Characterization of Wave Slamming Forces for a Truss Structure within the Framework of the WaveSlam Project

Available online at www.sciencedirect.com

ScienceDirect Energy Procedia 80 (2015) 276 – 283

12th Deep Sea Offshore Wind R&D Conference, EERA DeepWind'2015

Characterization of wave slamming forces for a truss structure within the framework of the WaveSlam project. Ignacio E. Rausaª*, Michael Muskulusb, Øivind A. Arntsenc, Kasper Wåsjød ª, b ,c Department of Civil and Transport Engineering, Norwegian University of Science and Technology, 7491 Trondheim, Norway. d

Reinertsen AS, Leiv Eiriksson senter, 7010 Trondheim, Norway.

Abstract One increasingly popular type of foundations for offshore wind turbines in shallow water are truss structures. These are exposed to wave slamming forces from breaking wave events. These forces depend, among other parameters, on the slamming factor Cs that typically takes values between π -2π. So far, several studies about slamming forces have been done for monopile structures, but not much work has been done regarding truss structures such as offshore jackets. This paper is based on the WaveSlam project in which an instrumented multi-membered truss model has been subjected to regular and irregular waves in the large wave flume at FZK Hannover in 2013. The structure was built at scale 1:8 and equipped with force transducers along the bracings and columns that measured the structural response from the breaking waves. The goal of this study was to characterize the breaking wave forces acting on the front bracings of the structure, in order to estimate the respective slamming factors. The tested structure has been modelled and validated with a finite element model in ANSYS and a wave run test is analyzed. The wave loads have been defined as uniform loads with a triangular force time history acting along the bracings. Through a fitting procedure, the initial responses from ANSYS and from the data were matched with a relative error of 3% for one single wave test. From this, a slamming factor of 4.78 is found in the highest part of the front bracings. The characterization of more breaking wave loads is recommended in order to get an estimate of the largest slamming factor, which is relevant for design purposes. © Published by Elsevier Ltd. Ltd This is an open access article under the CC BY-NC-ND license © 2015 2015The TheAuthors. Authors. Published by Elsevier (http://creativecommons.org/licenses/by-nc-nd/4.0/). Selection and peer review under responsibility of SINTEF Energi AS. Peer-review under responsibility of SINTEF Energi AS Keywords: Truss structures; Inverse problem; Transient finite element analysis; Slamming coefficient; Offshore wind energy.

1. Introduction Offshore wind turbines are designed to withstand environmental loads for 20-30 years. Because offshore wind farms are not yet competitive with other solutions as fossil fuels, the costs have to come down by around 40% in the next decade. Det Norske Veritas GL, one of the largest technical energy consultancies in the world, has recently issued an “offshore wind cost reduction manifesto” (2013) [1] in order to reduce the costs by 25%, where the optimization of the substructure is a highlighted point for improving of the existing processes. The design of such structures in shallow water regions is predominantly subjected to loads from plunging breaking waves, which *Corresponding author: Tel: +47 94 289 359. E-mail address: [email protected]

1876-6102 © 2015 The Authors. Published by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/). Peer-review under responsibility of SINTEF Energi AS doi:10.1016/j.egypro.2015.11.431

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are usually larger than Morison forces. Thus, a better comprehension and reduction of the uncertainties in these slamming wave forces will imply a reduction of the wrong assessment risks for those loads, and therefore an optimization of the structure’s design. That could mean for example lower requirements for some structure elements, such as smaller beams diameters, which could lead into a direct reduction of the energy cost. This work is focused on truss substructures, which are used predominantly in shallow waters from 5 to 40 meters, typically called ‘jackets’. The so called wave slamming forces caused by plunging breaking waves produce very rapid and high intense impacts, which govern the response of the structure. In recent works it has been found that the slamming forces (1) are proportional to the square wave celerity Cb, the impact area of the wave ληb, water density ρw, the radius of the element R, and a slamming coefficient Cs. This load factor has been intensively studied and most studies found values between π to 2π for a single vertical and inclined pile, Goda et al. (1966) [2], Wienke and Oumeraci (2005) [3]. Therefore, some of the most commonly used guidelines, such as DNV (2010 a, b) [4] and ISO 21650 (2007) [5], recommend a value of 5.15 to 2π for truss structures.

Fs

Cs ˜ Uw ˜ OK b ˜ Cb 2 ˜ R

(1)

The goal of this study is to characterize the slamming forces on truss structures and determine what values of the slamming coefficients Cs are associated to them. In 2013, a consortium headed by the University of Stavanger (UiS), Norway and the Norwegian University of Science and Technology (NTNU), Trondheim, Norway carried out the WaveSlam project (Arntsen and Gudmestad, 2014) [6]. In this project a prototype jacket (Fig. 1a) was built in a large scale 1:8 and subjected to thousands of wave impacts in the Large Wave Flume at FZK Hannover. The base of the channel was modified and set up with a slope of 1:10 in order to recreate plunging breaking waves in front of the structure. The structure was equipped with a total of 12 two-axis force transducers distributed along six bracings of the structure. Ten force transducers mounted in 40 mm high sections on the front legs provided information on the vertical distribution of the forces (Fig. 1b). The starting point for characterizing the wave slamming forces on the bracings is to analyze the response recorded on the four transducers FTBF01 to FTBF04. For that purpose the structure was modelled using a multiple degree of freedom (MDOF) model in a finite element solver. Through a fitting procedure, the wave slamming loads were tuned until the response on the numerical model matched the response data. a)

b)

Figure 1. a) Tested structure in Hannover (reproduced with permission from the WaveSlam project). b) Location of bracing transducers FTBF01-02-03-04 and Impulse hammer tests, , . Units in [m].

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2. Modelling of the Structure in ANSYS 2.1. Numerical Modelling The software used was ANSYS (Ver. 14.5 Mechanical, ANSYS Inc., Canonsburg, USA). When a body has an uniform cross section and small lateral dimensions, it is usually modelled as a slender beam structure. This way of modelling is specially indicated for truss structures in order to create a dimensional idealization of a 3D structure. 2.1.1. Geometry and material properties The truss structure is a reproduction of the prototype. This truss structure is mainly composed of steel St37 with young modulus of 2.10·1011 Pa and a density of 7850 kg/m3, for the columns and bracings with an external diameter of 139.7 mm. The three instrumented legs were designed with a solid cross section of aluminum with the same outer diameter 139.7 mm as the rest of the structure, a young modulus of 7.00·1010 Pa and a density of 2700 kg/m3. The remaining structure is composed of steel tubes with a wall thickness that varies depending on whether the tube is instrumented or not, from 5 to 4 mm, respectively. See visualization of the process in ANSYS (Fig. 2). a)

b)

c)

Figure 2. a) Initial geometry defined as line body in ANSYS, b) definition of each section, c) structure meshed.

2.1.2. Validation of the Model The validation process of a numerical model represents a key part in any modelling process in order to make it reliable. As the main goal of the numerical model is to characterize the wave slamming forces, using a comparison between the results obtained with it and the response recorded in the experimental tests, the fidelity of the numerical model is a must. Several excitation loads (hammer tests), were applied on points 7-12 (Fig. 1b). The validation process was focusing on the local response of the instrumented bracings. For that purpose, hammer test no. 8 is examined and the response at FTBF01 to FTBF04 is studied in the following. The wave slamming forces will be defined as impulse loads within a short time interval. Thus, the validation of the local element properties is fundamental, especially for the first milliseconds of the response, where the highest slamming forces are produced. a)

b) FTBF01-FH / Hammer test at 8

FTBF02-FH / Hammer test at 8

4500 Response [N]

Response [N]

4500 3000 1500 0 -1500

3000 1500 0 -1500

0

0.002 Data

0.004

0.006 Ansys

0.008

0.01 Time [s]

0

0.002

0.004 Data

0.006 0.008 Ansys

0.01 Time [s]

Figure 3. a) Comparison between data and numerical response at FTBF01, for hammer test 8, b) Comparison between data and numerical response at FTBF02, for hammer test 8.

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An initial analysis for the hammer test applied at position no. 8 (Fig. 1b) showed a high deviation especially for the intensity of the initial response (Fig. 3 a, b). The relative error for the initial peak on both transducers was 90-70%, which was obtained from the comparison of the Data and ANSYS values recorded for the first peak, respectively. A modal analysis for the local vibration of the front bracings showed an eigenfrequency of around 274 Hz (Fig. 4b). This frequency from the numerical model can be compared with the response spectrum from the experimental analysis. A first analysis of the hammer response spectrum showed an eigenfrequency of 80-100 Hz (Fig. 4a). It is important to remark that the bracing transducers were not modelled exactly as they were built up in the physical model because of their complexity and some uncertainties about the installation. Thus, extra mass was added on the bracings in the numerical model to consider their contribution as a simplification. These initial studies point out that the instrumented bracing in the numerical model seems much more rigid than what it was in the experiment. Thus, if it is assumed that the impulse load (i.e., hammer test) can be described by a triangular load ˆ‘ with an impact duration ‫כݐ‬, the dynamic response is influenced for the vibration of the beam as described in Fig. 5. This figure shows the maximum dynamic response ܷ݉ܽ‫ݔ‬ǡ for different values of ‫כݐ‬ and the eigenfrequency of the element, where ܶ‫ ܦ‬is the period associated to this frequency and ݂଴Τ݇ represents the static response. The dynamic response becomes lower when the natural period of oscillation is larger, that means a smaller frequency of oscillation of the bracing. a)

b)

Figure 4. a) Spectrum at FTBF01 for the response hammer test at position no. 8, b) Local frequency analysis of the front bracings in ANSYS.

The eigenfrequency for a beam depends on the boundary conditions WN, the mass per unit of length m, length l, inertia I, and young modulus E (2). In order to reduce the vibrational frequency of the beam and avoid modifications of the boundary conditions of the beams in the numerical model, the Young modulus of the material has been modified until a better match was obtained. This reduction of the Young modulus will modify the local dynamics of the beam, reducing the frequency of it, thus an improvement in the force response is expected (Fig.5)

WN WN

ܷ௠௔௫ ݂௢ Τ݇

(2)

E˜I m ˜ l4 Impulse load [N]

ʹ ͳͷ ͳǤͷ ͳ

0.5

ANSYS ݂௢

‫כݐ‬

Time [s] ‫כݐ‬ 0.868 0.8688 0.8696 0.8704 ܶ஽ Figure 5. Value of the dynamic response compare to the static response for different ratios of impact duration ‫ כݐ‬and eigenfrequency ͳΤܶ஽ of any element. The figure on the right side represents the Impule Hammer test 2406201325 at position nº8. D Data

ͳ

ʹ

͵

Ͷ

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The adapted Young modulus for the front bracings was set at a value of 2.10·1010 Pa. The new response of the numerical model represents a significant improvement (Fig. 6), with an average deviation for the initial peak of 7% for both responses. The relative error regarding the time of the response for the first peak is less than 9%, which is very similar to obtained in the previous analysis. The rest of the peaks are lower in intensity and not only affected by local dynamics, but also influenced by global dynamics which is out of the scope in this paper. a)

b) FTBF01 -FH / Hammer Test at nº8

FTBF02 - FH / Hammer Test at nº8

3000

2000

Response [N]

Response [N]

3000 1000 0 -1000

2000 1000 0 -1000 -2000

-2000 0

0.002

0.004 Data

0.006 Ansys

0.008

0

0.01 Time [s]

0.002

0.004 Data

0.006 Ansys

0.008

0.01 Time [s]

Figure 6. a) Comparison between data and numerical response at FTBF01, b) Comparison between data and numerical response at FTBF02.

3. Characterization of wave slamming forces For offshore substructures, the most adverse load to which they are exposed is the horizontal force when the wave breaks just in front of the structure, or some short distance before it. This scenario leads to a relatively high and rapid force acting on the different elements where the impact is produced. The characterization of the wave loads on the bracings has as ultimate goal to determine the slamming factor Cs, occurring at the beginning of the impact (3).

Cs

Fs

(3)

U w ˜ R ˜ Cb 2 ˜ OK b

3.1. Study case: Wave test 2013061414 A specific wave test has been chosen for the characterization of the wave slamming forces. This wave test corresponds to run no. 14 from the 14th of June, 2013. The main reason for selecting this specific wave among the others, is because the hitting time for the lower part and for the upper part of the front bracing is well-separated. That allows us to get a more reliable analysis and also a better identification on parameters such as ߣ௡௕ (Fig.7-8). The corresponding wave height is Hwave = 1.97 m and the horizontal response on the instrumented front bracings is shown in the figure 7. It can be seen how the wave hits first FTBF01 at around 132.966 s, and a peak value of 1300 N was recorded. On the right front instrumented bracing the wave hits later on the lower side, FTBF04. The impact is observed at around 132.977 s with a peak value of 1600 N. That means the wave is hitting the structure asymmetrically. Focusing on the wave impact at the upper parts of the bracings it is seen that the peak response is almost double than the one in the lower part. The impact on FTBF02 is at 132.993 s, whereas the highest peak on FTBF03 is recorded at 132.989 s. It is observed that the wave is not acting at the same time along the whole bracing, because an initial impact is localized at FTBF01 and FTBF04, and after a finite time, around 0.02 s, a maximum response is reached on the upper transducers, FTBF02 and FTBF03. Due to this long time lapse between the impacts on the lower and upper part, both impact areas can be defined independently one from the other in that study case. So, the sequence of the impact is FTBF01-FTBF04-FTBF03 and finally FTBF02, where two different and well separated impact areas could be defined. All the others wave tests need to be studied in detail and carefully analyzed to see how the wave impacts and how this affects to the response on the other transducers.

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Figure 7. Force-time response for the front bracings.

To simulate this impact sequence numerically two impact areas were defined (Fig. 8a). A first uniform load was applied from the lowest part of the left front bracing until the middle of it, then the same was repeated at the right bracing with a certain offset in time. This takes place within the impact area no. 1. After that, another uniform load was defined from the middle until the upper part of the same bracing and finally, the last load acts in the upper part of the left bracing, within the impact area no. 2. The wave load was defined as a uniform load with a triangular time history (Fig. 8b). A total of four parameters have to be calibrated regarding the duration of the load τ, the peak time Tp, the maximum force Fp, and the offset time toff. The wave crest height is defined as ηb1 and ηb2, whereas ληb1 and ληb2 refers to the height of the impact area. Besides, it seems consistent to consider the wave particle velocity ‫ܥ‬௕ at the free surface of the breaking wave as the wave celerity, due to the fact that the wave breaks when the particle velocity at the crest exceeds it. a)

b)

Force [N]

1 Impact Area 1

p Lim

pac

t

3

act

Wave load 2

OKb1

4

Wave load 1

OKb2

Force, Fp

2

Kb1

Impact Area 2

Kb2

Lim

Time [s]

Tp t off

W

Figure 8. a) Representation of the two impact areas on the front bracings, b) Characterization of the wave load.

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800 600 400 200 0 -200 -400 -600 0.000

FTBF01-FH - Run Test I 4000 2000 0 -2000 0.005

0.010

0.015

Data

0.020

Ansys

0.025

0.030

0.035

Triangular Impulse load

Impulse force [N]

Response [N]

A large number of wave loads were defined and calibrated on the numerical model until a good match between the model and the experimental data was obtained. The following figures summarize the process for FTBF01 and FTBF02 by showing the wave slamming loads that resulted in a response closest to the data.

-4000 0.040 Time [s]

Figure 9. Comparison between the Data response and ANSYS at FTBF01-FH. Table 1. Results for the analysis of FTBF01-FH. FTBF01-FH ηb2 [m]

1.06

ληb2 [m]

0.294

toff [s]

0

d +ηb2 [m]

3.06

limpact [m]

0.635

Tp [s]

0.0005

Cb [m/s]

5.48

Fp

2800

τ [s]

0.005

[N]

Cs

2.09

Relative Error

Force [%]

7.01

Time [%]

5.08

7000 5000 3000 1000 -1000 -3000 -5000 0.040 Time [s] Impulse force [N]

Response [N]

FTBF02-FH - Run Test I 2000 1500 1000 500 0 -500 -1000 -1500 0.000

0.005

0.010 Ansys

0.015 0.020 Data

0.025 0.030 0.035 Triangular Impulse load

Figure 10. Comparison between the Data response and ANSYS at FTBF02-FH. Table 2. Results for the analysis of FTBF02-FH. FTBF02-FH ηb1 [m]

1.35

ληb1 [m]

0.294

toff [s]

0.025

d+ ηb1 [m]

3.35

limpact [m]

0.635

Tp [s]

0.0008

Cb [m/s]

5.74

Fp

7000

τ [s]

0.008

[N]

Cs

4.78

Relative Error

Force [%]

1.24

Time [%]

1.30

The response for the first slamming load acting along the lower left front bracing reproduces almost the exact initial local response of the recorded data. This good fit is not only for the first peak, but recreates faithfully most of the signal (Fig. 9). The analysis of the next peaks is more complex because the response is affected by the subsequent impacts of the wave as it does not hit the structure uniformly and for the global dynamics of the structure. Thus the response at 0.01 s and 0.03 s is influenced by the wave hitting the lower part of the right bracing. The value of Cs obtained is 2.09, with a relative error of 7.01% (Table. 1). An almost identical response is obtained on the upper part of the bracing (Fig. 10). The wave load hits the structure with a time delay of 0.025 s from the initial impact, with a peak intensity of 7000 N during 0.008 s. The deviation for the impact in term of forces is only 1.3%. That situation leads to a value of Cs equal to 4.78. (Table. 2).

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4. Conclusions The largest slamming coefficient found for the wave test analyzed Cs = 4.78, is smaller than the one found by Oumeraci (2005), Cs = 2π, but is quite similar to other slamming factors obtained when a truss structure was studied, Aune (2011) [7] who obtained a value of 4.77. Apart from the intensity of the wave slamming loads, another parameter that has a large influence on the results is the duration of the wave slamming load τ. These values are found within the range = [0.2 - 0.5] D/Cb , set by different researchers (Arntsen et al., 2011) [8]. Besides, the numerical model offers a notable initial local response while approximating the wave loads as uniform with a triangular time force history. The response from ANSYS gives an average relative error for the initial peak force of 2.65%. Moreover, the behavior described by the physical model when the impact takes place is faithfully described on ANSYS. Based on that, this numerical model seems a promising tool to continue with further analysis. In light of the randomness in the location and duration of the wave impacts, it does not seem possible to automate the process for all observed breaking wave load records, however. It is important to remark that this paper only contains the analysis of a single wave test, so it means that the highest slamming coefficient obtained is not representative of the largest slamming coefficient that might be found in a complete analysis on the upper side of the front bracings. However, the numerical model gives a really good approach using a simplified triangular load model as input. Thus finally is encouraged to analyze more wave records for obtaining a better estimate of the highest slamming coefficient.

Acknowledgement This work has been supported by the European Community's Seventh Framework Programme through the grant to the budget of the Integrating Activity HYDRALAB IV within the Transnational Access Activities, Contract no. 261520. Disclaimer This document reflects only the authors' views and not those of the European Community. This work may rely on data from sources external to the HYDRALAB IV project Consortium. Members of the Consortium do not accept liability for loss or damage suffered by any third party as a result of errors or inaccuracies in such data. The information in this document is provided "as is" and no guarantee or warranty is given that the information is fit for any particular purpose. The user thereof uses the information at its sole risk and neither the European Community nor any member of the HYDRALAB IV Consortium is liable for any use that may be made of the information.

References [1] Det Norske Veritas (DNV·GL, 2013). DNV GL’s Offshore wind cost reduction manifesto. [2] Goda, Y., Haranaka, S. and Kitahata, M. 1966. Study of impulsive breaking wave forces on piles. Report of Port and Harbor Research Institute, Japan, Vol. 5. No. 6, pp. 1 – 30 (in Japanese). Concept also in English language in: Watanabe, A. and Horikawa, K. (1974): Breaking wave forces on large diameter cell. Proc. of 14th International Conference on Coastal Engineering, Ch. 102, pp. 1741 – 1760. [3] Wienke, J., & Oumeraci, H. (2005). Breaking wave impact force on a vertical an inclined slender pile – theoretical and large-scale model investigations. Coastal Engineering 52, 435-462 [4] Det Norske Veritas (DNV, 2010 a,b). RP-C205 Environmental conditions and Environmental Loads [5] International Organization for Standarization (ISO, 2007). ISO 19902: Petroleum and natural gas industries. Fixed Steel Offshore Structures. Geneva, Switzerland. [6] Arntsen, Øivind A, and Gudmestad, O. T. (2014). Wave Slamming Forces On Truss Structures In Shallow Water. Proceedings of the HYDRALAB IV Joint User Meeting, Lisbon, July 2014. http://www.hydralab.eu/flashdrive/documents/TA-FZK-05.pdf. [7] Aune, L. (2011). Master thesis: Bølgjeslag mot jacket på grunt vatn. Department of Structural Engineering, Trondheim, NTNU. [8] Arntsen, Ø.A., Ros, X. and Tørum, A. (2011). Impact forces on a vertical pile from plunging breaking waves. Proceedings of the 6th International Conference. Yokohama, Japan, 6 – 8 September 2011.

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