Data Categories 1 to 5 - Geometric Definition and Static Environment
The primary function of these data categories is to describe the structure being modeled. This includes the mass and inertia of the structure and its geometry, from which the hydrostatic and hydrodynamic properties are calculated. In addition, the coordinates of all positions referenced in subsequent data categories and the parameters relating to the environment (for example, density of water) are input. These parameters are normally considered to remain constant for an analysis of a particular structure.
All the Aqwa programs require Data Categories 1 to 5, if starting an analysis from Stage 1.
The data that may be input via Data Categories 1 to 5 are as follows:
- Data Category 1
Node and coordinate information
- Data Category 2
Element topology
- Data Category 3
Material properties
- Data Category 4
Geometric properties
- Data Category 5
Water depth Water density Acceleration due to gravity
The following sections show the specific required data when including tethers in an analysis.
Tethers may be included in a simulation either in a towing operation, or in an installed condition, subjected to wave environmental loading. Installed tethers may go slack and impact during operation. Tethers are considered by Aqwa as flexible tubes whose diameters are small compared to the wavelength. Tethers are classified as a type of mooring.
The analysis of towed tethers is an independent process and requires no backing files from other programs in the Aqwa suite. For installed tethers, an Aqwa-Line run is required for diffracting structures but for non-diffracting structures which do not require an Aqwa-Line analysis, a tube model can be used.
As tethers are regarded as a mooring capability, a nominal structure must be input for towed tethers. This defines the position of the axis system, in which the towed tether displacements are output, and in which the eigenvalue solution is performed. The structure plays no other part in the analysis.
The modelling techniques are based on the following limitations and assumptions of the program.
No Axial Motion - Towed tethers are not considered to move in the axial direction or rotate about the axis of the tether; that is, displacements of the tether are 2 translations and 2 rotations at each node. These displacements are considered as small motions from the tether axis (TLA q.v.)
Note: Although current in the axial direction will produce stabilizing effects, if the tether spring at the ends are very soft, large rotations (>30 degrees) may be produced, which will invalidate the analysis. The program also takes full account of the change in encounter frequency, due to the component of the current in the direction of the waves.
Axial Tension - Both the wall and effective tensions in a towed tether are assumed to be zero, and hence the bending stiffness is purely structural. The tether responses, especially in the fundamental mode, may be inaccurate if this tension is significant.
Note: This also means that the tether may not be analyzed, if any point moves to a depth where the effective tension is significant, i.e. for upending.
Small Motions - It is assumed that the lateral and rotational motions of the tether from the defined tether axis are small. This means that the program is unsuitable for large rotations about the Y or Z axis, e.g. for upending. However, full account is taken of the phase shift of the waves, due to movement in the direction of the wave/wave spectrum.
Mass/Stiffness - The mass/stiffness ratio of any element must not be too small. Very short elements inherently have small mass/stiffness ratios. This gives rise to very high frequencies. These high frequencies may cause stability problems and roundoff errors in the programs. A general rule is that natural periods of less than 1/100th second are not allowed. These periods are output from the eigenvalue analysis.
Very short elements should therefore be modelled with a value of Young's modulus reduced so that no periods less than 1/100th second are present. The user can check that the bending of short elements is still small, using the graphical output.
Timestep - The timestep must be small enough to resolve the response motion of the tether. This includes any transients that may be present either initially or, more importantly, throughout the analysis. Although a good rule of thumb is that the timestep should be 1/10th of the period of any response, the best method of checking the timestep is to re-run a short simulation with half the timestep and compare the bending moments or stresses for both runs. These should be approximately the same for both runs. Timesteps of 0.25 seconds are typically used.
For towed tethers, the local axis (TLA) must be defined parallel to, and in the same direction as, the X axis of the fixed reference axes (FRA) i.e. XY in the water plane and Z vertical. The X axis coincides with the zero current wave direction. The nodes of the tether increase with positive X. The last node of the tether, at zero FRA displacement, lies at the TLA origin. For installed tethers, the TLA is parallel to the FRA, when the tether is vertical. In general, the TLA X axis goes from the anchor node to the attachment node, the Y axis is in the plane of the XY FRA, and the Z axis follows the right hand rule. The TLA origin is at the anchor node.
Input for Towed Tethers
- Data Category 1
The coordinates of the nominal vessel center of gravity. This should always be zero, but must be input.
The coordinates of the trailing end of the tether. The X coordinate should be minus the total tether length. The Y value must be zero. Z value may be input as zero but see below.
The Z coordinate may be input to define the TLA (tether axis) above or below the water surface. Input of a Z coordinate will mean that:
the eigenvalue analysis will be performed with the tether axis at this Z value. Depending on the value of Z, the tether may be
completely out of water (Z greater than the largest element diameter)
partially submerged
fully submerged.
all displacements will be output with reference to this Z value.
the initial position of the tether (for the motion response analysis stage) will have this Z value. It is not recommended to "drop" the tether into the water from a height (positive Z value) as this will produce large initial transients.
The relative coordinates of the towed tether nodes are defined along the X axis, with the Y values zero.
- Data Category 2
A point mass element to represent the vessel
- Data Category 3
A mass to represent the vessel One or more densities for the tether elements - Data Category 4
Inertia of the point mass representing the vessel Diameter, thickness, drag and added mass coefficients for each different tether element - Data Category 5
Water depth Water density Acceleration due to gravity
Input for Installed Tethers
For installed tethers the vessel must be described using the standard data requirements. For the tether itself the following additional data is required.
- Data Category 1
The coordinates of the tether attachment points to the vessel The coordinates of the tether anchor points The relative coordinates of the installed tether nodes are defined along the Z axis, with the X and Y values zero. - Data Category 3
One or more densities for the tether elements
- Data Category 4
Diameter, thickness, drag and added mass coefficients for each different tether element