer method is applied 

by placing a damping zone (2λ in the wave propagation 

direction) in front of the down wave boundary in order to 

absorb the outgoing and reflecting waves without creating 

additional numerical disturbance. Note that the sponge-layer 

damping zone method has been tested. It successfully absorbs 

the waves in a numerical wave tank without the presence of the 

absorber. 

FIGURE 4. COMPUTATIONAL DOMAIN AND 

BOUNDARIES OF THE NUMERICAL WAVE TANK 

MOORING CONFIGURATION 

The FPA is connected to a mooring system to contain its 

horizontal and rotational motions. We are not trying to model a 

particular mooring system in this study. For design and 

optimization purposes, we use OrcaFlex to conduct the mooring 

line configuration study, which is a fully 3D time domain fluid 

and structural dynamic modeling tool. It has widely been used 

for modeling the dynamics of the offshore systems. The 

excitation forces on the absorber include the buoyancy force 

and the hydrodynamic wave loads that are calculated through 

the use of Morison’s equation. The dynamics of the absorber 

and the mooring system are then modeled using a finite element 

method. The drag and added-mass coefficients for the 

Morison’s equation are given based on [19]. Note that the 

effects of wave diffraction and radiation as well as the 

nonlinear interaction between waves and the floating body are 

not considered in the modeling. Although OrcaFlex has its 

limitations, it can provide us first-cut results in a very short 

time. 

Based on the approach used by Fitzgerald and Bergdahl [20], 

and after running a series of OrcaFlex simulations with various 

mooring configurations, we present an "acceptable" mooring 

design (Fig. 5), for which the deviation of pitch is less than 25 

degrees. The FPA model is connected to eight mooring lines 

that are divided into two layers. Each layer has four lines in the 

configuration of a cross, and each mooring line is connected to 

a spring system. The spring stiffness is equal to 160kn/m and is 

determined based on a series of OrcaFlex runs. 

Incident wave 

direction

Heave

Sway

Surge

Yaw Pitch

Roll

Inflow 

boundary 

Slip wall 

boundary 

Symmetry 

boundary 

Slip wall 

boundary 

Bottom wall 

boundary 

Point wave 

absorber Top boundary 

(pressure) 

Sponge-layer 

zone 
4 

FIGURE 5. MOORING CONFIGURATION IN ORCAFLEX 

MODELING 

In the RANS simulation, the sway, roll and yaw motions are 

constrained, and the FPA is only allowed to move freely in 

surge, heave, and pitch. The mooring system is designed based 

on the one used in the OrcaFlex modeling. Given that a 

symmetry boundary is applied, only four mooring lines are 

specified along the symmetry boundary in the RANS 

simulation (Fig. 6). 

FIGURE 6. MOORING CONFIGURATION IN RANS 

MODELING 

RANS SIMULATION 

To model the details of the flow around the FPA, including 

wave overtopping and the nonlinear interaction between waves 

and the moored FPA, we utilized the RANS method. The FPA 

wave energy system is analyzed in both regular and irregular 

waves, where a 5th-order Stokes wave with a height of 10 m is 

applied for the regular wave study and a JONSWAP spectrum 

wave is applied for the irregular analysis. 

Meshing 

As shown in Fig. 7, the mesh is finer near the free surface in 

order to capture the wave dynamics and has a higher resolution 

around the FPA to model the details of the flow around it and 

its interaction with waves. In addition, prism-layer cells are 

placed along the FPA surface so that y+ satisfies the turbulence 

model requirement. 

The grid size Δx (in the wave propagation direction) is 

adjusted with the incident wavelength, and it is smaller than 

λ/80. The grid size Δz (in the vertical direction) near the free 

surface is in the range between H/10 and H/20, where H is the 

wave height. The total number of cells is on the order of 0.7 

million for the regular wave analysis and 1.5 million for the 

irregular wave analysis. 

FIGURE 7. MESH AROUND THE POINT WAVE 

ABSORBER MODEL 

In addition, a very small time step is utilized to avoid highly 

distorted cells, created by the morphing model due to the large 

movement of the FPA at each time step. The time step size is 

also given based on the incident wave period, and it is 

approximately T/300 in the regular wave analysis and Tp/600 in 

the irregular wave analysis, where T and Tp are the period and 

the peak period for the regular and irregular waves, 

respectively. 

All the RANS simulations are carried out on NREL’s highperformance computing (HPC) system. Each compute node 

consists of dual socket/quad-core 2.93 GHz Intel Nehalem 

processor with 12 GB of memory shared by all 8 cores. It takes 

about 8 hrs on 64 cores to complete 10 wave periods of time 

(approximately 3,200 time steps) for the regular wave analysis 

and 36 hrs on 128 cores to complete 15 peak wave periods of 

time (approximately 10,000 time steps) for the irregular wave 

analysis. 

Long linear wave comparison 

For long linear waves, the comparison of the heave and surge 

motions of the FPA are plotted in Fig. 8, which shows the 

results from the RANS method and OrcaFlex are in good 

agreement. When the wave is linear and the wave period is 

large, the vertical component of the excitation force is 

dominated by the buoyancy force, and the horizontal 

component is determined by the hydrodynamic wave loads. The 

buoyancy force is proportional to the immersed volume of the 

FPA, and the hydrodynamic wave loads in the horizontal 

direction can be calculated accurately through the use of 

Morison’s equation because the size of the FPA is much smaller 

StarCCM+

mooring line

StarCCM+

mooring line

=45°

OrcaFlex

mooring line

OrcaFlex

mooring line

Sps SpoCos
5

than the incident wavelength and wave overtopping barely 

occurs.

FIGURE 8. COMPARISON OF THE HEAVE AND SURGE 

MOTIONS FROM RANS AND ORCAFLEX (T=17.5 SEC)

Regular wave analysis

The response amplitude operators (RAOs) obtained from 

OrcaFlex only have good agreements with those obtained from 

the RANS method when the wave period is larger than 17 sec 

(Fig. 9). When the wave period is small, the RAOs predicted by

the RANS method are smaller than those predicted by

OrcaFlex. As opposed to the OrcaFlex results, the RANS 

solutions do not experience a resonance period in heave, at least 

within the range of wave periods that are studied. As shown in 

[18], the heave motion of the FPA generally follows the wave 

elevation when the incident wave period is sufficiently larger 

than the body natural period. When incident wave period 

decreases, the phase shift between the wave elevation and the 

FPA heave motion increases. As a result, the waves are more 

likely to overtop the FPA model (Fig. 10), particularly in 

extreme wave scenarios, where a wave with a height of 10 m is 

generally nonlinear when the wave period is smaller than 11 

sec. In addition, flow separation is observed around the float 

and the reaction plate in the RANS simulation. These nonlinear 

effects generally provide additional damping that constrains the 

FPA motions.

FIGURE 9. COMPARISON OF RAOS FROM RANS AND 

ORCAFLEX

FIGURE 10. THE POINT WAVE ABSORBER MODEL IN 

WAVES (T=7.5SEC)

Figure 11 plots the surge and pitch of the FPA in waves. The 

surge response is in the range between 3 m and 6 m, and the 

pitch angle is around 5 degrees. Both the surge and the pitch 

increase slightly as the wave period decreases.

FIGURE 11. SURGE AND PITCH MOTIONS OF THE FPA 

MODEL FROM RANS SIMULATIONS
6

Figure 12 shows the hydrodynamic pressure distribution near 

the FPA model at a time instant of t/T=7.65, and Figure 13 plots 

the pressure distributions on the FPA surface at three time 

instants. Note that the absorber is subject to a wave at its peak 

at t/T=10.49, and at its trough at t/T=9.99. Because the motion 

of fluid particles decreases rapidly with increasing depth below 

the free surface, the hydrodynamic wave impact on the float is 

more significant than that on the reaction plate.

FIGURE 12. HYDRODYNAMIC PRESSURE (SCALED BY 

ρgD) CONTOUR AROUND FPA (T=12.5SEC; H=10M)

FIGURE 13. THE PRESSURE DISTRIBUTION ON THE FPA 

SURFACE AT t/T=9.99 (LEFT), t /T=10.32 (MIDDLE), AND t

/T=10.49 (RIGHT) (T=12.5SEC)

The corresponding horizontal and vertical forces, including 

the buoyancy force, wave impact, and the weight of the FPA 

device are plotted in Fig. 14. Given that the fluid particle 

velocity is proportional to the incident wave frequency, the 

forces increase as the incident wave period decreases as 

expected. The forces on the FPA body under extreme wave 

conditions are useful information for further cost assessment.

FIGURE 14. HORIZONTAL AND VERTICAL FORCES ON 

THE FPA

Irregular wave analysis

In our irregular wave analysis, we only present a scenario 

where the FPA is modeled using a JONSWAP spectrum wave 

with a significant wave height of 10 m and a peak period of 

17.5 sec. The corresponding hydrodynamic response histories 

from the RANS method are shown in Fig. 15. The maximum 

heave motion is on the order of the maximum wave height. We 

plan to conduct a more detailed analysis with a longer period of 

simulation and various wave conditions in the future.

FIGURE 15. FPA HYDRODYNAMIC RESPONSE IN 

JONSWAP SPECTRUM WAVES
7

DISCUSSIONS

As the wave period decreases, the phase shift between the 

FPA heave motion and the wave elevation increases. Therefore,

the nonlinear interaction between waves and the FPA device 

becomes more significant, especially in small wave period and 

large wave height scenarios. As a result, the additional damping 

forces, including those due to flow separation and wave 

overtopping, limit the motion of the FPA, particularly under the 

extreme wave conditions.

The Morison’s equation prediction is expected to be 

applicable when the wave is linear. However, for some linear 

wave scenarios, the OrcaFlex results are deviated from the 

RANS simulations, as shown in Fig. 9. In addition to the 

aforementioned nonlinear effects, the relationship between the 

buoyancy force and the hydrodynamic wave loads and the 

feasible values of the added-mass and damping coefficients for 

predicting the excitation force of this particular FPA geometry 

require further investigation, particularly in the body axial 

direction. A more rigorous method is to compute the 

hydrodynamic coefficients through the use of a potential flow 

method.

Although using OrcaFlex for predicting the FPA motions has 

its limitations, OrcaFlex is still an efficient numerical tool that 

provides us with a very useful first-cut analysis, particularly for 

small amplitude linear wave scenarios. The computational cost 

for running such a design and optimization tool is small. On the 

other hand, under extreme wave conditions, the hydrodynamics 

of a FPA is complex. The interaction between waves and the 

moored FPA is often fully nonlinear, and wave overtopping 

often occurs. Therefore, the use of RANS models is suggested.

CONCLUSIONS

In this paper, we presented the results of our study of the 

hydrodynamics of a moored FPA in extreme wave conditions. 

We analyzed the baseline mooring configuration using 

OrcaFlex and modeled the detail of the flow using a RANS

method. The study shows that waves often overtop the FPA 

when the FPA is under extreme wave conditions. The FPA 

motions are constrained by the effects of viscous damping as 

well as the nonlinear interaction between waves and the moored 

FPA. Furthermore, through a few irregular wave simulations, 

we find that the maximum heave motion of the FPA is on the 

order of the maximum wave height, although more simulations 

are needed to confirm this. Overall, we found our mooring line 

design to be effective. We also found that the Morison’s

Equation method can be only used for a very few scenarios and 

with caution for extreme wave scenarios analyses.

FUTURE WORK

With all the promising results presented here, we intend to 

continue our research with the following efforts:

• Conduct a more comprehensive irregular wave analysis to 

understand the FPA’s behavior in the open ocean 

environment.

• Perform a detailed analysis of the cost-effectiveness of the 

RANS tool to understand what setup we should use for the 

future design; it is still too costly even though we have 

access to a HPC system.

• Conduct experimental tests to validate the numerical 

simulation presented in this study.

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