Heaving sphere in regular waves¶
This benchmark corresponds to the simulation of a sphere in heave motion submitted to regular waves. This simulation is presented by the International Energy Agency (IEA) Offshore Energy System (OES) Task 10 [OES10] as a benchmark case for model validation and verification regrouping 25 organizations. Description of this test case and results obtained by FRyDoM are summarized in the following.
Description of the test case¶
The sphere considered in this simulation has a radius of \(5\) \(m\) and a total mass of \(2,618 .10^5\) \(kg\). At equilibrium, the center of the sphere is located on the mean water level and its center of gravity is located \(2\) \(m\) below the water line. Main properties of the sphere are presented in the next table.
Parameters  Values 

Radius  \(5\) \(m\) 
Initial sphere location  (\(0\), \(0\), \(0\)) 
Center of gravity  (\(0\), \(0\), \(2\)) 
Mass  \(261.8\times10^3\) \(kg\) 
Ixx  \(1.690\times10^6\) \(kg.m^2\) 
Iyy  \(1.690\times10^6\) \(kg.m^2\) 
Izz  \(2.606\times10^6\) \(kg.m^2\) 
Water depth  Inf 
Water density  \(1000\) \(kg/m^3\) 
K33  \(7.695\times10^5\) \(N/m\) 
K44  \(5.126\times10^6\) \(N.m\) 
K55  \(5.126\times10^6\) \(N.m\) 
The sphere is submitted to a regular wave field propagating positive along the xaxis. The wave periods considered in this test case varies from \(3\) \(s\) to \(11\) \(s\) with a steepness of \(0.2\) %.
Results in RAO¶
The response amplitude operator (RAO) in heave motion obtained from FRyDoM is presented in Fig. 38. Very good agreement with the results obtained by Nemoh [Nemoh] can be observed.
Effects of a nonlinear hydrostatic and FroudeKrylov approach¶
The time series of the same floating heaving sphere in waves are now compared. Two models are considered:
 a fully linear model;
 a weakly nonlinear model: the hydrostatic and FroudeKrylov loads are computed with a fully nonlinear approach.
A single regular wave of period \(3\) \(s\) and amplitude \(0.022\) \(m\) is present. The two time series are plotted in Fig. 39. Due to the small steepness of the waves (\(0.05\) %), the two models match perfectly, which validates their mutual implementation in regular waves.
References¶
[OES10] 

[Nemoh] 
