WaReS validation report [email protected]Marine Analytica https://marineanalytica.com Page 1 of 16 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. ∑ [− 2 ( + ) + + ] 6 =1 = + 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. (, ) = ( + ) [− 2 ( + ) + + ] 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. (, ) = (, ) − (, ) + (, ) (,) = (,)+ (, ) − (, ) (,) = (, ) + (, ) − (, ) 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. = 1 + √ 8 2 2 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. () = | ()| 2 ()
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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.
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).
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