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Contract No. DE-AC36-08GO28308

A RANS Simulation of the Heave 

Response of a Two-Body 

Floating Point Wave Absorber

Preprint

Y. Yu and Y. Li

To be presented at ISOPE 2011

Maui, Hawaii

June 19-24, 2011

Conference Paper

NREL/CP-5000-50980

March 2011
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1

A RANS Simulation of the Heave Response of a Two-Body Floating-Point Wave Absorber

Yi-Hsiang Yu and Ye Li

National Wind Technology Center

National Renewable Energy Laboratory (NREL)

Golden, CO, 80401, USA

ABSTRACT

This paper presents a preliminary study on a two-body floating-point

wave absorber. For this study, a Reynolds-Averaged Navier-Stokes 

(RANS) computational method was applied for analyzing the 

hydrodynamic heave response of the absorber in operational wave 

conditions. The two-body floating wave absorber contains a float

section and a submerged reaction section. For validation purposes, the 

model was first assumed to be locked. The two sections were forced to 

move together as a single rigid body. The locked single-body model 

was used in a heave decay test that validated the RANS result with the 

experimental measurement. For the two-body floating-point absorber 

simulation, the two sections were connected through a mass-springdamper system, which simulated the power takeoff mechanism under 

design wave conditions. Overall, the details of the flow around the 

absorber and its nonlinear interaction with waves were investigated.

The power absorption efficiency of the two-body floating wave 

absorber in waves with a constant value spring-damper system was also 

examined.

KEYWORDS

Wave energy conversion (WEC); heave; Reynolds-averaged NavierStokes (RANS) equations; volume of fluid (VOF); free surface; 

floating-point absorber (FPA); power take-off (PTO)

INTRODUCTION

The extraction of energy from ocean waves has gained interest in recent 

years (Thorpe, 1999). A wide variety of technologies have been 

developed for converting wave energy into useful power, and many 

wave energy conversion (WEC) designs have been proposed. Falcão

(2010) and Drew et al. (2009) recently reviewed the fundamental 

operating principles of the technologies that have been used for WEC 

devices. These include oscillating water columns, bottom-hinged pitch 

devices, floating pitch devices, overtopping devices, and floating-point 

absorbers (FPAs). The FPA is regarded as one of the simplest and most 

promising WEC systems and will be the focus of this paper.

The study of WEC can be traced back to 1970s. Researchers first 

investigated the potential for harnessing energy from waves by using 

potential flow methods. Their studies were focused on understanding 

the complex hydrodynamics of the FPA and on predicting the 

maximum wave power absorption. Specifically, the studies focused on 

the wave absorption width (Budal and Falnes, 1975; Evans, 1976; Mei, 

1976) and on the wave power that can be absorbed by a given 

submerged body volume (Budal and Falnes, 1980). Reviews on these 

analytical works were presented in Falnes (2002; 2007). More recent

research focuses on improving the wave absorption efficiency of the 

system. As demonstrated in an experimental analysis (Bjarte-Larsson 

and Falnes, 2006),the heave response and the converted power of an 

axisymmetric heaving WEC were significantly increased through the 

use of hydraulic power take-off (PTO) and latching control. Several 

additional studies focused on the optimal control strategy for waves

(Korde, 1999; Yavuz et al., 2007), and an introduction to the 

fundamental theories for control and related tuning methods were 

described in Falnes (2002). However, these potential flow methods 

cannot provide accurate results because the nonlinear interaction 

between waves and the WEC device are assumed to be small, and the 

wave breaking and overtopping effects are excluded. A comprehensive 

understanding of a device requires the use of experimental methods or 

more advanced numerical methods such as the Reynolds-averaged 

Navier-Stokes (RANS) method. For example, Agamloh et al. (2008)

used RANS to study the power capturing efficiency of cylinder type 

buoys with a PTO mechanism.

Typically, FPAs are either single-body or multiple-body devices. For 

the single-body FPA, Yeung (2010) presented a systematic study on 

both hydrodynamics and power electronic problems. This paper

presents a study on a two-body FPA system. In general, a two-body 

FPA system includes a float section and a reaction section, and the 

system converts energy by utilizing the relative motion between the two 

sections. An example of a two-body FPA is Ocean Power Technology’s

(OPT’s) Power Buoy. OPT deployed two 40-kW utility-scale systems, 

one in Santona, Spain in 2008 and the other in Ohau, Hawaii in 2009 

(Fig. 1).
2

Figure 1. A prototype of OPT’s PowerBuoy wave energy generation 

system. NREL PIX # 17114

The ability to design efficient PTO systems is critical for the success of 

the wave energy industry. In particular, it is essential to understand the 

complex hydrodynamics of FPA wave energy systems. Accordingly, 

the main objective of this research was to analyze the hydrodynamics 

of a two-body FPA system and its power output in operational wave 

climates. Only the heave motion was considered in this study. After 

presenting the numerical method and the numerical wave tank settings,

a heave decay test was performed to validate the numerical model, 

where the floating section and the reaction section were assumed to be 

locked and moved as a single rigid body. The two sections of the FPA

were connected through a mass-spring-damper system, which was 

applied to model the PTO mechanism. The details of the flow around 

the FPA model, the translating motion of the two sections, as well as 

their motion velocity, were examined. In addition, the maximum power 

that this particular two-body FPA model can absorb was studied.

MODELING

RANS method

A finite volume method-based RANS model (StarCCM+) was applied 

for solving the details of the unsteady incompressible flow field around 

the FPA under various wave conditions. The continuity equation and 

the Navier-Stokes equations are given as

U U U F T

U

+ ⋅∇ = −∇ + + ∇ ⋅

∇ ⋅ =

t p b ( )

0,

ρ

(1)

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 were discretized over a computational mesh

and were solved using the transient SIMPLE algorithm to linearize the 

equations and to achieve pressure-velocity coupling. The resulting set 

of algebraic equations was solved through the use of an algebraic 

multigrid method. A k-ω SST turbulence model was applied with a 

two-layer all y+ wall treatment model, and a second order implicit 

scheme was applied for time marching. The water free surface was 

captured using a VOF method. The mesh around the FPA followed the 

FPA motion. A morphing model was adopted to move the mesh, and an 

arbitrary Lagrangian-Eulerian method was applied for handling the cell 

movement and its deformation.

In the study, the FPA only was allowed to move in heave, and the 

mooring system was not considered. The heave response was calculated 

by solving the equation of motion, which is given as

mb t = Fd + FPTO a (2)

where mb is the mass of the body, at is the acceleration, and Fd is the 

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

force, and the weight of the body. In addition to Fd, the PTO force FPTO

is the only external force acting on the system. The corresponding 

heave displacement was calculated by integrating the accelerations over 

time, and the equation of motion calculation was coupled with the 

RANS simulation through iterations.

Numerical wave tank settings

Figure 2 shows the computational domain and the domain boundaries 

of the numerical wave tank. To reduce the size of the problem, a 

symmetric boundary was applied along the x-z plane. The water depth 

was equal to 70m. The computational domain was 100m wide 

(0m≤y≤100m), 170m high (-70m≤z≤100m), and 7 wavelengths long (-

2λ≤x≤5λ). The incident wave condition was specified at the inflow 

boundary. A sponge-layer method was applied, in which a damping 

zone (2λ in the wave propagation direction) was placed in front of the 

down wave boundary to absorb the outgoing and reflecting waves,

without creating additional numerical disturbance. This sponge-layer 

method was tested successfully using the same numerical wave tank 

settings and without the presence of the absorber.

Figure 2. Computational domain and domain boundaries

FPA model and PTO

The geometry of the FPA was designed using SolidWorks. The 

designed weight of the full-scale model was about 249.5 metric tons, 

and the center of gravity was located 22.4 m below the mean free 

surface. The FPA geometry was further modified in the numerical 

model. The supporting jacket on the bottom of the central column and 

the detail of the reaction plate were further simplified. Nevertheless, the 

center of buoyancy was kept close to the SolidWorks design. Here, we 

only considered a basic structural design of the FPA model and ignored 

the effects of mooring lines.
3

As shown in Fig. 3, two FPA models were used in the study. The single 

body system assumes that the absorber was locked, and the whole 

device moved as a rigid body. All the parts were, therefore, moving in 

tandem. The two-body model assumed that the whole FPA model was 

separated into two sections, a floating one and a fully submerged one

(neutrally buoyant), and the two were connected through the use of a 

mass-spring-damper system. The diameter of the vertical column

sections was also modified to maintain the same immersed volume. 

Note that the investigation was not focused on the optimal control 

strategy or the feasible value of the spring stiffness. The spring was 

utilized only to connect the two sections, and a small value of 19.7

kN/m was applied. A damper was utilized to represent the PTO 

mechanism. FPTO and the generated power PPTO are defined as

and , 2

PTO PTO FPA PTO PTO FPA F = C u P = C u (3)

where CPTO is the damping coefficient, and uFPA is the relative 

translating velocity between the floating section and the reaction 

section. The value of the damping coefficients used in most of the 

simulations was 254 kNsm-1

, which was on the same order of the one 

used in Agamloh et al. (2008) after scaling.

Figure 3. FPA geometry and dimensions

Meshing

Figure 4. Mesh around the point wave absorber model

To capture both the wave dynamics and the details of the flow around 

the FPA, the mesh was finer near the free surface and near the FPA 

(Fig. 4), where hanging node cells also were implemented. In addition, 

prism-layer cells were placed along the FPA surface, and the height of 

the first layer was set so that the value of y+ satisfied the turbulence 

model requirement. Furthermore, the grid size ∆x (in the wave 

propagation direction) was determined by the incident wavelength, and 

it was smaller than λ/80. The grid size ∆z (in the vertical direction) near 

the free surface was adjusted according to the wave height H, and it 

was in the range between H/16 and H/24. The total number of cells for 

the mesh used in the RANS simulation was on the order of 0.8~1.0

million. Moreover, mesh morphing can create highly distorted cells if 

the time step is not sufficiently small. Therefore, a small time step of 

T/300 was utilized in the study, where T is the incident wave period. 

All the RANS simulations are carried out on NREL’s high-performance 

computing (HPC) system1

VALIDATION

. It takes about 12 hours on 64 cores to 

complete 8~10 wave periods of time (approximately 3000 time steps).

To validate the numerical prediction, a wave tank test was conducted at 

UC Berkeley's wave tank in December 2010. A 1:100 scale single body

model was built based on the full scale SolidWorks design. When the 

FPA model was at rest, the mean water level was approximately 

0.018m (model scale) from the top of the float, and wave tank was 68

m long, 2.4 m wide, and 1.5 m deep (Fig. 5).

Figure 5. The single body FPA model in the experimental wave tank

including tank dimensions

To capture the FPA motion, a 2D motion tracking system next to the 

wave tank was utilized, and the motion tracking system used passive 

markers on the buoy to create targets for the motion tracking software. 

 1 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.

Tank water level

2.44 m

1.5 m

1/100 scale model

Initial heave 

displacement: 0.02m

FPA model

View window
4

The motions were captured as a 2D projection orthogonal in the 

direction of the propagation of waves in the tank. A LabVIEW data 

acquisition system, based on a National Instruments Compact RIO 

controller, with a channel-to-channel optically isolated analog input 

module (NI 9239), was used to collect the data.

The heave decay test was performed with an initial displacement of 

0.02m (model scale). The comparison of the heave decay test between 

the RANS simulation and the experimental measurement is presented 

in Fig. 6. The heave decay period was about 10 seconds, and the RANS 

result agreed fairly well with the experimental data. A small 

discrepancy was probably due to the slight difference in the model 

geometry.

Figure 6. Heave decay from RANS and from the experimental 

measurement

REGULAR WAVES ANALYSIS

Both the single model and the two-body model were examined in the 

numerical wave tank through the use of the RANS method. A 5th-order 

Stokes wave was specified at the inflow boundary.

Single body FPA model

Figure 7. Comparison of the FPA response in heave (scaled by H) in 2 

m and in 4 m waves

The heave response amplitude operator (RAO) of the (locked) singlebody FPA model in two different incident wave heights, 2 m and 4 m; 

is plotted in Fig. 7. The heave response was proportional to the incident 

wave height for large wave period scenarios. A resonant period of 10 

seconds was observed in the 2 m wave scenarios. This was consistent 

with the natural decay period obtained from the decay test. However, 

this resonance was not observed in the 4 m wave scenarios, and it is 

discussed in a later section.

The instantaneous heave response of the FPA in 2 m waves, with 

different wave periods and the linear theory-based wave elevation, are 

plotted in Fig. 8. When the wave period was large, the heave response 

generally followed the wave motion. On the other hand, the phase shift 

between the FPA heave motion and the wave elevation increased as the 

wave period became smaller. When the phase shift was increased, the 

nonlinear interaction between waves and the FPA model became more 

significant, especially under waves with larger wave heights.

Figure 8. Heave response of the FPA model in waves

Figure 9. FPA model in waves at t/T=8.76 (left) and t/T=9.43 (right)

For this particular single body FPA model, wave overtopping was not 

observed in the 2 m wave scenarios. On the other hand, wave 

overtopping occurred in the FPA in the 4 m wave scenarios, when the 

wave period was smaller than 12 seconds. In one of the 4 m wave 

scenarios (T=7.5 seconds), the entire float was out of the water when 

t/T=8.76, and waves overtopped the float when t/T=9.43 (Fig. 9). This 
5

suggests that wave overtopping could induce additional constraint on 

the FPA heave motion, as shown in Fig. 7, where the RAO for the 4 m 

wave scenarios was smaller than that for the 2 m wave scenarios when 

the wave period was smaller than 12.5 seconds.

Figure 10 shows the hydrodynamic pressure distribution near the FPA 

model at a time instant of t/T=9.43. Since the motion of fluid particles 

decreases rapidly with increasing depth below the free surface, the 

hydrodynamic wave impact on the float was more significant than on 

the reaction plate. Moreover, when wave overtopping occurred, the 

nonlinear hydrodynamic effect provided an additional damping force to 

reduce the FPA heave motion.

Figure 10. Hydrodynamic pressure (scaled by ρgD) contour around the 

single body FPA model (T=7.5seconds; H=4m)

Two-body FPA MODEL

Figure 11. Heave response of the float and the reaction sections

This section presents the prediction for the hydrodynamic heave 

response of the two-body FPA model and an estimation of generated 

power, without applying any control method. The effect of PTO on the 

hydrodynamic response of the float and reaction sections was 

investigated here, where a wave with a height of 4 m and a period of 

12.5 seconds was given. The heave response of the two sections, with 

and without the presence of PTO, is plotted in Fig. 11. Since the 

hydrodynamic wave effect decreases with the depth, the amplitude of 

the heave motion for the float section was greater than that for the 

reaction section. When PTO was considered, the relative motion 

between the two bodies was reduced, and a phase shift was induced.

An example of the instantaneous velocity of the two sections and the 

relative velocity uFPA is plotted in Fig. 12. The generated power was 

calculated by following Eq. (3). It is proportional to the square of the 

relative translational velocity of the two sections.

Figure 12. Translational velocities of the float and the reaction sections

and the relative velocity between the two

Figure 13. Instantaneous power of the two-body FPA system in waves

(T=12.5 seconds)

The power generation under different wave heights also was 

investigated, and an example of the instantaneous power of the FPA 

system (with a given spring stiffness and a damping coefficient) is 

shown in Fig. 13. Through a series of RANS simulations (Fig. 14), the 

study showed that the generated power increased nonlinearly with the 

incident wave height. According to linear theory, the maximum wave 

absorption is proportional to H2

. However, the prediction from the 
6

RANS method was less than that, especially when the wave period was 

smaller, and the nonlinear effects were more significant. This indicated 

that those nonlinear effects, created by the complex geometry of the 

two-body FPA, the mass-spring-damper system, the flow viscosity, and 

the nonlinear interaction between waves and the FPA, influenced the 

FPA motion as well as the resulting power generation in operational 

wave conditions.

Figure 14. Maximum peak power generation for the two-body FPA 

system in different wave conditions (wave breaking occurred

in the 7 m wave scenarios, when the wave period was smaller 

than 6 seconds)

In fact, wave overtopping was also observed in the large wave height 

scenarios. Figure 15 shows the hydrodynamic pressure contour around 

FPA along the z=0 plane at a time instant of t/T=5.38, where the wave 

height was 7 m and the wave period was 7.5 seconds. Similar to those 

single body FPA scenarios, the hydrodynamic pressure on the float 

section was increased and an additional heave reduction force was 

induced.

Figure 15. Hydrodynamic pressure (scaled by ρgD) contour around the 

two-body FPA model (T=7.5seconds; H=7m)

According to Budal and Falnes (1975), the maximum wave power Pmax

that a heaving axisymmetric body can absorb is

, max max P = JL (4)

where J is the wave energy flux, and Lmax is the absorption width, 

which is defined as Lmax=λ/2π. For linear deep-water waves, λ=g/2π

and J=ρg2

TH2/(32π). Budal and Falnes (1980) proposed another upper 

limit (also referred to as Budal’s upper bound) for the wave power Pu

that can be absorbed by a given submerged body volume ∀. It is 

4T .

Pu πρgH <

∀

(5)

The two curves represent the theoretical prediction of the maximum 

wave energy that can be captured by a semi-submerged heaving body

with optimum heaving amplitude (Falnes, 2007).

Figure 16 plots the RANS prediction of the maximum peak power 

generated from the heave motion of the two-body FPA and the 

comparison with the theoretical upper limit obtained from Eqs. (4) and 

(5). The point of intersection of the two theoretical curves can be 

defined as (T, P) = (Tc, Pc), where

T (32 g /H) and P ( /8)( / 2) . 3/ 2 3 5 1/ 4

c

4 -2 1/4

c = π ∀ = ρg ∀ H (6)

For this particular two-body FPA system, the resonance occurred when 

the incident wave period was around 7 seconds. In addition, given that 

no specific control method was applied in the RANS simulation, the 

power capturing efficiency was lower than the theoretical solution, as 

expected.

Figure 16. Maximum peak power generation for the FPA system from 

the RANS method and the theoretical curves for the 

maximum power absorption (modified after Falnes 2007)

DISCUSSION

The RANS simulation showed that the phase shift between the FPA 

heaving motion and the wave elevation increases as the wave period 

decreases. As a result, the nonlinear interaction between waves and the 

FPA device can be significant, and wave overtopping may occur. Given 

that the weight of the float section for the two-body FPA is less than the 
7

weight of the single body FPA, the resonant period for the float section 

is smaller. Therefore, wave overtopping only was observed in the large 

wave scenarios. Nevertheless, the nonlinear effects can mitigate the 

FPA heave motion, and the resulting power output can be reduced.

For the maximum power generation analysis, Falnes (2007) mentioned 

that there is a significant improvement on the power absorption 

efficiency if latching control is applied. Furthermore, when control is 

applied and T=Tc, the maximum power absorption can reach up to 50% 

of the intersection value Pc, depending on the wave height, the 

immersed volume (buoyancy force), and the absorber geometry.

However, our RANS simulation was performed with a constant value

mass-spring-damper system, and the system was not optimal (no 

control was applied). As a result, the maximum power absorption was 

only about 30% of Pc, and the power absorption efficiency decreased

rapidly in the sup-resonant period region. The application of control in 

the FPA system and the optimal geometry and dimension for the device 

requires further investigation.

CONCLUSIONS

This paper presented preliminary results of the hydrodynamics of a

particular FPA obtained with a RANS model. The RANS model was 

first validated with the experiment in a heave decay test. Through a 

series of RANS simulations, the FPA heave response in waves was 

studied, with and without the present of PTO mechanism. In addition,

the maximum power that the FPA can generate under operational wave

conditions, with a constant value mass-spring-damper system, was also 

investigated. The study showed that the effect of the nonlinear 

interaction between waves and the FPA device on power generation can

be significant, even in operational wave conditions, since power 

generation was directly associated with the motion of FPA. In addition, 

the maximum power absorption efficiency of this particular two-body

FPA system was about 30% when the incident wave was at the resonant

period. Overall, the performance of the FPA wave energy system is 

promising.

FUTURE WORK

There are a number of problems to be addressed in studying this 

particular FPA. The following summarizes intended future research:

• This RANS model is only validated with a single body decay 

test. More experimental tests, especially two-body tests, will

be conducted for validation.

• The power prediction of the FPA’s motion is without optimal 

control. Thus, a study on optimizing the power absorption 

efficiency, in both regular and irregular waves, is required. 

This will include the application of a control method and the 

feasible value of the damping coefficient for representing the 

PTO mechanism.

• Studies on the effects of the mooring system and other 

translational and rotational motions on power absorption 

efficiency are needed.

• More importantly, this study only focuses on the

hydrodynamics of the FPA. A comprehensive design of an

FPA should combine both hydrodynamics and power 

electronics as presented by Yeung et al. (2010) . Thus, a 

coupling study of this two-body FPA will be conducted.

REFERENCES

Agamloh, E., Wallace, A. and Von Jouanne, A. (2008). "Application of 

fluid-structure interaction simulation of an ocean wave energy 

extraction device", Renewable Energy, Vol. 33, No. 4, pp. 748-757.

Bjarte-Larsson, T. and Falnes, J. (2006). "Laboratory experiment on 

heaving body with hydraulic power take-off and latching control", 

Ocean Engineering, Vol. 33, No. 7, pp. 847-877.

Budal, K. and Falnes, J. (1975). "A resonant point absorber of oceanwave power", Nature, Vol. 256, pp. 478-479, corrigendum 257:626.

Budal, K. and Falnes, J. (1980). "Interacting point absorbers with 

controlled motion", Power from sea waves, pp. 381-399.

Drew, B., Plummer, A. and Sahinkaya, M. (2009). "A review of wave 

energy converter technology", Proceedings of the Institution of 

Mechanical Engineers, Part A: Journal of Power and Energy, Vol. 

223, No. 8, pp. 887-902.

Evans, D. (1976). "A theory for wave-power absorption by oscillating 

bodies", Journal of Fluid Mechanics, Vol. 77, No. 01, pp. 1-25.

Falcão, A. (2010). "Wave energy utilization: A review of the 

technologies", Renewable and Sustainable Energy Reviews, Vol. 14, 

pp. 899-918.

Falnes, J. (2002). "Ocean waves and oscillating systems", Cambridge 

University Press.

Falnes, J. (2007). "A review of wave-energy extraction", Marine 

Structures, Vol. 20, No. 4, pp. 185-201.

Korde, U. (1999). "Efficient primary energy conversion in irregular 

waves", Ocean Engineering, Vol. 26, No. 7, pp. 625-651.

Mei, C.C. (1976). "Power extraction from water waves", Journal of 

Ship Research, Vol. 20, pp. 63-66.

Thorpe, T.W. (1999). "A brief review of wave energy", Harwell 

Laboratory, Energy Technology Support Unit.

Yavuz, H., Stallard, T., McCabe, A. and Aggidis, G. (2007). "Time 

series analysis-based adaptive tuning techniques for a heaving wave 

energy converter in irregular seas", Proceedings of the Institution of 

Mechanical Engineers, Part A: Journal of Power and Energy, Vol. 

221, No. 1, pp. 77-90.

Yeung, R.W., Peiffer, A., Tom, N. and Matlak, T. (2010). "Design, 

analysis,and evaluation of the UC-Berkeley wave-energy extractor", 

Proc. 29th Int. Conf. on Ocean, Offshore and Arctic Eng., OMAE, 

Shanghai,China.
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A RANS Simulation of the Heave Response of a Two-Body Floating 

Point Wave Absorber: Preprint

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14. ABSTRACT (Maximum 200 Words)

A preliminary study on a two-body floating wave absorbers is presented in this paper. A Reynolds-Averaged NavierStokes computational method is applied for analyzing the hydrodynamic heave response of the absorber in 

operational wave conditions. The two-body floating wave absorber contains a float section and a submerged reaction 

section. For validation purposes, our model is first assumed to be locked. The two sections are forced to move 

together with each other. The locked single body model is used in a heave decay test, where the RANS result is 

validated with the experimental measurement. For the two-body floating point absorber simulation, the two sections 

are connected through a mass-spring-damper system, which is applied to simulate the power take-off mechanism 

under design wave conditions. Overall, the details of the flow around the absorber and its nonlinear interaction with 

waves are investigated, and the power absorption efficiency of the two-body floating wave absorber in waves with a 

constant value spring-damper system is examined.

15. SUBJECT TERMS

RANS simulation; offshore wind turbines; two-body floating point wave absorber; Wave Energy Conversion (WEC); 

heave; Reynolds-averaged Navier-Stokes (RANS) equation; Volume Of Fluid (VOF); free surface; Floating-Point 

Absorber (FPA);Power Take Off (PTO)

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