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 T n =4 seconds. Severe 50-year wave conditions, or so-called Ultimate Limit State (ULS) conditions, may typically have peak periods, T p, of 11-13 seconds. This means that 3ω 4ω loads are important, since they will excite resonant, flexible response at period T n 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 mudline. 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. Figure 1: Monopile wind turbine schematic (https://www.theengine er.co.uk/issues/30-april- 2012/wind-energy-getsserial/) A simple method which may be able to capture these events is Morison s equation: df m = ( ρπ 4 D2 C m a 1 + 1 2 ρdc Du 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 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 ω 2 = gk tanh kh, where k = 2π/λ is the wave number. c. Apply the undisturbed wave kinematics from linear wave theory (acceleration a 1 and velocity u), a drag coefficient of C D = 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 C D = 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 highorder 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.