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Contract No. DE-AC36-08GO28308

Importance of Second-Order 

Difference-Frequency WaveDiffraction Forces in the 

Validation of a Fast SemiSubmersible Floating Wind 

Turbine Model

Preprint

Alexander J. Coulling and Andrew J. Goupee

University of Maine

Amy N. Robertson and Jason M. Jonkman

National Renewable Energy Laboratory

Presented at the ASME 2013 32nd International Conference on 

Ocean, Offshore and Arctic Engineering

Nantes, France

June 9-14, 2013

Conference Paper

NREL/CP-5000-57697

June 2013
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IMPORTANCE OF SECOND-ORDER DIFFERENCE-FREQUENCY WAVEDIFFRACTION FORCES IN THE VALIDATION OF A FAST SEMI-SUBMERSIBLE 

FLOATING WIND TURBINE MODEL

Alexander J. Coulling

University of Maine

Orono, Maine, U.S.A.

Andrew J. Goupee

University of Maine

Orono, Maine, U.S.A.

Amy N. Robertson

National Renewable Energy Laboratory

Golden, Colorado, U.S.A.

Jason M. Jonkman

National Renewable Energy Laboratory

Golden, Colorado, U.S.A.

ABSTRACT

To better access the abundant offshore wind resource, 

efforts are being made across the world to develop and improve 

floating offshore wind turbine technologies. A critical aspect of 

creating reliable, mature floating wind turbine technology is the 

development, verification, and validation of efficient computeraided-engineering (CAE) tools. The National Renewable 

Energy Laboratory (NREL) has created FAST, a 

comprehensive, coupled analysis CAE tool for floating wind 

turbines, which has been verified and utilized in numerous 

floating wind turbine studies. Several efforts are underway to 

validate the floating platform functionality of FAST to 

complement its already validated aerodynamic and structural 

simulation capabilities. The research employs the 1/50th-scale 

DeepCwind wind/wave basin model test dataset, which was 

obtained at the Maritime Research Institute Netherlands 

(MARIN) in 2011. This paper describes further work being 

undertaken to continue this validation. These efforts focus on

FAST’s ability to replicate global response behaviors associated 

with dynamic wind forces and second-order differencefrequency wave-diffraction forces separately and 

simultaneously.

The first step is the construction of a FAST numerical 

model of the DeepCwind semi-submersible floating wind 

turbine that includes alterations for the addition of second-order 

difference-frequency wave-diffraction forces. The 

implementation of these second-order wave forces, which are 

not currently standard in FAST, are outlined and discussed. 

After construction of the FAST model, the calibration of the 

FAST model’s wind turbine aerodynamics, tower-bending 

dynamics, and platform hydrodynamic damping using select 

test data is discussed. Subsequently, select cases with coupled 

dynamic wind and irregular wave loading are simulated in 

FAST, and these results are compared to test data. Particular 

attention is paid to global motion and load responses associated 

with the interaction of the wind and wave environmental loads. 

These loads are most prevalent in the vicinity of the rigid-body 

motion natural frequencies for the DeepCwind semisubmersible, with dynamic wind forces and the second-order 

difference-frequency wave-diffraction forces driving the global 

system response at these low frequencies. Studies are also 

performed to investigate the impact of neglecting the secondorder wave forces on the predictive capabilities of the FAST 

model. The comparisons of the simulation and test results 

highlight the ability of FAST to accurately capture many of the 

important coupled global response behaviors of the DeepCwind 

semi-submersible floating wind turbine.

INTRODUCTION

The next frontier in offshore wind energy is that of floating 

offshore wind technology, as evidenced by the multiple 

research efforts being put forth by entities across the world

(e.g., see [1-6]). Floating technologies vastly expand the 

opportunity for capturing offshore wind energy compared to 

current fixed-bottom technologies that require shallow-water 

sites; suitable shallow-water sites are not as prevalent as 

suitable deep-water sites. In addition to harnessing the higher 

energy winds in deeper water, floating wind turbine technology 

provides opportunities for reducing the cost of offshore wind 

energy by eliminating many of the expensive installation 
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procedures employed in current fixed-bottom systems. To 

bring floating offshore wind turbine technology to maturity, 

however, efficient, accurate computer-aided-engineering (CAE) 

tools must be created, verified, and validated.

In this paper, the focus is on FAST [7, 8], the popular opensource floating wind turbine CAE tool that was created by the 

National Renewable Energy Laboratory (NREL). FAST has 

been previously verified [1, 2], and current efforts focus on 

validating its coupled aero-hydro-servo-elastic predictive 

capabilities for floating wind turbines. Recently, progress has 

been made in validating FAST for floating wind turbine 

systems that are supported by a tension-leg platform [9], a sparbuoy [10], and a semi-submersible platform [11] that uses the 

DeepCwind 1/50th-scale wind/wave basin model test data [5, 6, 

12-14]. In the investigations of the DeepCwind semisubmersible floating wind turbine system, strong correlations 

were observed between the FAST predictions and test data in 

many scenarios. However, one major exception was an absence 

of low-frequency responses associated with second-order 

difference-frequency wave-diffraction loads in the FAST output

[11]. The low-frequency response of the DeepCwind semisubmersible is driven by dynamic wind loading, second-order

difference-frequency wave loads, and their interaction with one 

another [5, 14]. Exclusion of the second-order wave forcing in 

the current version of FAST prevents a proper prediction of the 

system response in this frequency range. To better assess the 

importance of FAST’s omission of these physics, this work 

revisits the semi-submersible validation while including 

second-order wave-diffraction forces using the simple-toimplement Newman’s approximation [15, 16].

This paper is organized as follows: In the first section, a 

brief overview of the semi-submersible floating wind turbine 

model is given along with the methods employed to construct a 

calibrated FAST model of the system. The next section 

discusses the implementation of the second-order differencefrequency wave-diffraction forces into the FAST tool. 

Subsequently, the environmental conditions employed in this 

work are detailed. Afterward, the improvement in the FAST 

simulation predictions when including second-order wave 

diffraction effects is assessed. Then, the ability of the improved 

FAST model to predict the interaction of the second-order wave 

forcing and dynamic wind loads for the floating wind turbine 

global response is evaluated. The paper concludes with a 

discussion of the results presented.

MODEL DESCRIPTION

In this section, a brief description of the DeepCwind semisubmersible floating wind turbine is presented. In addition, a 

short discussion on tuning the FAST model with key pieces of 

test data is also given. This tuning is required to account for 

unknown test parameters and some imperfections in the 

numerical model. Fig. 1 depicts the degrees of freedom (DOF)

and the general wind and wave orientations used in this study.

Fig. 1 Depiction of degrees of freedom, wind orientations and 

wave orientations.

Photo by: Andrew Goupee, University of Maine

Fig. 2 Image of 1/50th-scale model of the DeepCwind semisubmersible floating wind turbine.

Froude scaling (e.g. see [17]) was employed to create a 

1/50th-scale model of the DeepCwind semi-submersible, shown 

in Fig. 2, in addition to an assortment of scaled environmental 

conditions, for testing in the Maritime Research Institute 

Netherlands (MARIN) offshore basin. The properties of the 

DeepCwind semi-submersible, and the corresponding test 

results discussed in this paper, are all presented at full scale. 

More information on the specific scaling methods employed for 

the DeepCwind tests can be found in [12, 18].

As illustrated in Fig. 2, the DeepCwind semi-submersible 

floating platform consists of three outer columns connected 

through a series of slender pontoons and braces to a central 

column. The platform, which was designed to be rigid, 

supports a modified version of the NREL 5-MW reference wind 

turbine [19]. The wind turbine modifications include zero 

blade precone, zero shaft-tilt, a slightly larger mass, and finally, 

rigid blades to eliminate the aero-elastic complexities of 

flexible blades during testing. The wind turbine is connected to 

the platform via a flexible tower. The entire system is moored 

via three slack, catenary lines attached to the outer columns. 

An overview of key system properties is given in Tables 1-3. 
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Wind turbine and tower properties are given in Table 1, floating 

platform properties in Table 2, and mooring properties in 

Table 3.

Table 1 Wind turbine and tower gross properties.

Rotor Orientation, Configuration Upwind, 3 Blades

Rotor, Hub Diameter 126.0 m, 3.0 m

Hub Height Above Still-water Line 

(SWL)

90.0 m

Height of Tower-Top Flange Above SWL 87.6 m

Overhang, Shaft Tilt, Precone 10.58 m, 0°, 0°

Vertical Distance Along Tower Centerline 

Between Tower Top and Shaft 

2.4 m

Total Tower-Top Mass 397,160 kg

Tower Height 77.6 m

Tower-Base Elevation Above SWL 10.0 m

Total Tower Mass 302,240 kg

Table 2 Floating platform gross properties.

Total Draft 20.0 m

Elevation to Platform Top (Tower Base) 

Above SWL

10.0 m

Platform Mass, Including Ballast 13,444,000 kg

Displacement 13,986.8 m3

Center of Mass (CM) Location Below 

SWL Along Platform Centerline

14.4 m

Platform Roll Inertia About CM 8.011×109 kgm2

Platform Pitch Inertia About CM 8.011×109 kgm2

Platform Yaw Inertia About Platform 

Centerline

1.391×1010 kgm2

Table 3 Mooring system properties.

Number of Mooring Lines 3

Angle Between Adjacent Lines 120°

Depth to Anchors Below SWL (Water Depth) 200.0 m

Depth to Fairleads Below SWL 14.0 m

Radius to Anchors from Platform Centerline 837.6 m

Radius to Fairleads from Platform Centerline 40.868 m

Unstretched Mooring Line Length 835.5 m

Equivalent Mooring Line Mass in Water 108.63 kg/m

Equivalent Mooring Line Cross Section 

Extensional Stiffness 753.6×106 N

Additional information on system properties, such as platform 

geometry, hydrodynamic parameters, and mooring restoring 

forces, can be found in [11, 13]. Information on the model 

wind turbine performance is detailed in [11, 12].

As a final step in the completion of the FAST floating wind 

turbine model, certain aspects of the model must be tuned. 

These include wind turbine aerodynamics, tower-bending 

dynamics, and platform hydrodynamic damping. Tuning of the 

wind turbine aerodynamics is required to emulate the correct 

wind turbine torque, and more importantly, the thrust because 

this is the major aerodynamic global response driver, under 

multiple tip-speed ratios. The tuning is performed through a 

numerical optimization procedure that tailors the wind blade 

airfoil section lift and drag coefficients, initially created with 

XFOIL [20], to match the experimentally measured wind 

turbine performance. A comparison of the measured and tuned 

wind turbine thrust curves for a steady hub-height wind speed 

of 21.80 m/s is given in Fig. 3. A complete summary of the 

wind turbine performance tuning is covered in [9, 11].

Fig. 3 Comparison of wind turbine thrust data and calibrated 

FAST results under a steady wind of 21.80 m/s.

Next, the tuning of the FAST tower inputs is discussed. 

After generating and inputting the distributed tower properties 

and finite-element-method-generated tower mode shapes 

required for FAST simulations, FAST’s modal stiffness tuners 

[7] were altered to match the experimentally measured, 

fundamental tower-bending frequencies. This process, detailed 

in [11], yields fundamental tower-bending frequencies in the 

fore-aft and side-side directions of 0.35 Hz and 0.38 Hz 

respectively.

To complete the tuning of the FAST model, a quadratic 

hydrodynamic drag damping model is added to the FAST 

model to account for the omitted viscous drag, and the 

coefficients are tuned to emulate rigid-body motion, free-decay 

experimental results. The tuning of the drag model, which 

augments the radiation damping found in the standard version 

of FAST, is documented in [11]. Because the surge response is 

of primary concern in this work, a comparison of the surge 

DOF damping ratio as a function of amplitude from 

experiments and the tuned FAST model is given in Fig. 4. The 

surge quadratic-drag damping coefficient employed in [11] 

(1.25×106 Ns2

/m2) corresponds to the simulation in Fig. 4, 

which correlates well with the test data for modest surge 

amplitude motions (1.5 to 3.5 m). In this work, as will be 

discussed in a later section, a mild, operational sea state is 

considered wherein the quadratic-drag damping coefficient 

used in [11] tends to over-predict the surge damping for the 

small surge motions the sea produces. Therefore, a second 

surge quadratic-drag damping coefficient will be investigated 

that is 10% of that used in [11] (1.25×105 Ns2

/m2). The free 

decay simulation corresponding to this reduced surge drag 
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damping coefficient is also shown in Fig. 4. As can be seen in 

the figure, the reduced quadratic-drag coefficient produces a 

better fit to the experimental data for surge amplitudes of 1 m 

or less.

Fig. 4 Comparison of surge free-decay damping response from

test data and FAST simulations. 

To complete this section, a comparison of the rigid-body 

natural periods as obtained from test data and FAST 

simulations is given in Table 4. As the table shows, there is 

good agreement between the test data and FAST predictions.

Table 4 Rigid-body natural periods obtained from test data and 

FAST simulations.

DOF Data (s) FAST (s)

Surge 107 107

Sway 112 113

Heave 17.5 17.3

Roll 26.9 26.7

Pitch 26.8 26.8

Yaw 82.3 82.7

SECOND-ORDER DIFFERENCE-FREQEUNCY WAVEDIFFRACTION FORCE FORMULATION

In the current standard version of FAST, the true linear 

time-domain hydrodynamics are implemented [7]. This 

formulation, however, omits the nonlinear, second-order wave 

diffraction effects that occur at the sum and difference of the 

frequency components in the incident waves (e.g., see [21]). 

As observed in [5, 13, 14], the second-order differencefrequency wave-diffraction forces are important for properly 

simulating the global response of the DeepCwind semisubmersible. In this paper, these second-order wave-diffraction 

forces are included in the custom FAST tool in order to assess 

the importance of including these effects in validating the 

DeepCwind semi-submersible numerical model. The 

remainder of this section outlines the formulation of the 

second-order wave-diffraction force implementation that is 

employed in the custom FAST tool. 

To begin, we note that the time-varying wave-surface 

elevation h(t) can be written as the sum of its wave frequency 

components in the form

h(t) = RR�an iωnt

N

n=1

, (1)

where N is the number of frequency components, an is the nth

complex-valued wave component amplitude (including phase), 

ωn is the nth wave component frequency, t is time and i is 

imaginary unity. With the coefficients an in Eq. 1 obtained 

from a simple discrete Fourier transform analysis of the 

experimentally measured calibrated wave-elevation time series, 

the second-order difference-frequency wave diffraction force 

Fj

D(t) can be computed with the equation (e.g., see [22])

Fj

D(t) = RR� � anam

∗

N

m=1

Dn

(j) i(ωn−ωm)t

N

n=1

, (2)

where Dn

(j) is the complex difference-frequency second-order 

transfer function for the j

th DOF and the superscript * denotes 

the complex conjugate. As shown in [22], Eq. 2 is often 

separated into terms that are constant (mean-drift force) and 

those that are not (slowly-varying force). This is accomplished 

by first separating Eq. 2 into three regions: n = m, n > m, and 

n < m. Upon setting k = n − m, noting that Dn

∗(j) = Dm

(j)

, and 

performing a series of straightforward manipulations, the 

desired result is produced:

Fj

D(t) = �|an|

2

N

n=1

Dnn

(j) + RR � Xk

(j) iωkt

N−1

k=1

, (3)

where the first term is the mean-drift force, the second is the 

slowly varying force and Xk

(j) is computed as

Xk

(j) = 2 � am+kam

∗ Dm+k,m

(j)

N−k

m=1

. (4)

For implementation in the custom FAST tool, only those 

second-order wave diffraction forces associated with the surge 

DOF (j = 1) are included because they are the most prominent 

second-order wave-diffraction forces for the DeepCwind semisubmersible.

To carry out the calculation of Fj

D(t) in Eq. 3, the 

quantities Dn

(j) must be obtained. To determine the coefficients

Dn

(j)

, use is made of the mean-drift coefficients Dnn

(j) derived 

from a first-order WAMIT analysis [23] in conjunction with 

Newman’s approximation [15]. 
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The particular formulation used is that developed in [16], which 

approximates Dn

(j) from Dnn(j) using the relation 

Dn

(j) =

(5) �

ss �Dnn

(j)

� ��Dnn

(j)

Dmm

(j) � ii ss �Dnn(j)

� = ss �Dmm

(j) �

0 ii ss �Dnn

(j)

� ≠ ss �Dmm

(j) �

,

where ss (∙) indicates the sign (either positive or negative) of 

the argument. It is worth stating that it would be best if Dn

(j)

were computed from a second-order WAMIT analysis. 

However, Newman’s approximation is justified for this work 

for the following two reasons:

1) Performing the second-order WAMIT analysis requires 

significant computational expense, whereas computing the 

coefficients Dnn

(j) requires solution of only the first-order wavediffraction problem.

2) Assuming that the second-order transfer function Dn

(j) is 

continuous, and also assuming that only slowly-varying loads 

associated with resonance of the surge DOF (natural frequency 

of 0.0093 Hz) are important (i.e., only Dn

(j) near the diagonal 

Dnn

(j) terms need be approximated accurately).

Therefore, Newman’s approximation should yield suitable 

results for the DeepCwind semi-submersible study conducted 

here.

To complete this section, the magnitude of the approximated 

second-order transfer function Dn

(1) = D(1)

(ω1, ω2) is shown 

via a surface plot in Fig. 5. 

Fig. 5 Surface plot of the D(1)

(ω1, ω2) second-order 

difference-frequency transfer function.

ENVIRONMENTAL CONDITIONS

To investigate the impact of including second-order 

difference-frequency wave-diffraction forcing in FAST for 

analyzing the DeepCwind semi-submersible, a particular wind 

and wave condition is chosen. The details of these 

environmental conditions comprise the remainder of this 

section.

In this analysis, the chosen wind condition is temporally 

dynamic and follows a Norwegian Petroleum Directorate 

(NPD) [24] spectrum. In the basin, the mean wind speed at the 

hub height was Um = 20.6 m/s, the standard deviation was 2.04 

m/s, the maximum wind speed was 28.7 m/s, and the minimum 

wind speed was 12.9 m/s. This wind is chosen because it 

produces thrust loads similar to those experienced in the rated 

wind speed condition of the NREL 5-MW reference wind 

turbine when paired with the low thrust coefficient turbine 

employed in the wind/wave basin tests [12].

For the purposes of simulation, FAST hub-height wind 

files are employed which possess a constant spatial variation in 

wind profile, albeit, wind speed magnitudes that are timevarying. Based on surveys of the wind-generation machine 

output, which were recorded in the wind/wave basin [5, 13], the 

FAST hub-height wind file is created by multiplying the 

measured hub-height velocity by 0.952 and employing a wind 

shear exponent of 0.0912. The tested wind field possessed 

some spatial variation in wind speed. Hence, these hub-height 

wind file choices yielded the best possible representation of the 

wind field utilized during testing, using only the simple hubheight wind file option in the FAST simulations. The spectrum 

of the NPD wind used in this study is given in Fig. 6.

Fig. 6 Spectra for the Um = 20.6 m/s NPD dynamic wind and 

Hs = 2.0 m JONSWAP wave conditions.

Regarding the wave condition, an operational sea with a 

significant wave height of Hs = 2.0 m and a peak-spectral 

period of Tp = 7.5 s following a Joint North Sea Wave Project 

(JONSWAP) [25] spectrum is chosen for this work. This 

condition is selected because it produced large responses 

associated with the second-order difference-frequency wavediffraction forces relative to those caused by the linear wave 
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forces. In addition, this sea state will produce wave loadings 

that are in decent proportion to the wind loads expected with 

the chosen wind, based on typical joint probabilities (e.g., see 

[8]). For the waves tested in the basin, the wave-elevation 

standard deviation was 0.49 m, the maximum crest 2.14 m, the 

minimum trough 1.87 m and the maximum wave height 3.64 m. 

The spectrum of the JONSWAP wave considered here is given 

in Fig. 6.

WAVE-ONLY COMPARISONS

In this section, the calibrated FAST model is used to 

simulate the response of the DeepCwind semi-submersible 

subjected to the Hs = 2.0 m sea state in the absence of wind. 

Because there is no wind, the wind turbine rotor is parked 

(0 rpm) and the blades are feathered. Simulations are 

conducted with and without the inclusion of the second-order 

difference-frequency wave-diffraction forces and compared to 

test data. All simulations are 3 hr in length with 1000 s of 

additional settling-in time prior to recording data. This timing

is similar to the actual model tests, which were 3 hr in length 

with 1800 s of settling-in time.

Fig. 7 Comparison of surge frequency-domain response from 

test data and three different FAST simulations.

A comparison of the surge frequency-domain response, 

computed as a power spectral density, is given in Fig. 7 for the 

test data and three different FAST simulations. The FAST 

simulations consist of a standard analysis with linear wavediffraction wave forces, an analysis including the second-order 

difference-frequency wave-diffraction forces, and lastly, 

another analysis including the second-order wave forces, albeit 

with a reduction in the surge quadratic-drag model coefficient 

to 10% of the initial calibrated value from Ref. [11]. Noting 

that the ordinate axis is displayed on a logarithmic scale, it is 

clearly seen by the test data shown in Fig. 7 that the lowfrequency response at the rigid-body surge natural frequency 

(0.0093 Hz) dominates the entire surge response of the system. 

When comparing the test data to the FAST analyses, it is 

evident that the FAST model that uses only linear wavediffraction forcing severely under-predicts the low-frequency 

response of the system. Including the second-order differencefrequency wave-diffraction forces improves the correlation 

between the simulation and test data significantly, as seen in 

Fig. 7. However, because the large response is created via 

resonance with relatively small second-order wave loads, the 

magnitude of the response at the surge natural frequency is 

highly dependent on the damping employed in the FAST 

model. As seen in Fig. 7, the model using the calibrated surge 

drag model coefficient of Ref. [11] under-predicts the response 

near surge resonance. Utilization of the reduced quadratic-drag 

model damping coefficient, which was discussed in the Model 

Description section, yields simulation results that compare 

much better with experimental values, as shown in Fig. 7. The 

final observation to be made from Fig. 7 is that the test data and 

all simulations correspond well with one another in the waveenergy frequency range (approximately 0.1 Hz to 0.3 Hz shown 

in Fig. 6). Although there is some discrepancy at frequencies 

higher than 0.2 Hz, the magnitude of the response is much 

lower and the error appears larger due to the log scaling.

To continue the wave-only comparison, Figs. 8 and 9 show

two examples of surge response time-series comparisons 

between the test data and various FAST simulations for the 

same Hs = 2.0 m sea state. 

Fig. 8 Comparison of surge time-series response for 0 to 500 s 

from test data and three different FAST simulations.

Fig. 9 Comparison of surge time-series response for 8000 to 

8500 s from test data and three different FAST simulations.
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As can be seen in the figures, the inclusion of the second-order 

difference-frequency forces greatly improves the correlation 

between the test data and simulations. This stated, the 

simulations that include the second-order wave-diffraction 

effects using Newman’s approximation do not always capture 

the appropriate local time-domain response that is measured in 

the basin. As can be seen in Fig. 8, the FAST simulation overpredicts the amplitude of the second-order response in the noted 

time range 0 to 500 s, and in Fig. 9, the FAST simulation underpredicts the second-order wave-diffraction-associated response 

and predicts the incorrect phase of this response in another time 

range (8000 to 8500 s) of the same simulation. 

Table 5 Surge motion statistics for the wave-only case.

Statistic Data Linear 2nd-Ord. 2nd-Ord.*

Mean (m) 0.735 0.000 0.307 0.307

Std. Dev. (m) 0.354 0.103 0.218 0.343

Max. (m) 2.200 0.486 1.137 1.385

Min. (m) -0.507 -0.382 -0.378 -0.711

Range (m) 2.707 0.868 1.515 2.096

*Reduced Surge Drag Damping

As a next step in this wave-only simulation discussion, the 

statistics for the surge response from the test data and three 

simulations is given in Table 5. As shown in the table, without

inclusion of the second-order difference-frequency wavediffraction forces, very poor predictions of the surge behavior 

are obtained. For the simulation using only linear wavediffraction forces, the mean surge is zero, and the standard 

deviation and range of the surge DOF over the simulation are 

only 29.1% and 32.1% of those measured from the test. For the 

best simulation, which includes the reduced surge quadraticdrag damping coefficient, the surge mean, standard deviation, 

and range are 42.3%, 96.9%, and 77.4% of the experimental 

values, respectively. 

To complete the wave-only comparison, the response of the 

upwind mooring line (which lies along the negative surge axis) 

fairlead tension is investigated. Figure 10 compares the test 

data and the three FAST simulations for the fairlead tension in 

the frequency domain.

Fig. 10 Comparison of upwind mooring line fairlead tension 

response from test data and three different FAST simulations.

Table 6 compares the fairlead tension statistics of the test data 

and three simulations. As can be seen in Fig. 10, the frequencydomain fairlead tension comparison is similar to the surge 

comparison at low frequencies.

Table 6 Upwind fairlead tension force statistics for the wave 

only case.

Statistic Data Linear 2nd-Ord. 2nd-Ord.*

Mean (kN) 1161 1105 1120 1120

Std. Dev. (kN) 18.6 4.7 10.1 16.0

Max. (kN) 1247 1128 1160 1173

Min. (kN) 1097 1089 1090 1075

Range (kN) 150.0 39.0 70.0 98.0

*Reduced Surge Drag Damping

This indicates that the mooring tension response is accurately 

predicted for the DeepCwind semi-submersible at low 

frequencies if the second-order difference-frequency wavediffraction forces are included. However, the fairlead tension 

response in the linear wave-energy frequency range is 

significantly under-predicted. This is theorized to be a product 

of using a quasi-static catenary line solver in FAST [8], which 

ignores mooring line dynamics and direct wave particle 

excitation. The interplay of improved low-frequency prediction 

and poor linear wave-energy frequency range simulation is 

captured in the statistics of Table 6. For the best simulation, 

which includes second-order wave-diffraction loads and a 

reduced quadratic-drag damping coefficient, the standard 

deviation and range are 86.0% and 65.3%, respectively, of the 

experimental values. While these are improvements compared 

to the simulation that includes only linear wave loads, these 

improvements are less than what was found for the surge 

response earlier in this section.

COMBINED WIND/WAVE COMPARISONS

With the wave-only comparisons complete, this section 

describes the investigation of the interaction of the dynamic 

wind and second-order difference-frequency wave-diffraction 

loads, both of which influence the global response of the 

floating structure at low frequencies. The investigation will be 

conducted by comparing the response of the DeepCwind semisubmersible subjected to the following conditions: NPD windonly, the irregular wave-only, and the simultaneous application 

of the wind and wave. Note that the Um = 20.6 m/s dynamic 

wind and Hs = 2.0 m irregular wave are detailed in the 

Environmental Conditions section. For tests and simulations 

with wind, the rotor blade pitch is fixed in the operational 

position and the rotor speed is held constant at 12.7 rpm. For 

the test and simulations without wind, the blades are feathered 

and the rotor is parked. Finally, all simulations use the reduced 

surge quadratic-drag damping coefficient of 1.25×105 Ns2

/m2. 

Fig. 11 depicts the frequency-domain surge response of the 

wind-only, wave-only and combined wind and wave case as 

computed from the model test data. As can be seen by 

comparing the combined condition case to the other two 
8 

This report is available at no cost from the 

National Renewable Energy Laboratory (NREL) 

at www.nrel.gov/publications.

scenarios in the figure, the dynamic wind loads control the 

response of the DeepCwind semi-submersible for frequencies 

less than 0.05 Hz, not the second-order wave-diffraction loads 

for the environments considered here. For frequencies between 

0.05 to 0.25 Hz, the linear wave loads understandably control 

the response of the system.

Fig. 11 Comparison of model test data surge response from 

wind-only, wave-only, and combined wind and wave 

conditions.

Fig. 12 Comparison of FAST simulation surge response from 

wind-only, wave-only and combined wind and wave conditions.

With the comparative responses and trends established 

from model test data, the same three identical cases are 

simulated using the custom FAST tool. The frequency-domain 

surge response for the three cases, as computed from FAST 

simulations, is given in Fig. 12. As can be seen by comparing

Figs. 11 and 12, it is clear that FAST captures the same trends 

observed in the model test data. For low frequencies, the 

dynamic wind loads control the response of the system, and for 

frequencies above 0.05 Hz, the linear wave loads dictate the 

DeepCwind semi-submersible surge response. To further 

emphasize the correlation between the combined wind and 

wave case and the model test data and simulation, the surge 

motion statistics for the combined environment cases are given 

in Table 7. Table 7 clearly shows a fair agreement between the 

test data and the simulation including second-order wavediffraction forces for this condition. However, comparing the 

values in Tables 5 and 7 indicates that most of the response in 

the combined wind and wave case is driven by the wind loads 

because the mean, standard deviation, and maximum values are 

all much larger when the wind loads are present.

Table 7 Surge motion statistics for the combined wind and 

wave case.

Statistic Data Linear 2nd-Ord.*

Mean (m) 8.153 7.208 7.436

Std. Dev. (m) 1.131 1.221 1.232

Max. (m) 11.54 11.06 10.99

Min. (m) 4.281 3.073 2.882

Range (m) 7.259 7.987 8.108

*Reduced Surge Drag Damping

To complete this section, an additional simulation is 

performed for the combined wind and wave case, including 

only the linear wave-diffraction forces. The surge response 

statistics for this case are also given in Table 7, alongside the 

test data and simulation with second-order difference-frequency 

wave-diffraction forcing. As the table clearly shows, neglecting 

the second-order wave-diffraction forcing for the combined 

wind and wave case studied here is not of significant concern 

for the DeepCwind semi-submersible. Excluding the secondorder difference-frequency wave-diffraction forces in the 

simulation results in reductions of only 3.1% for the mean 

surge, 0.9% for the surge standard deviation, and 1.5% for the 

surge range.

CONCLUSIONS

In this work, a numerical model of the DeepCwind semisubmersible floating wind turbine was created in the opensource coupled aero-hydro-servo-elastic CAE tool FAST. The 

model was calibrated using select DeepCwind model test data, 

and subsequently, was used to simulate wave-only and 

combined wind and wave cases from the model test program. 

Second-order difference-frequency wave-diffraction forcing 

played a significant role in the global response of the 

DeepCwind semi-submersible based on the analysis of model 

test data. This study included these forces in the FAST CAE 

simulator via Newman’s approximation in an effort to 

understand the importance of including these effects.

For wave-only simulations, the inclusion of second-order 

difference-frequency wave-diffraction forces greatly improved 

the frequency-domain and statistical correlation between the 

simulation output and test data for surge and mooring fairlead 

tension response. To best capture the low-frequency response 

near the surge resonance frequency, the coefficients employed 

for the quadratic surge damping model had to be tailored to suit 

the small amplitude motions created by the operational Hs = 2.0 

m sea state. This situation stemmed from two factors. First, 

the low-frequency resonant surge response is sensitive to the 
9 

This report is available at no cost from the 

National Renewable Energy Laboratory (NREL) 

at www.nrel.gov/publications.

quadratic-drag damping coefficient used in the simulation. 

Second, the quadratic-drag damping model employed here is 

unable to capture the damping characteristics of the 

DeepCwind semi-submersible over a large range of surge 

amplitudes, and can at best capture the damping response of the 

system over a limited range of motion amplitudes. It was also 

found that the Newman’s approximation implementation 

utilized here yielded improvements in the time-series 

comparisons of the surge response; however, the amplitudes 

and phases of the low-frequency response were often not in 

great agreement. In addition, while the inclusion of the secondorder wave-diffraction forces improved the low-frequency 

correlation of the fairlead tension response, a significant 

discrepancy between the simulation and test data still persisted 

in the wave-energy frequency range, likely due to the 

hydrodynamic loading of the mooring line and mooring line 

dynamics that are currently excluded in the FAST CAE tool.

Upon completion of the wave-only portion of the study, 

simulations of a combined wind and wave environment were

performed and compared to the test data. For the case studied, 

where the relationship of wind and wave environmental loads 

was considered to be representative of a realistic operating 

condition, the dynamic wind loads dominated the lowfrequency surge response of the system, as opposed to the 

second-order difference-frequency wave-diffraction forces. 

This was confirmed by comparing FAST simulations with and 

without the second-order wave-diffraction forces. Excluding 

the second-order wave-diffraction forces for the combined wind 

and wave case resulted in a small 3.1% reduction in the mean 

surge value, and even smaller reductions in the surge standard 

deviation and range. These small reductions indicate that 

excluding the second-order wave forces, as is done in the 

current version of FAST, is likely a reasonable approach when 

simulating floating wind turbines subjected to simultaneous 

wind and wave loading. However, for instances where the rotor 

is parked/idling, and the rotor blades are feathered to reduce the 

rotor thrust coefficient, the response is driven by the wave loads 

with negligible influence of the wind loads, even in large 

winds. This conclusion is based on previous analysis of the 

DeepCwind semi-submersible test data. In other words, this 

turbine configuration leads to responses very similar to a waveonly condition. Therefore, neglecting the second-order wavediffraction forces may no longer be advisable for parked/idling 

turbine scenarios, as supported by the results obtained from the 

wave-only analyses conducted in this work. 

ACKNOWLEDGMENTS

The authors gratefully acknowledge the financial support 

from the Department of Energy through DeepCwind Grants 

DE-EE0002981 and DE-EE0003728 and National Renewable 

Energy Laboratory Grant DE-AC36-08GO28308, the National 

Science Foundation through Grant IIP-0917974 and the 

University of Maine. In addition, the expertise and support of 

MARIN in conducting the model test is greatly appreciated.

REFERENCES 

[1] Jonkman, J.M., 2009, “Dynamics of Offshore Floating 

Wind Turbines – Model Development and Verification,” Wind 

Energy 12(5), pp. 459-492. 

[2] Jonkman, J. and Musial, W., 2012, “IEA Wind Task 23: 

Offshore Wind Technology and Deployment, Subtask 2: The 

Offshore Code Comparison Collaboration (OC3),” Final 

Technical Report. 

[3] Nielsen, F.G., Hanson, T.D. and Skaare, B., 2006,

“Integrated Dynamic Analysis of Floating Offshore Wind 

Turbines,” Proc. 25th ASME International Conference on 

Offshore Mechanics and Arctic Engineering, Hamburg, 

Germany, pp. 671-679.

[4] Roddier, D., Cermelli, C., Aubault, A. and Weinstein, A., 

2010, “WindFloat: A Floating Foundation for Offshore Wind 

Turbines,” Journal of Renewable and Sustainable Energy 2(3), 

033104. 

[5] Goupee, A.J., Koo, B.J., Lambrakos, K.F. and Kimball,

R.W., 2012, “Model Tests for Three Floating Wind Turbine 

Concepts,” Proc. 2012 Offshore Technology Conference, 

Houston, Texas. 

[6] Kimball, R.W., Goupee, A.J., Coulling, A.J. and Dagher, 

H.J., 2012, “Model Test Comparisons of TLP, Spar-buoy and 

Semi-submersible Floating Offshore Wind Turbine Systems,” 

Proc. 2012 SNAME Annual Meeting and Expo, Providence, 

Rhode Island. 

[7] Jonkman, J.M. and Buhl, Jr., M.L., 2005, “FAST User’s 

Guide,” NREL Technical Report No. EL-500-38230.

[8] Jonkman, J.M., 2007, “Dynamics Modeling and Loads 

Analysis of an Offshore Floating Wind Turbine,” NREL 

Technical Report No. TP-500-41958.

[9] Stewart, G., Lackner, M., Robertson, A., Jonkman, J. and 

Goupee, A., 2012, “Calibration and Validation of a FAST 

Floating Wind Turbine Model of the DeepCwind Scaled 

Tension-leg Platform,” Proc. 22nd International Offshore and 

Polar Engineering Conference, Rhodes, Greece, pp. 380-387.

[10] Browning, J.R., Jonkman, J., Robertson, A. and Goupee,

A.J., 2012, “Calibration and Validation of the FAST Dynamic 

Simulation Tool for a Spar-type Floating Offshore Wind 

Turbine,” Proc. 2012 Science of Making Torque from Wind 

Conference, Oldenburg, Germany.

[11] Coulling, A.J., Goupee, A.J., Robertson, A.N., Jonkman, 

J.M. and Dagher, H.J., 2012 “Validation of a FAST Semisubmersible Floating Wind Turbine Model with DeepCwind 

Test Data,” Journal of Renewable and Sustainable Energy, in 

review.

[12] Martin, H.R., Kimball, R.W., Viselli, A.M., and Goupee,

A.J., 2012, “Methodology for Wind/wave Basin Testing of 

Floating Offshore Wind Turbines,” Proc. 31st ASME 

International Conference on Offshore Mechanics and Arctic 

Engineering, Rio de Janeiro, Brazil. 

[13] Koo, B., Goupee, A.J., Lambrakos, K. and Kimball, R.W., 

2012, “Model Tests for a Floating Wind Turbine on Three 

Different Floaters,” Proc. 31st ASME International Conference 

on Offshore Mechanics and Arctic Engineering, Rio de Janeiro, 

Brazil.
10

This report is available at no cost from the 

National Renewable Energy Laboratory (NREL) 

at www.nrel.gov/publications.

[14] Goupee, A.J., Koo, B, Kimball, R.W., Lambrakos, K.F. 

and Dagher, H.J., “ Experimental Comparison of Three 

Floating Wind Turbine Concepts,” Proc. 31st ASME 

International Conference on Offshore Mechanics and Arctic 

Engineering, Rio de Janeiro, Brazil.

[15] Newman, J.N., 1974, “Second-order, Slowly-varying 

Forces on Vessels in Irregular Waves,” Proc. Dynamics of 

Marine Vehicles and Structures in Waves, pp. 193-197. 

[16] Standing, R.G., Brendling, W.J. and Wilson, D., 1987, 

“Recent Developments in the Analysis of Wave Drift Forces, 

Low-Frequency Damping and Response,” Proc. 1987 Offshore 

Technology Conference, Houston, Texas.

[17] Chakrabarti, S.K., 1994, Offshore Structure Modeling, 

World Scientific Publishing Co. Pte. Ltd., Singapore.

[18] Jain, A., Robertson, A.N., Jonkman, J.M., Goupee, A.J. 

and Swift, R.W., 2012, “FAST Code Verification of Scaling 

Laws for DeepCwind Floating Wind System Tests,” Proc. 22nd

International Offshore and Polar Engineering Conference, 

Rhodes, Greece, pp. 355-365. 

[19] Jonkman, J.M., Butterfield, S., Musial, W. and Scott, G., 

2007, “Definition of a 5-MW Reference Wind Turbine for 

Offshore System Development,” NREL Technical Report No. 

TP-500-38060. 

[20] Drela, M., 1989, “XFOIL: An Analysis and Design 

System for Low Reynolds Number Airfoils,” Conference on 

Low Reynolds Number Airfoil Aerodynamics, University of 

Notre Dame.

[21] Kim, M.H. and Yue, D.K.P., 1991, “Sum- and DifferenceFrequency Wave Loads on a Body in Unidirectional Gaussian 

Seas,” Journal of Ship Research 35(2), pp. 127-140. 

[22] Langley, R.S., 1986, “On the Time Domain Simulation of 

Second Order Wave Forces and Induced Responses,” Applied

Ocean Research 8(3), pp. 134-144.

[23] Lee, C.H. and Newman, J.N., 2006, WAMIT® User 

Manual, Versions 6.4, 6.4PC, 6.3S, 6.3S-PC, WAMIT, Inc., 

Chestnut Hill, Massachusetts.

[24] API Recommended Practice 2A-WSD, 21st Edition, 

Recommended Practice for Planning, Designing and 

Constructing Fixed Offshore Platforms – Working Stress 

Design, 2000.

[25] IEC 61400-3, Wind turbines – Part 3: Design 

Requirements for Offshore Wind Turbines, 2009.