WaReS validation report - Marine Analytica

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

= 𝐹𝑖𝐹𝐾 + 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.

𝐻𝑗𝐺(𝜔, 𝜃) =

(𝐹𝑖𝐹𝐾 + 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.

𝐻𝑋𝑃(𝜔, 𝜃) = 𝐻𝑋

𝐺(𝜔, 𝜃) − 𝑦𝑃 𝐻𝑅𝑍𝐺 (𝜔, 𝜃) + 𝑧𝑃 𝐻𝑅𝑌

𝐺 (𝜔, 𝜃)

𝐻𝑌𝑃(𝜔, 𝜃) = 𝐻𝑌

𝐺(𝜔, 𝜃) + 𝑥𝑃 𝐻𝑅𝑍𝐺 (𝜔, 𝜃) − 𝑧𝑃 𝐻𝑅𝑋

𝐺 (𝜔, 𝜃)

𝐻𝑍𝑃(𝜔, 𝜃) = 𝐻𝑍

𝐺(𝜔, 𝜃) + 𝑥𝑃 𝐻𝑅𝑌𝐺 (𝜔, 𝜃) − 𝑦𝑃 𝐻𝑅𝑋

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.

𝑏𝑒𝑞 = 𝑏1 + √8

𝜋 2𝜋

𝑇𝑧𝜎𝑅𝑋 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.

𝑆𝑅(𝜔) = |𝐻𝑗𝑃(𝜔)|

2 𝑆𝑊(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:

𝑚𝑛,𝑟(𝜔) = ∫ 𝜔𝑛∞

0

𝑆𝑅(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 = ∫ 𝑆𝑅(𝜔)𝑑𝜔∞

0

𝑈𝑀𝑃𝑀 = 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

𝑆𝑅(𝜔) Response spectrum

𝑆𝑤(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) = 𝐴𝛾 𝑆𝑃𝑀(𝜔) 𝛾 𝑒(−0.5(

𝜔−𝜔𝑝

𝜎𝜔𝑝)

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

[d

eg]

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

Blin

ear

[%B

crit

]

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[d

eg/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[d

eg/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[d

eg/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[d

eg/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[d

eg/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[d

eg/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[d

eg/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[d

eg/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[d

eg/m

]






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5 WARES GLOBAL RAO 2D




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WaReS validation report - Marine Analytica

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