Floating turbines

Articles on this page:

• Comparing coupled and uncoupled modes for floating turbines
• Initial conditions for floating turbines
• Modelling cable suspended counterweights in Bladed
• Limitations of Bladed BEM hydrodynamics when modelling floating wind turbines that yaw significantly
• Getting error message "Invalid map <K,T> key"

Problem

For my floating turbine, the tower first uncoupled mode (calculated in modal analysis) and the first coupled mode (calculated in a Campbell diagram) don’t match well in frequency. Why don’t the first coupled and uncoupled modes match?

Solution

For a fixed base turbine, the first tower attachment mode (the first uncoupled mode) often matches the first tower coupled mode frequency (from the Campbell diagram) well. This is because the attachment mode represents the displacement that occurs in the tower when a force is applied to the tower top and the tower base is fixed. This is close to what happens in reality for a fixed base turbine, and during a Campbell diagram calculation.

For a floating turbine with soft moorings, the deflection shape of the tower when a load is applied to the top in the Campbell diagram calculation doesn’t correspond to the first attachment mode, as the base is not fixed. So, the cantilever attachment mode shapes calculated in modal analysis are not seen individually in the Campbell diagram deflections. When a load is applied to the tower top of a floating turbine, the deflection in the tower will take a form that is a combination of various normal and attachment modes, so the first coupled tower mode will be a combination of various uncoupled modes.

Keywords

Floating; Mode shapes; Coupled; Uncoupled

Problem

How do you set the initial conditions for the six degrees of freedom when modelling a floating platform?

Solution

You can set the initial conditions for the six degrees of freedom using the initial conditions tab in the Calculation Parameters window (see below).

Keywords

Initial conditions; Floating platform

Problem

This article discusses modelling a support structure with a cable-suspended counterweight in Bladed. The current limitations are discussed, and guidance on the most appropriate way to model the cables is offered.

Solution

Some floating wind turbine concepts include a counterweight that is suspended in the water via a number of cables. In the Bladed tower screen, users can define a set of slender members, representing the cables, that connect a member with large mass, representing the counterweight, to the remainder of the support structure. As cables don’t have any bending or shear stiffness, they should in principle be modelled by bar elements (rather than beam elements) which have zero bending and shear stiffness.

Cable-suspended counterweight systems rely on gravity and buoyancy loads to tension the cables. In a vertical configuration in the water with tensioned cables, the whole support structure is relatively stiff. However, without the gravity and buoyancy loads, the counterweight can potentially move freely relative to the remainder of the support structure. This presents a problem for the modal analysis calculation in Bladed, as this calculation does not take account of gravity or buoyancy loads. During the modal analysis, some of the calculated mode shapes will be zero-frequency “rigid body” modes, where parts of the support structure move relative to each other without stiffness. Currently, Bladed does not support the calculation and use of such “rigid body” mode shapes. Therefore, an error will be shown when trying to model this type of structure using bar elements.

In this instance, the current recommended approach is to model the cables using beam elements. This is considered to be a reasonable approximation, as the bending and shear stiffness of very slender beam elements will be small. The majority of the cable stiffness actually results from “geometric stiffness” as a result of the gravity and buoyancy loads causing a large tension in the cables. This effect will be included on the slender beam elements.

Keywords

Floating; Guyed towers; Bar elements

Problem

Only small platform yaw motions permitted

The Bladed Boundary Element Method (BEM) hydrodynamics calculation has been implemented in the global frame and assumes that the platform yaw motion throughout time domain simulation remains small.

This modelling assumption mean that when a floating platform is subject to large rotations (such as platform yaw) a simulation is unlikely to produce accurate engineering results or will become numerically unstable. This situation will most likely affect platforms that make use a of single point mooring system (SPM) or where a mooring line has failed. Platforms that are constrained in yaw via mooring lines are unlikely to experience this issue as yaw motions will be small. In addition, using only Morison elements to describe hydrodynamic loading on the support structure is another way of avoiding this issue.

If the platform is expected to have large yaw deviations during the simulation there are some assumptions that will produce inaccurate results as discussed below.

Excitations forces are based on initial platform yaw position

Bladed assumes that the excitation amplitudes and phases are fixed for the duration of the simulation depending on the initial yaw rotation of the platform and the direction of incident waves. At the start of the simulation the SEA file is read and for each wave component (frequency + direction) the corresponding amplitude and phase is identified from the excitation data. This is then used for the remainder of the simulation. As a consequence, if the platform yaws, the first order excitation loads due to wave action will not be accurate.

Rotation parameterisation for large yaw angles affecting hydrostatic restoring load

When rotations become large (e.g. due to large yaw), then the way that the rotation is parameterised becomes significant. Bladed uses the “axis-angle” convention to represent rotations of the platform as documented in this article, for example to define the initial platform orientation, as highlighted in the image below.

A relatively simple example is explained in the "Axis-angle representation in Bladed" knowledge base article. To achieve a geometrically equivalent pitch of a floating platform a user could either define platform pitch directly or alternatively yaw the platform first by 180 degrees and then pitch. In the former case the axis angle will match closely with the desired rotation. In the latter the axis-angle will have non-zero roll, such that the platform is tilted around global y (desired result from user perspective), while according to the axis-angle convention, the rotation is about x, so a restoring moment is applied about global x direction instead of about y.

The above example is simplistic but highlights an issue in the calculation of the restoring moment in cases where a floating platform experiences large yaw motion.

Solution

For customers looking to model floating platforms with large yaw rotations, such as the SPM system please follow this guidance:

If radiation-diffraction of the structure is not significant such that the BEM hydrodynamics method is not required then it is possible to use Morison elements instead where this issue will not be observed.

It is also possible to program a dynamic link library and apply loads during a time domain simulation via the external loads dll. Therefore if users have a hydrodynamic loading calculation this could be integrated into Bladed. Alternatively users could implement an improved hydrostatic restoring calculation in the external loads dll to replace the BEM hydrodynamic calculation and switch this contribution off in Bladed (to avoid double counting).

Finally. This is not a problem for floating platforms that are constrained in yaw but only for cases where yaw is significant such as SPM systems.

Keywords

Floating; Yaw; Axis-angle; BEM hydrodynamics; Hydrodynamics

Problem

Sometimes when running floating turbine simulations I am getting the obscure error message Invalid map <K,T> key - what does this refer to and how do I prevent it?

Solution

This issue seems always to occur in a model where the "BEM Hydrodynamics" option is defined but not used - e.g. if it was set up and then disabled afterwards. Any subsequent changes to the model, especially the tower and substructure, can trigger the error.

The BEM Hydrodynamics model is generally still present in the project file even if it is not being used in the run. If this is the situation, then there is a simple workaround which is to delete the Hydrodynamics section in the project file, so that you are left with only the opening and closing tags, like this:

Keywords

Invalid map; BEM; Floating