Multi-Part Blades

The simplest approach used in Bladed to model the blade flexibility is to model the blade as a single linear finite element body. Several linear mode shapes that include deflections of the whole-blade are calculated to account for blade deflection. This is illustrated in Figure 1.

Figure 1: Linear single part blade

Using whole-blade linear modes results in fast simulations as the number of degrees of freedom to model the blade deflections is small, and the freedom frequencies are relatively low. This approach often gives an accurate representation of blade dynamics. However, for this approach to be valid, the deflections of the blade must be small. Many modern blade designs are very flexible, meaning that the small deflection assumption in the linear model become invalid. This can lead to inaccuracies in predicting the blade dynamic response, in particular the blade torsion.

One method to maintain the small angle assumption for the blade modes is to split the blade into several linear parts. Figure 2 shows a schematic of modelling a blade using two linear parts.

Figure 2: Non-linear wind turbine blade model using two linear parts

The outer blade part can undergo a rigid body rotation based on the deflection and rotation of the inner part, as well as including linear mode deflections. The deflections within each linear part are therefore smaller than if using a single linear blade part. Splitting the blade into several parts allows for non-linear load transfer between each linear part, and a more accurate model of the blade deflection.

Specifying Blade Parts

The user needs to specify the boundaries of the parts in the blade. This is done by the section property: IsBladePartBoundaryAtThisSection. This property can either be true or false, where true indicates a boundary of a part. This is illustrated in Figure 3 for a 3 part blade.

Important

It is required to have the first section of the blade as a boundary - "IsBladePartBoundaryAtThisSection" = true.

Figure 3: Illustration of how to use IsBladePartBoundaryAtThisSection to define the blade parts.

The number of included modes per part is specified using NumberOfModesPerBladePart property which is part of the Modelling options for the blade. The user needs to carefully validate the included whole-blade modes and consider whether it includes the wanted dynamic responses such as torsional or flapwise modes etc.

For maximum accuracy, enough blade parts should be specified to ensure that deflections remain small within each blade part. When performing convergence tests for multi-part blade models, it is recommended to run some time domain tests with the maximum number of blade parts in order to establish a baseline converged dynamic response.

Note

For blades with more than one part, it is recommended to use the implicit Newmark-β integrator to improve simulation speed while retaining accurate solutions.

Note on Damping and Multi-Part Blades

The user must specify whole-blade modes even when using multi-part blades, as Bladed will calculate the appropriate damping ratios for the individual blade parts based on the specified whole-blade damping. This is also valid FiniteElementBladeModelling models, as Bladed will convert the whole-blade shapes into finite element degrees of freedom. Explained in further details below.

When a blade is split into several linear parts, mode shapes (or finite element degrees of freedom) are calculated for each linear part. In the Bladed modal structural dynamics formulation, modal damping must be specified for each mode on each blade part. However, in general the damping value for these individual modes would not be known by the blade designer, as these modes for the individual blade parts cannot be observed individually in reality to measure their damping.

To overcome this difficulty, Bladed calculates whole-blade modes for the multi-part blade by solving the Eigenvalue solution for all of the blade parts together. The whole-blade modes are made up of contributions from the individual blade part modes. The whole-blade modes should have very similar shapes and frequencies to the usual whole-blade mode shapes found for a linear blade model, if enough modes have been specified on each part. Damping ratios can then be specified for the whole-blade blade modes, and Bladed will calculate the appropriate damping ratios for the individual blade parts.

The number of whole-blade modes for the blade is equal to the total number of modes on all of the blade parts. For example, for a blade split into 4 parts with 8 modes on each part, there are 32 whole-blade modes.