Structural Dynamics of Offshore Wind Turbines subject to Extreme Wave Loading

Transcription

1 Structural Dynamics of Offshore Wind Turbines subject to Extreme Wave Loading N ROGERS Border Wind Limited, Hexham, Northumberland SYNOPSIS With interest increasing in the installation of wind turbines offshore of the UK and the preferred foundation method likely to be monopiles rather than gravity foundations, attention must be focussed on the structural analysis and design of the monopile and tower. While the effects of operational loads and wind loads are well understood, the consequences of wave loading need to be assessed. At first sight, with the first natural period of the structure being of the order of 2 seconds and waves with significant energy having periods of 8 to 1 seconds, the problem of structural excitation would appear to be minimal. For most sites in UK waters however, the depth will be such that breaking or near-breaking waves will occur and the phenomenon of ringing will cause significant magnification of stresses and displacements. This paper presents predictions of the stresses and displacements from a six mass model of an offshore wind turbine subjected to a train of extreme wave loads. Dynamic magnification of stresses and displacement is clearly demonstrated. The sensitivity of the results to variation in wave period, bed conditions and damping is also presented. INTRODUCTION Dynamically-sensitive structures in deep water are common in the oil and gas industry, but such structures are not generally subjected to breaking waves. The effects of breaking waves on relatively rigid structures (jetties, breakwaters etc) is also well understood. However, offshore wind turbines on monopile foundations are dynamically-sensitive structures which are subjected to breaking waves and as such present a relatively unusual design problem. Although the overall period of the breaking wave is generally well above the first natural period of the structure, the breaking wave contains harmonics which will cause structural excitation. This phenomenon is known as ringing and is described in a number of papers (1,2). Reference 2 describes the results of tests in which breaking waves impacting on a 1:2 scale model of a 1m diameter cylinder produce measured forces 1.5 to 2 times greater than predicted by existing design codes due to dynamic amplification effects caused by ringing of the structure after wave impact. STRUCTURAL MODELLING

2 Figure 1 shows a typical 75kW wind turbine mounted on a monopile foundation in a maximum water depth of 12 metres. Figure 2 shows the 6 mass model of this structure, where the masses are assumed to be concentrated at 6 nodes, separated by massless elements having finite bending stiffness m The model allows a sinusoidally-varying load of a particular frequency to be applied at each nodal position. Bending Stiffness (m*m*m*m) 6 Node Mass (tonne) m dia 1mm 9.6 m m 12mm 7.2 m Max Water Level Bed Level 12. Depth to Fixity 14mm 16mm mm 2.6 m dia m dia 7.2 m 5.65 m 18. m 5.2 m High Water 3 Low Water Sea Bed m 6. m 6. m 6. m 5.2 m Figure 2: 6 mass model of 75 kw wind turbine (2 pile diameters to full fixity) Figure 1: 75 kw wind turbine on monopile foundation (2 pile diameters to full fixity) To model the stiffness of the ground, the lowest element is assumed to be fixed against rotation at its lower end at a point some distance below the seabed, the so-called point of full fixity. Allowance has been made for hydrodynamic added mass to 12m above seabed level and added rock mass from bed level to the point of full fixity. To allow for appurtenances, the tower mass has been increased by 5%. The model allows for the damping in terms of a damping coefficient at each node, the damping force being the product of the damping coefficient and the instantaneous nodal velocity. For the purposes of comparison, results are presented for the case of zero damping and the effects of damping assessed as a special case. STRUCTURAL RESPONSE UNDER SINUSOIDALLY-VARYING LOADING Figure 3 shows the displacement profiles of the monopile and tower when subjected to sinusoidally-varying loads of different periods, T, at node 3. For these cases, zero damping has been assumed. A negative displacement indicates motion out-of-phase with the load. The main features demonstrated are as follows: For T=1 seconds, (effectively the static load case), the tower top deflection is 45mm. For T= 4 to 2 seconds, (the range of periods for waves), the dynamic magnification of the tower top deflection is negligibly small. For T=1.9 seconds, the tower top deflection is over 3mm. This is the first natural period of the structure.

3 For T=1 second, the mode shape is different due to excitation of the second natural period. breaking wave must be broken down into its Fourier components for input to the structural model. In the practical case considered here, the wave loading is not sinusoidal. The loading from the T = 1 sec T = 1.4 secs T = 1.8 secs T = 1.9 secs T = 2 secs t = 2.2 secs T = 3 secs T = 4 secs T = 1 secs T = 1 secs Figure 3: Displacement profiles of monopile and tower subject to sinusoidaly-varying load 3sin(2*PI*t/T) at Node 3

4 BREAKING WAVE LOADING AND SIMULATION BY FOURIER ANALYSIS Reference 3 (1982) describes a method for evaluating breaking wave forces on offshore wind turbines. Reference 4 (1991) summarises the range of wave theories currently available for different combinations of wave height, wave period and water depth. The estimated maximum wave loading on the monopile has been calculated here from water particle velocities and accelerations from Dean s Stream Function theory with an 11 th order solution and Morrison s theory with drag and inertia coefficients as follows: Drag coefficient Cd = 1. Inertia coefficient Ci = 2. A maximum water depth of 12m was assumed. The wave period was taken to be 8 seconds. For these conditions, the maximum breaking wave height was predicted to be 7.78m. The total waveload on the 2.6m diameter monopile and its variation during one complete wave cycle is shown in Figure Total Waveload Node 4 Node 3 Node 2 Node 1 Figure 4: Total Waveload on a 2.6m diameter monopile. Details of the corresponding waveload at each of the nodal positions on the monopile are shown in Figure Figure 5: Waveload at each node

5 Provided that the incoming waveform is part of a train of identical waves rather than a solitary wave, Fourier analysis can be used (Ref 4) to model the complex waveform from individual sine and cosine components. These individual components can be used as inputs to the structural model to predict stresses and displacements of the structure, the overall stress or displacement at a particular location being the sum of the results from each sine and cosine component. Figure 6 shows the wave load at Node 3 assembled from the individual Fourier components. This should be compared with the actual waveload distribution from Figure 5. Figure: 6 Waveload at node 3 assembled Waveload for Node 3 compiled from Fourier components Figure 7: Bending moments in Height above fixity point (m) Height above fixity point (m) T = 8 secs Bending moment (knm) T = 1 secs (static case) Bending moment (knm) monopile/tower from breaking wave (dynamic and static case, 2D fixity depth, zero damping) -5 from Fourier components Figure 8: Displacement of monopile/tower BENDING MOMENTS AND DISPLACEMENTS FOR BREAKING WAVES Dynamic Magnification of Stresses and Displacements Height above fixity point (m) T = 8 secs Horizontal The waveloads shown in Figure 5 were input to the model shown in Figure 2 for the case of zero damping and with wave periods of 8 seconds and 1 seconds, the latter case representing the static load case. The resulting bending moments and displacements in the monopile and tower are shown in Figures 7 and 8 at the instant of maximum tower top displacement. The following conclusions are drawn: Height above fixity point (m) T = 1 secs (static case) Horizontal from breaking wave (dynamic & static cases, 2D fixity depth, zero damping) Due to dynamics:

6 the bending moment at the point of fixity is increased by 13% from 85 to 96 knm.; the bending moment at the seabed (height above fixity = 5.2m) is increased by 19% from 65 to 72 knm.; bending moments exist in the tower, above the point of application of the load.; the displacement at the top of the tower is increased by 7% The increase in bending moments due to dynamics for this case are not large, but as will be seen in the next section, the effects of small variations in the incident wave period can potentially have a large effect on both the bending moments and displacements of the monopile/tower.. Stress (N/mm2) Stress (N/mm2) Bending Stress at base of tower Bending Stress at point of fixity of monopile Figure 9: Sensitivity of bending stress to period of breaking wave (2D fixity depth, zero damping) Sensitivity to Wave Period The waveloads shown in Figure 5 were input to the model shown in Figure 2 for the case of zero damping and with wave periods of between 7.4 and 8 seconds. At a wave period of approximately 7.66 seconds, significantly removed from the natural period of the structure of 1.9 seconds, very large stresses and tower top displacements are predicted (See Figures 9 and 1) due to ringing. This is the effect by which the shorter period harmonics within the breaking wave cause excitation of the structure. Tower top displacement Displacement (m) Figure 1: Sensitivity of displacement to period of breaking wave (2D fixity depth, zero damping) Sensitivity to Different Bed Conditions For a particular offshore windfarm site, it is conceivable that the bed conditions could vary significantly. By varying the depth to effective fixity, the sensitivity of bending moments and displacements to variation in seabed geology can be examined. The waveloads shown in Figure 5 were input to the model shown in Figure 2 for the case of zero damping and wave period equal to 8 seconds, with depths to effective fixity of between one and five pile diameters. At a fixity depth of 2.8 pile diameters, very large tower top displacements are predicted due to ringing. (See Figure 11).

7 Displacement (m) Tower top displacement Fixity depth (diam.) Figure 11: Sensitivity of tower top displacement to fixity depth (breaking wave period T = 8 secs, zero damping) Effects of Varying the Damping Factor The values of damping coefficient to assume at each node are difficult to ascertain. Damping arises from a number of sources - aerodynamic, hydrodynamic, structural and inertial. For a dynamically sensitive system subject to perturbation, if the damping is heavy, oscillatory motion will not occur; the system is said to be overdamped. If the damping is light, oscillation is possible; the system is said to be underdamped. A critically-damped system is one in which the amount of damping is such that the resultant motion is on the borderline between these two cases. The perturbed system will simply return to its equilibrium position. The degree of damping is often defined by the damping factor which is the ratio between the actual damping and the critical damping. Reference 4 gives guidance on the magnitude of damping factor to be expected in welded steel offshore structures and suggests values between.2 and.8 for structures in air and between.8 and.3 for structures in water. Reference 5 suggests values of.1 to.5 for logarithmic decrement. This is directly related to damping factor and corresponding values also range between.2 and.8. Reference 6 suggests a structural damping factor of.2 and presents a method for determining aerodynamic damping, which is significant, but only if the turbine is running. For most design applications, the structural response is not sensitive to the value of damping assumed and accurate values are not essential. This is not the case for breaking wave loads acting on an offshore wind turbine with a monopile foundation. Figures 12 and 13 show the effects of values of damping factor of,.1 and.1 on the monopile and tower bending stresses and on the tower top displacements. Damping is seen to have a significant effect on reducing the structural response. However, if damping factors as low as.1 are realistic, then stresses of the order of 15 N/mm2 can occur. Stresses of this magnitude will be significant in the design of the monopile and tower, considering the additional stresses caused by wind loading which have not been considered here. Stress (N/mm2) Stress (N/mm2) E =.1 Bending Stress at base of tower E = E =.1 Bending Stress at point of fixity E = E =.1 E =.1 Figure 12: Effects of damping on bending stresses from breaking wave (2D fixity depth)

8 Displacement (m) Tower top displacement E = E =.1 E = Figure 13: Effects of damping on displacement from breaking wave (2D fixity) Texas. Volume 2 Platform and Marine System Design OTC 867 PP Swift R H and Dixon J C Design Wave Forces on Offshore Structures. BWEA 4 th Wind Energy Conference. Cranfield. 4. Barltrop N and Adams. Dynamics of Fixed Marine Structures. 3 rd Edition Oxford. Butterworth-Heinemann. 5. Regulations for the Certification of Offshore Wind Energy Conversion Systems. IV Non-Marine Technology. Part 2 - Offshore Wind Energy. Germanischer Lloyd 6. Sinclair F M and Clayton B R. Excitation and Damping forces on Offshore Wind Turtbines. Wind Engineering Vol 13 No CONCLUSIONS Breaking waves will potentially cause significant dynamic magnification of structural response for offshore wind turbines on monopile foundations sited in relatively shallow water. In analysing the structure, attention needs to be paid to the sensitivity of the results to small changes in wave period, ground stiffness and damping. The level of damping is crucial in determining the structural response and further work is required to establish true values of damping factor for offshore wind turbines. REFERENCES 1. Spidsoe N and Karunakaran D 1997: Effects of Non-Gaussian Waves to the Dynamic Response of Jack-up Platforms. Elsevier Science Ltd. Marine Structures 1 (1997) Kriebel D L, Berek E P, Chakrabarti S K and Waters J K Wave-Current Loading on a Shallow Water Caisson. OTC 96 - Offshore Technology Conference Proceedings. Houston,