The purpose of this numerical simulation is to validate the SixDegreeofFreedom (6DoF) solver with a case of “Free heave motion of a floating cylinder”. The main objective was to achieve the following:
The numerical simulation type was a Transient, multiphase with laminar flow and a dynamic mesh 6DoF free body motion. The numerical simulation results of SimScale were compared to the experimental and theoretical results as shown in [1] and [2].
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The geometry of the study is a 2D straight cylindrical body in a water tank (see Fig.1.). The details of the cylinder and tank dimensions are provided by the table below.
Length  Diameter  

Cylinder  0.2 m
$0.2m$

0.1524 m(6 inch)
$0.1524m(6inch)$

Length (Ydir)  depth (Xdir)  width (Zdir)  

Tank  20 m(65.5 feet)
$20m(65.5feet)$

2.4384 m(8 feet)
$2.4384m(8feet)$

0.2 m
$0.2m$

The flow domain is the Tank with the cylinder body. For a 2D analysis, it was required to have 1 cell in the width (Zdir) dimension (see Fig.2.). A 2D structured hexahedral mesh was created with the open source ‘BlockMesh’.
The grid nodes are distributed by a geometric grading in the vicinity of the cylinder. Further, the nodes are clustered near the water line to better resolve the waterair interface. This was critical to achieve the accurate equilibrium floating level and base value of the free heave motion.
The complete details of the mesh are listed in the following table:
Mesh and Element types :
Mesh type  Number of nodes  Number of cells  Type 

blockMesh  169980  84200  3D hexahedral 
The numerical analysis performed is detailed as follows:
Tool Type : OPENFOAM®
Analysis Type : Transient MultiPhase Flow (incompressible)
Turbulence model : Laminar
Advanced Concepts : SixDegree of Freedom
Fluid Phase0:
Air: – Kinematic viscosity(ν
$\nu $) =1.55×10−5m2.s−1
$=1.55\times {10}^{5}{m}^{2}.{s}^{1}$– Density (ρ
$\rho $) =1.19198kg.m−3
$=1.19198kg.{m}^{3}$
Fluid Phase1:
Water: – Kinematic viscosity(ν
$\nu $) =1.06×10−6m2.s−1
$=1.06\times {10}^{6}{m}^{2}.{s}^{1}$– Density (ρ
$\rho $) =999kg.m−3
$=999kg.{m}^{3}$
In the experiments [1], the cylinder is initially displaced by 1 inch below the water level (with initial level of half immersed cylinder) and then released to move freely in the heave direction only. To replicate the same effect, the initial water depth taken for the numerical simulation was a baseline value of 1.2192 m for a half immersed body ( or 4 ft as was in the experiment ) plus a water level increment of 0.0254 m (1 inch) at the start of the simulation. This initialized the flow domain (water level) similar to the experimental setup.
The water tank surfaces were taken as frictionless walls. The cylinder surfaces were taken as viscous Noslip walls. The top surface was defined as an openboundary. The following table provides the further details.
Boundary type  Velocity  Pressure  Phasefraction  

Tank walls  WALL  slip  Zero Gradient  Zero Gradient 
Cylinder  WALL  Noslip  Zero Gradient  Zero Gradient 
Top  CUSTOM  Pressureinletoutlet velocity  Total pressure  inletOutlet 
2D sides  CUSTOM  2D empty  2D empty  2D empty 
The 6DoF model constraints applied are given by table below:
Motion type  Translation constraint  Rotation constraint  Center of rotation 

1 DoF  line (1,0,0)  fixed orientation  (0,0,0) 
3 DoF  plane normal (0,0,1)  Axis (0,0,1)  (0,0,0) 
The numerical simulation results of ‘Transient heave decay response’ are compared with experimental data provided by Soichi Ito [1] and theoretical data by Maskell and Ursell [2]. Similar to the experiment [1], the numerical setup constrains the rotation of the cylinder and allows only a pure heave motion (1 DOF) for the 2D case. A ‘Mesh independence’ study was done with 3 meshes, coarse, moderate and fine to see the effects on the results. Moreover, a 2D case was analysed using 3 degrees of freedom with free translation in 2 directions and rotation about 1 axis. The result comparison between the 1 DOF and 3 DOF case is also presented.
Firstly, a comparison of the Heave response from different meshes is given in Fig.3. The figure shows that with the coarse mesh, the baseline heave displacement deviates a lot from the zero line. The moderate mesh also has minor deviations, while the fine mesh attains the best oscillation behaviour about the baseline due to high resolution of the WaterAir interface.
The comparison of numerical simulation (fine mesh) with theoretical and experimental data is presented by the Fig. 4 below.
The comparison of the numerical simulation results of 1 DOF (as in experiment) and 3 DOF cases is given in Fig. 5 below.
[1]  (1, 2, 3, 4) Soichi Ito, STUDY OF THE TRANSIENT HEAVE OSCILLATION OF A FLOATING CYLINDER, MASSACHUSETTS INSTITUTE OF TECHNOLOGY May, 1977 
[2]  Maskell, S. J., and Ursell, F., “The transient motion of a floating body,” J. Fluid Mech., 44, pp. 303313, 1970. 
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