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Table of Contents

Legacy Wave

The Legacy waves allow the user to select a range of linear and non-linear wave models. In the case of irregular waves non-linear waves can be blended into the water train. In addition, for irregular waves, diffraction affects can be corrected for using the MacCamy-Fuchs model or a simple frequency cut-off option. The Legacy waves calculation is restricted to unidirectional waves.

Click the Sea state icon on the toolbar and select the type of wave model required:

  • None: no waves are required.

  • Regular waves: Choose from either linear Airy or stream function waves of a single frequency.

  • Irregular waves: Choose either a standard Jonswap or Pierson Moskowitz spectrum, or enter a user-defined spectrum. This will generate a stochastic wave train as a superposition of linear Airy waves with the appropriate spectral distribution. Note these are unidirectional waves.

For all wave types, enter:

  • Direction of approach (from North): the bearing from which waves arrive at the tower. Like wind direction, wave direction is defined as the direction which the waves are coming from. The angle increases positively to the East of North.

Then enter the appropriate data for the chosen model as described below.

In the case of irregular waves, it is also possible to add a Constrained wave, which guarantees that the irregular wave train will contain an extreme wave of a specified height.

Any specified waves will be ignored if the turbine is not offshore.

None (no waves)

In this case the tower is not subjected to wave loading. However, if the turbine is specified as being offshore, it can still experience hydrodynamic damping and a drag force from any specified currents.

Irregular waves

Irregular waves are generated using a digital filter. The calculation is carried out on a grid with fixed size as shown in Figure 1. Wheeler stretching is applied to extend the water particle kinematics to the instantaneous water level given by \(\eta\). The grid resolution in the horizontal direction is hard coded such that grid nodes are \(2 \bunit{m}\) apart. In the vertical direction the grid is biased with increased resolution towards the sea surface where the water particle velocity and acceleration is larger. The extent of the grid is auto-calculated at runtime or a user-defined wave extent can be defined. The grid is aligned with the mean wave direction and only unidirectional waves can be simulated. Interpolation of gridded data is used to determine the water particle kinematics and dynamic pressure at a structural location.

Alt text

Figure 1: Grid for wave computation. The grid is shown perpendicular to the direction of travel of the wave crests. The wave extent is denoted \(L\). The water depth is denoted \(d\) and the tide height is \(h\). The global origin is denoted \((X_g, Y_g)\).

Different realisations of the wave train but with matching statistical properties can be simulated. Enter:

  • Random number seed: an integer to be used as the seed value for the random wave generation. A different seed value will generate a different realisation of the irregular waves, but still conforming to the desired wave spectrum.

To define the wave spectrum, chose either Jonswap / Pierson-Moskowitz spectrum or User-defined spectrum, and specify the diffraction approximation to use.

Jonswap / Pierson-Moskowitz spectrum

This standard wave spectrum is described in the Theory Manual, and requires the following parameters:

  • Significant wave height: corresponding to the average height of the highest one third of the waves in the seastate. Given a time-history of wave height, this parameter can be calculated as four times the standard deviation of the water surface elevation.

  • Peak spectral period: the period of the most energetic component in the wave spectrum.

  • Peakedness parameter: this parameter controls the width of the frequency band containing most of the energy in the spectrum. It should take a value between 1 and 7. For a Pierson-Moskowitz spectrum, the peakedness parameter should be set to 1.

User-Defined Spectrum

If the wave spectrum is known at the site of interest, select this option and then click Define spectrum. A further window opens which allows up to 100 pairs of values of frequency and power spectral density to be entered. Data entry boxes may be created and deleted by clicking on the Add and Delete buttons respectively. Data points are automatically sorted by frequency. Clicking on the Show button will reveal a plot of the spectrum as defined. The values of power spectral density at the lowest and highest frequencies entered should be zero.

Wave diffraction approximation

Two options are available to account for diffraction effects at small wavelengths comparable to the size of the structure:

  • MacCamy-Fuchs approximation: enter a representative member diameter, or select Auto-define to find and use a minimum member diameter in the wave-zone.

  • Simple cut-off frequency: enter a frequency, or select Auto-define to select a suitable value. For non-surface piercing structures, no cut-off frequency is applied.

When using auto-define Bladed selects the member with the minimum diameter based on all members that are expected to be submerged throughout the simulation (including members in the wave-zone).

Constrained waves

An irregular wave history can be modified to include a prescribed extreme wave at a particular time. Two methods are available:

  • Linear NewWave: the linear Airy waves are constrained in such a way as to produce the desired extreme wave height at the specified time, or

  • Stream Function: a non-linear stream function wave is blended into the irregular wave history.

In each case, enter:

  • Constrained wave height: measured from trough to crest; in the case of Linear NewWave, the trough elevation is taken as the lower of the troughs on either side of the crest.

  • Time of constrained wave: determines at what point in the simulation the constrained wave occurs

For the Stream Function method, enter also the

  • Constrained wave time period.

Regular waves

This option generates a regular wave train, also sometimes used as a way of obtaining extreme deterministic waves.

Choose the type of regular wave model:

  • Linear Airy gives a simple linear wave of the specified period

  • Stream Function gives non-linear stream function waves, which are more appropriate for extreme waves.

In either case, the following parameters are required:

  • Wave height: defined from trough to crest.

  • Wave period: time taken between two wave crests.

The user has no control over the phase of the regular wave. By default at time \(t=0\) seconds, the wave crest will coincide with the global origin as illustrated in Figure 2.

Legacy wave phase origin

Figure 2: Schematic of regular (linear) wave surface elevation \(\eta\) about the mean water level defined by the water depth \(d\) and tide height \(h\) at time \(t=0 \bunit{s}\). The wave crest occurs at the global origin \((X_g, Z_g) = (0,0)\).

Custom Wave-Train extent

For floating turbines that move a large horizontal distance during the simulation, resulting in the “Turbine has floated beyond calculated wave train” message. It is possible to define your own wave train extent, as follows.

MSTART EXTRA
WaveExtent 150.0 *Extent of wave train in metres (upstream and downstream)
MEND

The custom wave train will extend by at least this distance, both upstream and downstream. This value will only be applied, in either direction, if its absolute size in that direction is greater than the default wave train extent auto-calculated during simulation.

Tower Acceleration

Total acceleration is the sum of the time derivatives and a convective term:

\[ \begin{equation} \frac{Du}{Dt} = \frac{\partial u}{\partial t} + (u \cdot \nabla)u \end{equation} \]

The water particle accelerations in Bladed only include the time derivative terms by default. The convective terms can be added when using the stream function for the water particle acceleration calculations, by adding the text below into Project Info.

If using irregular waves and a constrained wave is applied defined by a stream function then it is not recommended to turn total acceleration on in this way. This is because the water particle acceleration will be calculated using time derivatives for the irregular waves and total acceleration for the constrained waves and would therefore be inconsistent.

MSTART EXTRA
TotalAccWaveNonLinear 1 * 0: off (default) use time derivative term only
* 1: on use total acceleration
MEND

Last updated 10-09-2024