Wave Run Up Offshore Structures Engineering Essay

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Offshore Structures mainly consist of circular or rectangular members: for example, a jacket platform leg, a monopole or offshore wind turbine, semi-submersible columns etc. The wave run-up on these structures has been estimated by experimental and computational methods. The results reported so far are corresponding to waves approaching from only one primary direction. If two or more wave systems with different propagation directions attack the structure, then the values of run-up on these structures will be different from the ones which were reported in the past.


Personal Statement

Project was a new one, nobody had looked at the effects of multi directional waves before


Design choice, close communication with Neil wood in the Workshop,


Alot of the measurement apparatus was already available in the curved wave tank, only the model had to be made. There were set software to use


  • whether it was a new project or a continuation from previous years;

  • how you set about tackling the project and how much help you had in this from your supervisor and others;

  • the origin of any theoretical work presented, i.e. was it original? Was it developed from a previous project? Was it derived by your supervisor etc.? If the project has a direct connection to work carried out during the 4th year Industrial Placement a statement must be made indicating the divide between the Individual Project and the Placement work.

  • what contribution you made to the design and construction of the experimental apparatus and its instrumentation, i.e. did the apparatus already exist? Was it modified from an existing piece of equipment? How much help did the workshop give etc.?

  • how the project progressed and any major problems,

  • any aspects of the project to which you may wish formally to draw the attention of the examiners

Summary


1. Introduction

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Wave run-up is an important aspect of particular interest to engineers designing a safe and effective offshore structure. Wave run-up is defined as “The maximum vertical elevation of the wave crest above the still water level, resulting from incident waves interacting with the surface piercing element such as an offshore platform.” (Indrebo & Niedzwecki, 2004)


If run-up on an offshore structure is higher that designed for, then it poses serious safety risks and possible operational problems. If run-up is higher than the designed air-gap allows for, this can lead to overtopping of platform decks, and possible flooding of operational areas posing a safety risk to staff. It is also possible that high wave run-up could also cause damage to equipment mounted to the side of these structures.


Offshore structures are mainly constructed upon circular or rectangular leg sections. For example, square or rectangular sections are commonly used for older designs of Tension Leg Platforms and Semi-submersible structures. The use of square and rectangular was mainly due to manufacturing limitations at the time of design. An example of these structures is shown in Figure 1.[1]


More modern offshore structures now use cylindrical leg structures allowing better stress distribution and a more efficient use of material. Examples of these structures are monopole structures often used for offshore wind turbine, and Tension Leg Platforms. An example of this is shown in Figure 2.[2]


The wave run-up on these structures has been estimated by experimental and computational methods. Most studies carried out so far have been corresponding to waves approaching from only one primary direction. This provides a good understanding of run-up interaction with surface structures initially, but in a more realistic sea state waves can be observed from several directions at one time. It is common to find a predominant swell wave occurring from one direction, caused by a storm hundreds of miles away, and a smaller period wind wave occurring at a different direction, caused by the immediate wind.


If two or more wave systems with different propagation directions attack the structure, then the values of run-up on these structures will be different from the ones which were reported in the past.


Aims and Objectives

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This project aims to look at wave run-up where interaction of two or more deep-water wave systems, propagated from different directions attack the structure. The key objectives required to enable this are:-

  • Design and construct a scale model of an ‘offshore structure', suitably scaled to enable accurate testing in Edinburgh University's curved wave tank facility.

  • Plan a testing procedure to look at the effects of the orientation of the wave on run-up around the structure.

  • Carry out unidirectional regular and random wave testing on the structure and observe run-up effects around the structure.

  • Carry out Bidirectional tests with regular and random waves to observe the effects of multidirectional waves on the structure.

  • Analyse the data recorded from the experiments and compare with available theory.

2. Theory

Wave run up describes the physical phenomenon of a sudden up-rush of water when an incident wave meets a surface piercing body. The measured run-up on a column is measured from the still water level to the maximum 'green water' elevation, i.e. not including and spray of splashing that may be generated in steep waves.


Figure 3: Illustration of wave Run-up (Morris-Thomas, 2003)


A theoretical approach known as 'linear diffraction theory' using potential theory and assuming an idealised fluid domain, yields a velocity potential. The velocity potential at the free-surface position is then used with the 'unsteady' Bernoulli's equation in order to provide the free-surface elevation around the column. Linear diffraction theory has been shown to underestimate wave run up for all but very small steepness waves (Niedzwecki & Duggal, 1992). Linear diffraction theory will not be used during my project.


For Regular wave spectra, wave run-up has been empirically estimated using the 'velocity head method'. The ‘velocity head method' was initially suggested by Galvin & Hallermeier (1972). The method is based upon a steady state Bernoulli's theorem and is caused by the kinetic energy of the wave being forced into potential energy in the form of a potential head at the stagnation point, the fluid-structure interface. The kinetic energy, in terms of a 'velocity head' is described by the horizontal water particle velocity, u. Using linear wave (Airy) theory, The horizontal particle velocity at any point in a wave field can be expressed in term of its horizontal position from the origin, x, its distance from the seabed, z, and time, t:-


ux,z,t=πHTcosh[kd+z]sinh(kd)coskx-ωt=πHT


Where H is the wave height, T is the period of the wave, k is the wave number, d is the depth from the still water level to the sea bed.


The maximum horizontal particle velocity occurs when the particle is at the crest therefore u can be expressed as:-


umax=pHT


The energy expressed as a 'velocity head', is given by U2/2g. It is assumed that the entire kinetic energy of the water particles is converted into potential energy by the particles rising in distance equal to the velocity head above the maximum crest height, ?max. The run-up height is expressed as, Ru:-


Ru=ηmax+ u22g


3. Literature Review

Most previous experiments carried out to date have been based on cylindrical cross-sections with very little experimental work using square shaped cross sections.


One of the earliest experiments to look at wave run-up was done by Galvin & Hallermeier (1972) who looked at wave run-up on cylinders. Their main focus in the experiment was to discover if an incoming wave direction could be identified by the resulting wave height distribution around the column. They placed a series of conductive type wave gauges around their cylindrical model in order to capture the free surface elevations around the cylinder. Their results unfortunately showed that their wave spectrum was not uniform. This was put down to higher frequency waves being introduced due to a constant vibration in the wave generation system. Their study did show however that there was a clear symmetrical response of wave height elevations around a cylindrical structure.


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Chakrabarti & Tam (1975) carried out a similar study aimed at possibly finding the incident wave direction from observing the wave height distribution around a vertical cylinder using regular wave spectra. The results of Chakrabarti & Tam agreed with several observations made by Galvin & Hallermeier (1972), but they also noted that the dynamic pressure loads at the still water level closely conformed to wave probe measurements.


Hallermeier (1976) went on to compare the wave run-up with the 'velocity head' of Bernoulli's equation (U2/2g). Hallermeier used a powder deposit erosion technique on the cylinder surface in order to measure the wave run-up. Hallermeier's normalised form of run-up did not however compare well with the normalised form of the theoretical 'velocity head' (U2/2g).


Niedzwecki & Duggal (1992) carried out and experimental study on wave run-up on full length and truncated cylinders. They experimented with both regular and random wave spectra. Wave heights were measured using five conductive type wave gauges placed directly onto the cylinder surface. Linear diffraction theory was found to under predict the measured wave run-up for all but very low wave steepness. When using the 'velocity head' theory, they found that this theory also under predicts wave run-up especially at higher wave steepness. They then employed a variation of the 'velocity head' theory by using a coefficient, m, to give a linear fit. The found for a full length cylinder, m = 6.83.


Ru=ηmax+m u22g


Equation 1

One of the more recent studies into wave run-up, although looking at shallow water, was carried out by Vos et al. (2006). The study looks at the wave run-up distribution around cylindrical piles, but with two different shapes of foundations. The study looks at both regular and random waves. Their primary focus of this experiment was to observe the effects of the foundation structure on wave run-up. For a given theoretical wave steepness they compared measured run up predictions with all empirical estimations suggest by Hallermeier (linear velocity head theory), and the modified equations used by Neidzwecki. They stated that the linear wave theory under predicts wave run-up beyond a certain wave height. They also found that the modified 'velocity head' equations used by Neidzwecki and Duggal over predicted wave run-up for smaller wave height, but also greatly under predicted the run-up at larger wave heights. It is noted that using the velocity head method with non-linear wave crest kinematics, such as 2nd order Stokes theory, gives better predicted wave run-up agreement with the experimental values. Using second order Stokes theory to calculated the wave kinematics, the surface elevations


ηmax=H2+kH2H8coshkdsinh3kd(2+cosh2kd)


Equation 2

And the horizontal particle velocity at the wave crest, utop , is described by:-


utop=H2gkωcosh(kηmax+d)cosh(kd)+34kH24ωcosh(2kηmax+d)sinh4(kd)


Equation 3

The effects of random waves, namely JONSWAP spectrum are also considered in the report.


4. Experimental set-up


Description of facilities

The wave testing tank facilities used at Edinburgh University has a curved arrangement. The curved wave tank facility consists of 48 flat, bottom-hinged wave makers arranged at a radius of 9 meters over an arc of just over 90°. Each wave paddle is controlled independently by software developed by Edinburgh Designs. This configuration of wave makers allows not only curved multi-directional waves to be create, but also by accurately computer controlled phase shifting of the wave paddles, straight and parallel waves can easily be created.


Figure 4: Curved Wave Tank facility at Edinburgh University


The curved wave tank has a water depth of 1.2 meters, and can generate waves with amplitudes of up to 0.05 meters over the main frequencies between 1.0 to 1.5 Hz. The user interface of the Wave tank facility allows reproduction of regular waves as well as Jonswap, Bretschneider and other Random wave spectra.


Figure 5: Detailed drawing of curved wave tank Layout


Model Design

In order to carry out meaningful model tests, a structure of appropriate shape and scale had to be designed. It was decided to make a square style of structure in order to clearly show run-up on each of the faces of the structure, and for ease of manufacturing within the limitations of time and expense constraints.

When concerned with surface wave structure and wave run-up, the most important forces to be kept proportional are the inertia forces and gravitational forces, which govern the wave form and run-up around structures. The Froude number is governed by both these forces, therefore, keeping the Froude number constant the model can be appropriately scaled with respect to these forces.


Fr= umLmg= ufLfg Equation 4


For irregular wave is it not obvious what statistical quantity should be used in model design. The curved wave tank facility specify a set wave envelope for which the tank can produce reliable wave, with a period varying from 0.66 second to 1.6 seconds (0.6Hz to 1.5 Hz). The speed of the wave is a measure of the distance travelled, L, divided by the time taken to travel the distance T.


ux= LxTx

Fr= LmTmLmg= LmTmg= LfTfg


Assuming that the gravitational field is constant, at both model and full scale, the Froude number can be simplified to:-


LmLf=TmTf


Maximum typical wave periods in the North Sea are around 14 seconds, where as the maximum period which can be produced in the curved wave tank is around 1.4 seconds.


λ=LmLf= TmTf2=1.4142=0.01


The Scaling factor ?, is found to be 0.01 that of full scale, implying that the curved wave tank is approximately a 100th scale testing tank, (this is backed up by (Payne, 2008)). Typical full scale offshore structures are in the region of 10-20 meters in diameter, therefore requiring a model in the range of 0.1-0.2 meters in diameter. It was decided to keep the model as large as possible so that the run-up effects on the model are clearly observed. Several possible model designs were prepared in a CAD program. Initially it was assumed that a structure from above would retain the model in place as shown in Figure 6 and Figure 7.


Figure 6: CAD drawing of initial model

Figure 7: Artists impression of model placed in tank

The final design used a base structure to stand the model firmly in place in the wave tank.

Figure 8: CAD drawing of final design

Figure 9: Artists impression of final design in wave tank

Figure 10: Plan view of model section


Ideally the structure of the model would be made from a plastic material, so that the model could easily be moved by hand, but expense restraints ruled out this option. Steel Square box section 200 x 200 mm sourced from within the University proved to be an ideal model structure. Several design options included making a gravity base from concrete, as a relatively cheap form of mass, but the final design used steel for the base because steel retains its relative density in water much better than concrete and is much easier to manufacture. The base structure has a central column, with threaded top, upon which the box section can be freely rotated if required, but can also be clamped down onto the base using a large nut threaded onto the top section of the column. The final model design is shown in Figure 11.


Figure 11: Model completed in workshop


Detailed drawings of the final model design are attatched as appendix ***


Description of the Apparatus

In order to measure the wave run up on the model, conductive wave gauges are used around the model and several reference wave gauges were placed at a distance from the model to measure the original incident wave elevations.


Conductive wave gauges typically consist of two thin, parallel vertical metal rods partly immersed. The water height is derived from the conductivity between the rods which increases with the immersion of the rods. Conductive wave gauges must be recalibrated frequently due to the conductivity of the water changing. The gauges are calibrated dynamically every half day.


In order to calibrate the gauges, they are attached to the gantry crane in the testing tank facility and submerged in the water. Once the gauges are settled in the water, the gauges are slowly lifted out of the water whilst recording their conductivity. By measuring the conductivity change with respect to the change in elevation, appropriate gain properties can be applied to ensure each probe measures the wave height accurately. The program used provides a measure of how accurate the each probe has been calibrated by producing a residuals plot of how close each of the measurements were taken as shown in Figure 13. Calibration was carried out until all the wave gauge residuals were within 1mm. The software used to calibrate the wave gauges produces a calibration file, where the gain value for each wave probe is stated. This calibration file is then used in the data logging software in order to plot the water elevations.


Figure 13: Typical plot of wave gauge residuals


5. Experimental Set-up

When placing the model in the Curved wave tank it was important to ensure the model was located in a region of the tank where the waves had fully developed, at least one wavelength from the wave paddles, and also as far as possible from any reflective surfaces, the beach and glass panel.


Figure 14: Basic layout of model in curved wave tank

Figure 15: Model Positioned in the wave tank


The Model was placed in the wave tank aligned with existing marks on the tank floor (Figure 15) to ensure reproduction of results if the model had to be removed and repositioned. Once calibrated the wave gauges are then placed on and around the model in the arrangement shown in Figure 16.


Figure 16: Detailed view of wave gauge positions

Figure 17: Model and Wave gauge framework in position


Wave probes are placed on the front, side and rear face of the model with a 10mm gap between the wave gauge rods and the steel wall to ensure that the ‘green water' level rises and falls freely. Reference probes are placed at a distance to the model. It was intended to place the probes at a precise radius to the model, but unfortunately this was not feasible with the framework available.


Wave measurement technique

The wave gauges are connected to the computer via a DAQ (data acquisition module), measuring the voltage output of each gauge. Software written within Edinburgh University was used within MATLAB in order to record and plot the gauge outputs. For all experiments carried out in this project, a sampling rate of 32Hz was used.


A start-up period of one minute was left before recording any data. This was to ensure that the generated waves were fully developed and had reached a steady state. A typical start-up period for the Edinburgh University curved wave tank is suggested to be 30 seconds (Payne, 2008).


Similarly a settling time of at least one minute is left between stopping the wave paddles and starting the next wave spectrum in order to let the water become still, therefore making certain reflections and harmonics of the previous wave spectrum have died out. This ensures that there is no cross contamination of spectra between experiments.


Because we intended to perform Fast Fourier Transform (FFT) analysis on the data, the number of samples recorded should be 2k where k is a positive integer in ordered to use all of the samples without losing fidelity.


For regular wave experiments, wave heights were recorded for 64 seconds, but for irregular wave experiments a longer recording period of 128 seconds was used to ensure higher resolution of the frequency when FFT analysis.


A Note on Aliasing

The sampling frequency used to sample a continuous time series is dictates by the desired frequency range being recorded. (Payne, 2008) states that "The sampling rate must be at least twice that of the highest frequency component of the time series".


When sampling a frequency ƒs, the Discrete Fourier Transform process is unable to distinguish between components whose frequencies ƒ1 and ƒ2 are symmetrical with respect to ƒs/2. For example when using a sampling frequency of 32 Hz to sample a frequency of 1 Hz, a frequency of 31Hz will also be recorded. When returning the DFT output, the amplitudes of the measured frequencies ƒ1 and ƒ2 are split equally between the two frequencies. In order to compensate for this, all data above the symmetrical frequency of ƒs/2 is discarded and the all data before this frequency are doubled. This is acceptable as long as it is known that there are no signal frequencies above ƒs/2. The frequncy ƒs/2 is known as the 'Nyquist' frequency.


In the case of the curved wave tank it is known that there is electrical interference at around 9 Hz which is picked up by the DAQ. Although the frequency range that is to be measured is within in range of 0 - 2 Hz, the Nyquist frequency' must be chosen so that it is larger than all measured frequencies. For the curved wave tank the Nyquist frequency' is chosen to be 16Hz and therefore a sampling rate of 32Hz is used.


Experiment schedule


Unidirectional Regular waves

It was proposed to measure regular wave over a range of frequencies and amplitudes from one direction. For regular waves, the frequencies that can be accurately generated by the curved wave tank fall into an envelope as shown in Figure 18.


Figure 18: Wave generation envelope for curved wave tank


Angle of incidence

Frequency

Amplitudes (m)

-20

0.8

0.01

0.02

0.03

0.04

1

0.01

0.02

0.03

0.04

0.05

1.2

0.01

0.02

0.03

0.04

1.4

0.01

0.02

0.03

0.04

-15

0.8

0.01

0.02

0.03

0.04

1

0.01

0.02

0.03

0.04

0.05

1.2

0.01

0.02

0.03

0.04

1.4

0.01

0.02

0.03

0.04

-10

0.8

0.01

0.02

0.03

0.04

1

0.01

0.02

0.03

0.04

0.05

1.2

0.01

0.02

0.03

0.04

1.4

0.01

0.02

0.03

0.04

0

0.8

0.01

0.02

0.03

0.04

1

0.01

0.02

0.03

0.04

0.05

1.2

0.01

0.02

0.03

0.04

1.4

0.01

0.02

0.03

0.04

10

0.8

0.01

0.02

0.03

0.04

1

0.01

0.02

0.03

0.04

0.05

1.2

0.01

0.02

0.03

0.04

1.4

0.01

0.02

0.03

0.04

15

0.8

0.01

0.02

0.03

0.04

1

0.01

0.02

0.03

0.04

0.05

1.2

0.01

0.02

0.03

0.04

1.4

0.01

0.02

0.03

0.04

20

0.8

0.01

0.02

0.03

0.04

1

0.01

0.02

0.03

0.04

0.05

1.2

0.01

0.02

0.03

0.04

1.4

0.01

0.02

0.03

0.04


6. Results


7. Discussion

Sources of error - The gauges are spaced approximately 10mm away from the fluid-structure interface and therefore may not measure the entire run up.


The gauges are calibrated to within 1mm but it is suspected that several of the Reflection from the model and glass panel and beach may cause some additional harmonics.


8. Conclusions

[1] Marin website (Maritime Research Institute Netherlands) - http://www.marin.nl/upload_mm/f/a/8/386_fullimage_1153143436203-MP_192x192.jpg


[2] BBC website - http://www.bbc.co.uk/essex/content/images/2009/03/19/monopile_150_150x180.jpg