# Free Heave Motion: Floating cylinder¶

## Overview¶

The purpose of this numerical simulation is to validate the Six-Degree-of-Freedom (6-DoF) solver with a case of “Free heave motion of a floating cylinder”. The main objective was to achieve the following:

- Transient heave decay response after initial displacement.

The numerical simulation type was a Transient, multiphase with laminar flow and a dynamic mesh 6-DoF free body motion. The numerical simulation results of SimScale were compared to the experimental and theoretical results as shown in [1] and [2].

## Geometry¶

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 | \(0.2 m\) | \(0.1524 m (6 inch)\) |

Length (Y-dir) | depth (X-dir) | width (Z-dir) | |
---|---|---|---|

Tank | \(20 m (65.5 feet)\) | \(2.4384 m (8 feet)\) | \(0.2 m\) |

## Flow Domain¶

The flow domain is the Tank with the cylinder body. For a 2D analysis, it was required to have 1 cell in the width (Z-dir) 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 water-air interface. This was critical to acheive the accutare 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 |

## Analysis type¶

The numerical analysis performed is detailed as follows:

**Tool Type** : OPENFOAM®

**Analysis Type** : Transient Multi-Phase Flow (incompressible)

**Turbulence model** : Laminar

**Advanced Concepts** : Six-Degree of Freedom

## Simulation Setup¶

Fluid Phase-0:

**Air**:
- Kinematic viscosity(\(\nu\)) \(= 1.55 \times 10^{-5} m^2.s^{-1}\)
- Density (\(\rho\)) \(= 1.19198 kg.m^{-3}\)

Fluid Phase-1:

**Water**:
- Kinematic viscosity(\(\nu\)) \(= 1.06 \times 10^{-6} m^2.s^{-1}\)
- Density (\(\rho\)) \(= 999 kg.m^{-3}\)

- Surface tension \(= 0.07 kg.s^{-2}\)

### Initial Condition:¶

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 experimantal setup.

### Boundary Conditions:¶

The water tank surfaces were taken as frictionless walls. The cylinder surfaces were taken as viscous No-slip walls. The top surface was defined as an open-boundary. The following table provides the further details.

Boundary type | Velocity | Pressure | Phase-fraction | |
---|---|---|---|---|

Tank walls | WALL | slip | Zero Gradient | Zero Gradient |

Cylinder | WALL | No-slip | Zero Gradient | Zero Gradient |

Top | CUSTOM | Pressure-inlet-outlet velocity | Total pressure | inlet-Outlet |

2D sides | CUSTOM | 2D empty | 2D empty | 2D empty |

### Body Motion: 6 Degree of freedom¶

The 6-DoF 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 mass of the cylinder body is such that at equilibrium exactly a half-immersed body is achieved.

## Results¶

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 alot 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 Water-Air interface.

Fig.3. Mesh independence study for heave decay response.

The comparison of numerical simulation (fine mesh) with theoretical and experimantal data is presented by the Fig. 4 below.

Fig.4. Heave decay response comparison with experimental and theoretical data.

The comparison of the numerical simulation results of 1 DOF (as in experiment) and 3 DOF cases is given in Fig. 5 below.

A visualization of the phase fraction and motion of the body at different times is shown by Fig.6A and Fig.6B.

Fig.6. Phase fraction and motion of body at different times.

## References¶

[1] | 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. 303-313, 1970. |

## Disclaimer¶

This offering is not approved or endorsed by OpenCFD Limited, producer and distributor of the OpenFOAM software and owner of the OPENFOAM® and OpenCFD® trade marks. OPENFOAM® is a registered trade mark of OpenCFD Limited, producer and distributor of the OpenFOAM software.