WaReS Validation Report

WaReS validation report
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1 INTRODUCTION
WaReS is a code developed by Marine Analytica to calculate wave-induced loads and responses in floating
structures. This memo presents an extract of the verification report prepared for the future use of WaReS in
commercial projects. Responses in irregular sea states and RAO are compared with the results published in [MA.1]
for a typical 300 ft North Sea barge. The RAO and responses presented in [MA.1] have been calculated with the
3D diffraction package WADAM. WaReS results show good agreement over the range of wave frequencies
analysed.
2 WARES DESCRIPTION
WaReS stands for Wave Responses and are set of tools to perform hydrodynamic analysis in the linear frequency
domain. The input for WaReS is a mesh describing the wet surface of the body, the mass and hydrostatic properties
and the environmental data. The radiation and diffraction coefficients such as added mass, radiation damping and
wave exciting loads are computed with the 3D radiation-diffraction code Nemoh. This code is an open source
potential flow BEM solver developed at Ecole Centrale de Nantes see ref. [MA.2].
The motions of the floating body in regular waves are modelled as a linear mass-damping-spring system with
frequency dependent coefficients and linear exciting wave forces/moments.
∑ 𝑥𝑗[−𝜔2
(𝑚𝑖𝑗 + 𝑎𝑖𝑗) + 𝑖𝜔𝑏𝑖𝑗 + 𝑐𝑖𝑗]
6
𝑗=1
= 𝐹𝑖
𝐹𝐾
+ 𝐹𝑖
𝐷
The global RAO’s at the centre of rotation of the body are calculated by solving the equation of motion in the
frequency domain for every degree of freedom.
𝐻𝑗
𝐺
(𝜔, 𝜃) =
(𝐹𝑖
𝐹𝐾
+ 𝐹𝑖
𝐷
)
[−𝜔2(𝑚𝑖𝑗 + 𝑎𝑖𝑗) + 𝑖𝜔𝑏𝑖𝑗 + 𝑐𝑖𝑗]
Assuming small responses and a rigid body, the transfer functions at any arbitrary point (P) are calculated as
indicated in the equations below. The gravity horizontal components are incorporated in this analysis.
𝐻 𝑋
𝑃(𝜔, 𝜃) = 𝐻 𝑋
𝐺
(𝜔, 𝜃) − 𝑦 𝑃 𝐻 𝑅𝑍
𝐺
(𝜔, 𝜃) + 𝑧 𝑃 𝐻 𝑅𝑌
𝐺
(𝜔, 𝜃)
𝐻 𝑌
𝑃(𝜔, 𝜃) = 𝐻 𝑌
𝐺
(𝜔, 𝜃) + 𝑥 𝑃 𝐻 𝑅𝑍
𝐺
(𝜔, 𝜃) − 𝑧 𝑃 𝐻 𝑅𝑋
𝐺
(𝜔, 𝜃)
𝐻 𝑍
𝑃(𝜔, 𝜃) = 𝐻 𝑍
𝐺
(𝜔, 𝜃) + 𝑥 𝑃 𝐻 𝑅𝑌
𝐺
(𝜔, 𝜃) − 𝑦 𝑃 𝐻 𝑅𝑋
𝐺
(𝜔, 𝜃)
WaReS uses a potential non-viscous flow to calculate the hydrodynamic coefficients. For most of the DOF’s
damping is predominantly linear and well captured by radiation- diffraction codes. However, in some cases like roll
motions in mono-hulls the responses are dominated by viscous terms and therefore not well predicted by the
potential flow.
To consider non-linear damping in the linear frequency domain WaReS applies the stochastic linearization
technique. This method considers the characteristics of an incoming wave spectrum and computes an equivalent
amount of linear damping per sea-state. Multiple roll damping prediction methods are incorporated in WaReS
Figure 1 and Figure 2 show the influence of the Hs, Tp and wave direction on the amount of roll damping applied
to the 300ft barge.
𝑏 𝑒𝑞 = 𝑏1 + √
8
𝜋
2𝜋
𝑇𝑧
𝜎 𝑅𝑋 𝑏2
The floating body responses in irregular waves are calculated by combining the RAO’s with wave spectra for a set
of wave directions, significant wave heights and wave periods.
𝑆 𝑅(𝜔) = |𝐻𝑗
𝑃
(𝜔)|
2
𝑆 𝑊(𝜔)

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Figure 1 and Figure 2 show the impact of the wave height, period and direction on the amount of linearized roll
damping applied to the system. As can be seen the largest amount of damping is obtained in beam seas for wave
periods close to the barge roll natural period (T44 = 6.5 s). The linearized damping also increases with the design
wave height (larger roll responses).
Figure 1 Linearized roll damping (% critical damping) vs wave direction and Tp
Figure 2 Linearized roll damping (% critical damping) vs Hs and Tp
The n-th spectral moments of the response spectrum are given by:
𝑚 𝑛,𝑟(𝜔) = ∫ 𝜔 𝑛
∞
0
𝑆 𝑅(𝜔)𝑑𝜔
For comparison purposes the responses presented in this report are 3h single amplitudes Most Probable Maximum
(MPM). This correspond to a return period of 1/N, where N are the number of oscillations during the considered
period (3 hours).
𝜎2
= 𝑚0 = ∫ 𝑆 𝑅(𝜔)𝑑𝜔
∞
0
𝑈 𝑀𝑃𝑀 = 𝜎√2 ln (𝑁)

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2.1 Reference documents
Guidelines and standards
[GS1] DNVGL-RP-C205 Recommended practice for environmental conditions and environmental loads
Reference documents
[MA.1] Barge Transportation of Heavy Objects – Norwegian Technology University – June 2010
[MA.2] Theoretical and numerical aspects of the open source BEM solver NEMOH - A. Babarit, G.
Delhommeau.
2.2 Abbreviations
APP Aft perpendicular
Aij Added mass/inertia
Bij Radiation damping
B1 Linear damping
B2 Quadratic damping
Bcrit Critical damping
BEM Boundary element methods
BL Base line
Cij Hydrostatic stiffness
CL Centre line
deg degree
ft fee/foot
FFK
Froude-Krilov wave loads
FD
Diffraction wave loads
g gravity
Gmlong Longitudinal metacentric height
GMtran Transverse metacentric height
Hs Significant wave height
JONSWAP Joint North Sea Wave Project
kii Radius of gyration
kg kilogram
LCG/LCB Longitudinal Centre of Gravity/Buoyancy
λ Wavelength
m meter
m0 Zero spectral moment
Mij Mass/inertia
MPM Most Probable Maximum
N Number of oscillations
RAO Response Amplitude Operator, also presented as H (ω,θ)
σ Standard deviation
σRX Standard deviation of the roll velocity
s second
𝑆 𝑅(𝜔) Response spectrum
𝑆 𝑤(𝜔) Wave spectrum
TCG/TCB Transverse Centre of Gravity/Buoyancy
Tp Wave peak period
Tz Zero-up crossing period
VCG/VCB Vertical Centre of Gravity/Buoyancy
ω wave frequency

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2.3 Barge reference system
The global coordinate system of the barge is defined as follows, see Figure 3.
• X-axis (from APP) in longitudinal vessel direction pointing forward
• Y-axis (from CL) in transverse vessel direction pointing portside
• Z-axis (from BL) in vertical direction pointing upwards
Figure 3 Barge coordinate system
3 ANALYSIS DESCRIPTION
The verification is performed for a free floating 300ft North Sea barge with a module on 1000mT on deck as
described in [MA.1]. The main particulars of the barge and the loading condition are presented in Table 2. All the
dimensions are measured from the barge reference system described in Figure 3.
Figure 4 WaReS 300ft North Sea barge hull mesh
The maximum panel size has been defined based on the shortest wavelength to comply with the λ/7 rule. In this
case the maximum mesh size is 2.5 m suitable for wave frequencies between 0.2 rad/s and 1.85 rad/s. A total of
166 wave frequencies have been computed in steps of 0.01 rad/s. The diffraction/radiation analysis has been
performed with the following parameters:
Table 1 Radiation-diffraction analysis particulars
Description Units Quantity
Water depth [m] 300.0
Water density [kg/m3] 1025.0
Gravity [m/s2] 9.81

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Table 2 300ft barge main particulars
Description Units Quantity Description Units Quantity
Lpp [m] 91.40 LCF [m] 45.25
B [m] 27.40 TCF [m] 0
D [m] 6.00 LCB [m] 45.23
T [m] 2.78 TCB [m] 0
Tfwd [m] 2.49 VCB [m] 1.39
Taft [m] 3.07 GMtransv [m] 20.7
Δ [ton] 6263.00 GMlongit [m] 236.86
CB [-] 0.88 kMtransv [m] 25.68
LCG [m] 44.24 kMlongit [m] 241.84
TCG [m] 0.00 kxx [m] 10.63
VCG [m] 4.98 kyy [m] 28.47
Awl [m2] 2367.00 kzz [m] 29.49
The sea-states presented in Table 3 have been analysed.
Table 3 Design sea-states
Seastate Hs [m] Tp min [s] Tp max [s]
A 2.0 4.0 20.0
B 3.0 4.0 20.0
C 3.5 4.0 20.0
The wave energy is modelled by a JONSWAP spectrum with varying peak factor γ as function of the significant
wave height and period as described in [GS1]. No wave spreading is considered in the analysis.
𝑆𝐽(𝜔) = 𝐴 𝛾 𝑆 𝑃𝑀(𝜔) 𝛾 𝑒
(−0.5(
𝜔−𝜔 𝑝
𝜎𝜔 𝑝
)
2
)
The barge responses have been determined at the local points shown in Table 4 measured from the barge
reference system described in Figure 3.
Table 4 Barge local points analysed
Location P1 P2 P3 P4 P5
X [m] 42.72 27.72 57.72 27.72 57.72
Y [m] 0.00 6.00 6.00 6.00 6.00
Z [m] 14.60 7.50 7.50 21.50 21.50

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4 RESULTS
The following results were calculated and compared:
• 3h MPM roll motion, with additional roll damping as shown in Figure 5
• 3h MPM maximum accelerations at local points presented in Table 4.No viscous roll damping applied.
• Motion RAOs. No viscous roll damping applied.
Transverse accelerations (see Figure 8) present a consistent trend but a difference in amplitude between 5 and
10%. This can be explained by the different amount of (non-viscous) roll damping computed by the codes (see
peak of roll RAO - Figure 13). Which one is “more correct” can only be judged with model tests.
4.1 Roll motions with viscous damping
Figure 5 MPM (3h) roll motions
Figure 6 Viscous roll damping (% critical damping) applied to the barge
0
2
4
6
8
10
12
14
16
18
20
22
24
26
0.0 1.0 2.0 3.0 4.0 5.0 6.0 7.0 8.0 9.0 10.0 11.0 12.0 13.0 14.0 15.0
RX[deg]
Tz [s]
3h single amplitude MPM roll motions - Seastate B - Hs =3m WaReS Commercial package
0.0%
0.2%
0.4%
0.6%
0.8%
1.0%
1.2%
1.4%
1.6%
1.8%
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
Blinear[%Bcrit]
Tz [s]

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4.2 Maximum accelerations without viscous damping
Figure 7 Longitudinal accelerations + gravity component (3h MPM)
Figure 8 Transverse accelerations + gravity component (3h MPM)
Figure 9 Vertical accelerations without gravity (3h MPM)
0.59
0.38 0.38
0.92 0.92
0.55
0.35 0.35
0.91 0.91
0
0.2
0.4
0.6
0.8
1
P1 P2 P3 P4 P5
AX[m/s2]
Local point
Longitudinal accelerations - Seastate A Commercial package WaReS
5.85
3.96 3.91
7.79 7.75
5.32
3.48 3.53
7.29 7.37
0
2
4
6
8
10
P1 P2 P3 P4 P5
AY[m/s2]
Local point
Transverse accelerations - Seastate A Commercial package WaReS
1.22
2.65 2.65 2.65 2.65
1.20
2.50 2.56 2.50 2.56
0
0.5
1
1.5
2
2.5
3
P1 P2 P3 P4 P5
AZ[m/s2]
Local point
Vertical accelerations - Seastate A Commercial package WaReS

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4.3 Global motion RAO without viscous damping
Figure 10 Global surge motion RAO
0.0
0.2
0.4
0.6
0.8
1.0
1.2
0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0 2.2 2.4
X/ξ[m/m]
wave frequency [rad/s]
surge motion RAO - dir = 0 deg Commercial package WaReS
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0 2.2 2.4
X/ξ[m/m]
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0 2.2 2.4
X/ξ[m/m]

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Figure 11 Global sway motion RAO
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0 2.2 2.4
Y/ξ[m/m]
sway motion RAO - dir = 30 deg Commercial package WaReS
0.0
0.2
0.4
0.6
0.8
1.0
0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0 2.2 2.4
Y/ξ[m/m]
0.0
0.2
0.4
0.6
0.8
1.0
1.2
1.4
0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0 2.2 2.4
Y/ξ[m/m]

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Figure 12 Global heave motion RAO
0.0
0.2
0.4
0.6
0.8
1.0
1.2
0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0 2.2 2.4
Z/ξ[m/m]
heave motion RAO - dir = 0 deg Commercial package WaReS
0.0
0.2
0.4
0.6
0.8
1.0
1.2
0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0 2.2 2.4
Z/ξ[m/m]
0.0
0.2
0.4
0.6
0.8
1.0
1.2
0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0 2.2 2.4
Z/ξ[m/m]

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Figure 13 Global roll motion RAO (only radiation damping)
0.0
0.2
0.4
0.6
0.8
1.0
1.2
1.4
1.6
1.8
0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0 2.2 2.4
RX/ξ[deg/m]
roll motion RAO - dir = 30 deg Commercial package WaReS
0.0
1.0
2.0
3.0
4.0
5.0
6.0
7.0
0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0 2.2 2.4
RX/ξ[deg/m]
0.0
2.0
4.0
6.0
8.0
10.0
12.0
14.0
16.0
18.0
20.0
0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0 2.2 2.4
RX/ξ[deg/m]

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Figure 14 Global pitch motion RAO
0.0
0.3
0.6
0.9
1.2
1.5
1.8
2.1
2.4
0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0 2.2 2.4
RY/ξ[deg/m]
pitch motion RAO - dir = 0 deg Commercial package WaReS
0.0
0.2
0.4
0.6
0.8
1.0
1.2
1.4
1.6
1.8
2.0
0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0 2.2 2.4
RY/ξ[deg/m]
0.00
0.50
1.00
1.50
2.00
2.50
0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0 2.2 2.4
RY/ξ[deg/m]

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Figure 15 Global yaw motion RAO
0.0
0.1
0.2
0.3
0.4
0.5
0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0 2.2 2.4
RZ/ξ[deg/m]
yaw motion RAO - dir = 30 deg Commercial package WaReS
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0 2.2 2.4
RZ/ξ[deg/m]
0.00
0.10
0.20
0.30
0.40
0.50
0.60
0.70
0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0 2.2 2.4
RZ/ξ[deg/m]

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5 WARES GLOBAL RAO 2D

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