TMR7 Experimental methods in marine hydrodynamics - lab exercise 3 2017

Offshore Wind Turbine monopile in 50 year storm conditions

Trygve Kristiansen and Erin Bachynski,

Trondheim, 20.09.2017

Background and motivation In storm conditions, nonlinear wave loads on monopile offshore wind turbines

can induce resonant ringing-type responses. Ringing refers to transient, resonant

response which is triggered by steep, irregular wave events, and can occur for

flexible structures in storm wave conditions. The steep waves cause significant

higher-order wave loads. That means that the wave loads act at higher

frequencies than the carrying wave, typically at frequencies of 3𝜔 and 4𝜔,

where 𝜔 is the wave frequency of the carrying wave.

The first natural period of Offshore Wind Turbines (OWT) is typically around

𝑇𝑛 =4 seconds. Severe 50-year wave conditions, or so-called Ultimate Limit

State (ULS) conditions, may typically have peak periods, 𝑇𝑝, of 11-13 seconds.

This means that 3𝜔 − 4𝜔 loads are important, since they will excite resonant,

flexible response at period 𝑇𝑛 of the wind turbine. A resonant response may

potentially cause damage to the structure. In the particular case of a monopile,

piled into the sea floor, the critical loads are bending moments near the mud-

line.

Efficient methods which accurately capture such events in irregular waves in

intermediate or shallow water depth conditions are needed for design. More

specifically, how much steel is needed depends on the expected most severe

ringing loads in ULS conditions. Dedicated experiments and numerical studies

must be performed toward this goal.

A simple method which may be able to capture these events is Morison’s equation:

d𝐹𝑚 = (𝜌𝜋

4𝐷2𝐶𝑚𝑎1 +

1

2𝜌𝐷𝐶𝐷𝑢|𝑢|) d𝑧.

In this experiment, you will evaluate how well Morison’s equation works for capturing both first

order and higher order wave loads.

A sketch of the experimental set-up in Lilletanken during a commercial project for Statoil carried out

by SINTEF Ocean during 2015 is provided in Figure 2. In this exercise, we will re-use the major parts

of the set-up (not including the exact positions of the wave gauges). The main focus will be on the

wave-induced forces and moments. The bending moment near the mud-line is typically the most

critical.

Figure 1: Monopile wind turbine schematic (https://www.theengineer.co.uk/issues/30-april-2012/wind-energy-gets-serial/)

Figure 2: Model test set-up of ringing experiments for Statoil, for the development of Dudgeon Offshore Wind Turbine farm (from [1])

Video snapshots of two severe, irregular wave events are provided in Figure 3, from two of the most

severe ringing events in the experiments. Corresponding loads and responses (mud-line moments)

measured in these irregular wave events are provided in Figure 4.

Figure 3: Snapshots from video (from [1]).

Figure 4: Waves (measured at the position of the model without the model, so-called wave calibration tests, blue), loads (on rigid model, red) and responses (on flexible model, black). The response in the flexible model tests clearly illustrates the concept of “ringing” – a transient, resonant response triggered by a steep irregular wave event.

References:

[1] Erin Bachynski, Trygve Kristiansen and Maxime Thys (2017) Experimental and numerical

investigation of monopile ringing in irregular finite-depth water waves, Appl. Ocean Res. 68, 154-170

[2] Trygve Kristiansen and Odd M. Faltinsen (2017) Higher harmonic wave loads on a vertical cylinder

in finite water depth, J. Fluid Mech. (accepted for publication Sept 2017)

Exercise The present exercise will make use of the experimental set-up illustrated in Figure 2. We will

consider a stiff monopile model, focusing on the wave loads themselves, rather than the response.

Waves at 4-6 selected positions will be measured using wave gauges. Horizontal force and

overturning moments will be measured by a force transducer (based on strain measurements). A

model scale of 1:48 is used. The (full scale) water depth is ℎ = 27m (meaning 56.25cm in model

scale). The regular waves are characterized by wave period 𝑇 and wave steepness 𝐻/𝜆, where 𝐻 is

the wave height, and 𝜆 the wave length.

1. Experiments

a. Run the pre-determined set of regular waves, as given in full scale in the table below

b. Perform a “hammer test”, meaning knock gently on the model while recording a

test, to measure the natural frequency of the set-up (should be around 20-25Hz).

Period 𝑇 (s) Wave steepness 𝐻/𝜆

6 1/60

6 1/42

6 1/24

9 1/60

9 1/42

9 1/24

12 1/60

12 1/42

12 1/24

2. Video:

a. Use your mobile phone to capture video of some of the tests (preferably high-speed

video).

b. Study the free-surface near the cylinder. Are there local free-surface deformations?

Do the deformations depend on the wave steepness and wave periods? Describe

briefly your observations. You may include snapshots of your video in your report.

3. Experimental data analysis:

a. Load the measured waves, forces and moments time signals into Matlab or Python.

Present the load signals in your report. Include a brief textual description of the

signals. For the longest waves, the time-series should look similar to that in Figure 5

(see thick curve in the upper plot; the thinner lines represent the 𝜔, 2𝜔 and 3𝜔

components of the force).

b. Compare all the measured time series of wave elevation from different positions in

the tank. Does the monopile cause significant wave diffraction? For the longest wave

periods, due to the long wave length of the longest waves (9 and 12s), there should

be very limited free-surface diffraction. What is the so-called long wave limit 𝜆/𝐷?

What is 𝜆/𝐷 for the three wave periods in the tests?Hint: Cf. “Sea Loads” by

Faltinsen.

c. Compare the wave signal from the wave gauge next to the model (located to the

side of the model, at the same 𝑥 − position as the center of the model) and the load

signals (force and moment). The phase is typically 90 degrees out of phase with the

wave. This means the loads are inertia dominated. Explain this in terms of Morison

equation.

4. Theory:

a. Morison’s equation (see Background and Motivation): Explain the different terms

(cf. “Sea Loads” by Faltinsen).

b. Assume linear wave theory. The wave kinematics may then be calculated when you

know the water depth ℎ, wave period 𝑇 and wave steepness 𝐻/𝜆. What are the

wave lengths and wave heights of the regular waves studied here? Hint: use linear

wave dispersion relation 𝜔2 = 𝑔𝑘 𝑡𝑎𝑛ℎ 𝑘ℎ, where 𝑘 = 2𝜋/𝜆 is the wave number.

c. Apply the undisturbed wave kinematics from linear wave theory (acceleration 𝑎1

and velocity 𝑢), a drag coefficient of 𝐶𝐷 = 1, and integrate the 2D force as given by

Morison’s equation strip-wise along the model, from the sea floor 𝑧 = −ℎ to the

mean free surface 𝑧 = 0 to obtain an estimate of the force for the regular wave

tests you have tested. See Figure 6. (You may integrate Morison’s equation both

analytically and numerically, preferably do both and compare the results).

d. Compare the theoretical estimates and the measured horizontal force. You should

discuss the shape of the time series of the force, the amplitude of the force, and the

frequencies which are present in the measured force. A Fast Fourier Transform (FFT)

can be used to identify the frequency components of the force and compare their

magnitude. Hint: when using the fft function in matlab, it is convenient to choose a

section of the time signal which is a complete number of wave periods. It is also

convenient if your theoretical force and measured force are recorded with the same

time step.

e. How well does the theoretical estimate capture the force at different frequencies?

In which wave condition does the theoretical estimate work best?

f. Examine the effect of setting 𝐶𝐷 = 0. How important is the drag coefficient at the

important forcing frequencies?

Schedule

Group Day Time slot

3 Monday 9. October 12:15-15:15

4 Tuesday 10. October 08:15-11:15

5 Tuesday 10. October 12:15-15:15

6 Wednesday 11. October 08:15-11:15

7 Wednesday 11. October 12:15-15:15

8 Thursday 12 October 08:15-11:15

1 Thursday 12 October 12:15-15:15

2 Friday 13 October 08:15-11:15

Available Friday 13 October 08:15-11:15

Deadline for submission of report: Friday 27. October

Figure 5: Typical force time-series from a regular wave tests (upper) and corresponding theoretical calculations with a high-order theory model (FNV, lower). Note that the time-series axis has been normalized by the wave period 𝑇. (From [2])

Figure 6: Definition of coordinate system and geometric quantities.