Scale Experiments for the Measurement of Motions and ... - OnePetro

Proceedings of The Fourteenth (2004) International Offshore and Polar Engineering Conference Toulon, France, May 23−28, 2004 Copyright © 2004 by The International Society of Offshore and Polar Engineers ISBN 1-880653-62-1 (Set); ISSN 1098-6189 (Set)

Scale Experiments for the Measurement of Motions and Wave Run-Up on a TLP Model, Subjected to Monochromatic Waves S. A. Mavrakos(a) , I. K. Chatjigeorgiou(a), G. Grigoropoulos(a) and A. Marón(b) (a)

School of Naval Architecture and Marine Engineering, National Technical University of Athens, Athens, Greece (b) Canal de Experiencias Hidrodinámicas de El Pardo, C/ de la Sierra, s/n, Madrid, Spain.

According to this method the direct evaluation of the second order velocity potential can be avoided using an assisting radiation potential and the Green’s second identity. This method is generic and it was subsequently used by several researchers (Eatock Taylor et al., 1987; Abul-Azm et al., 1989b; Williams et al., 1990; Mavrakos et al., 1992; Moubayed et al., 1995; Liu et al., 1995; Rahman et al. 1999, McIver et al., 1984). According to the ‘direct’ method the second order velocity potential is calculated and then the associated pressure distribution on the body’s surface, the velocity field in the fluid domain and the second-order free surface elevation. Examples are the works presented by Loken (1986); Lee et al. (1994); Kim et al. (1989 & 1990), Huang et al. (1996), Eatock Taylor et al. (1997) and Teng et al. (1999).

ABSTRACT A model TLP subjected to monochromatic waves is tested experimentally. The measurements concern the wave run-up, the motions of the platform and the dynamic behavior of tendons. The wave crest elevation was measured in 16 points using wave probes that were installed in front of one of the vertical legs of the platform. The experimental results confirm the significant impact of wave run-up for both the fixed and the free-moving structure. The measurements which were taken during the experiments are in agreement with the conclusions drawn by other researchers in the past.

The solution of the second-order diffraction-radiation problems, as mentioned, allows the calculation of the nonlinear free-surface wave elevation and the consideration of the extreme nonlinearity close to the structure’s wall. In this context, Kriebel (1992) presented theoretical results for the second-order wave run-up around a large diameter vertical circular cylinder while Malenica et al. (1999) reported extensive numerical predictions for the second-order wave elevation for various arrangements of multiple vertical cylinders. Williams et al. (2000) discovered that the porosity of the structure may result in a significant reduction in both the hydrodynamic loads experienced by the cylinders and the associated wave run-up. Buchmann et al. (1998) simulated the interaction between waves, current and the structure by a 3D numerical model. Solving the problem in the time domain, they highlighted the importance of both the current and the second-order wave components in calculating magnitude and location of the maximum runup on the structure.

KEY WORDS: Tension leg platform; wave run-up; air gap; experiments; tendons; heaving resonance. INTRODUCTION The appropriate design of a floating platform requires consideration of the air gap between the wave crests and the underneath area of the platform’s deck in order to avoid catastrophic impacts, even in harsh environments. In the design process, this dimension is normally determined with reference to the still water surface. Generally, the term ‘air gap’ defines the clearance between the bottom area of the deck and the wave crests, while the term ‘wave run-up’ is used to describe the ascent of water on the structural components of the platform, usually on the vertical columns. The latter is a severely nonlinear phenomenon caused by the diffraction-radiation of the waves that occurs in the vicinity of the wall. The theoretical evaluation of wave run-up requires in most cases the consideration of the second order diffraction-radiation problem.

The importance of the issue was acknowledged by ISSC (2000) Loads Committee 1.2, which initiated a comparative study for the prediction of the wave run-up along platform columns. The model, which was selected as the subject of the investigation was a large catenary moored production platform (Nielsen et al., 1994). Six companies/universities contributed in this study and the conclusions are reported in a recent paper (Nielsen, 2003).

The solution of this problem attracted the interest of several researchers during the past two decades. The proposed solution methods can be separated in two categories: the ‘indirect’ and the ‘direct’ method. The ‘indirect’ method was introduced independently by Lighthill (1979) and Molin (1979) for the infinite and the finite depth cases, respectively.

There are also several experimental research efforts presented in the

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literature that intend to understand the impact of run-up on the vertical components of the floating platforms. Mercier et al. (1994) performed experiments on a cylinder which was rigidly attached to a load frame. Niedzwecki et al. (1992a) investigated the wave run-up on rigid fulllength and truncated circular cylinders under regular and random sea conditions; Niedzwecki et al. (1992b) measured the wave elevations on the vertical columns of a 1:250 scale model of the Hutton TLP, while Swan et al. (1997) discuss briefly their visual observations about wave run-up on the multi-legged Brent Bravo concrete platform. However, the majority of the experimental works refer to fixed models. The present paper aims at contributing in understating the features of the actual phenomenon associated with a free moving platform. The experimental measurements were obtained by carrying out physicalmodel tests on a scale model of the Troll Olje TLP (Nielsen et al., 1994; Nielsen, 2003). The model was tested as a TLP using hightension tendons at the corners. Additional measurements were taken having the model fixed and free to heave - free to pitch. The results that concern the later arrangement are not considered herein. The measurements concerned the wave run-up, the motions of the structure and the tension of the tendons at the point of connection with the platform. The experimental data illustrate the importance of the nonlinear wave elevation along the structural components of the platform. Also, critical conditions associated with the dynamic behavior of the tendons, and in particular to the so-called snap- slack- loading condition, are properly identified and discussed.

Fig. 1 Model illustration with tension sensors and wave probes installed 1 32,5

Wave front

14,2 32,8

2

45°

23°

The experiments were carried out in the El Pardo Model Basin in Spain. The main facility is a basin with a wave maker and a Computerized Planar Motion Carriage (CPMC). The basin is 150 m long and 30 m wide, with 5 m depth. The 60-flap wave maker is located in one of the 30 m sides and it can produce plan and oblique regular waves with lengths between 1 and 15 m and heights up to 0.9 m. The wave maker is powered by six hydraulic pumps with total output of 551 kW. On the opposite side to the wave maker there is a wave absorbing beach with good absorbing characteristics.

3 ° 23

147,5

EXPERIMENTAL ARRANGEMENT

4 DC B

The model dimensions were developed using a 1:100 scale of the platform that was used for the comparative study initiated by ISSC (2000). The geometric and the inertia characteristics of the model are shown in Table 1. The same table contains the properties of the tendons as well as the stiffness of the in-line connected springs that were used in order to adjust the pretension force, the elasticity of the lines and to achieve the required 40 cm draft. The four springs – each for every corner – were inserted in the connection between the tendons and the model in the location of the symmetrical axis of the vertical columns. The tension variation was measured in two of the tendons using tension sensors attached on the springs. The sensors were connected on the columns which faced towards the incoming waves (Fig. 1). The wave elevation was measured in 16 locations in the vicinity of one out of the two vertical columns in the wave maker side of the tank (Fig. 1). The arrangement, the spacing and the designation of the wave probes are shown in Fig. 2. Finally, the six degree of freedom motions of the free moving platform and the forces on the fixed platform were obtained using the optical tracking system and the dynamometers of the CPMC, respectively.

A

Fig. 2 Location and designation of wave probes (dimensions in mm)

MEASUREMENTS AND DISCUSSION Wave run-up Measurements of run-up were taken for both the fixed and the freemoving moored platform. The data which were obtained using H=0.16 m, are more illustrative and therefore will subsequently consume the largest part of the discussion. For this particular case the range of wave periods was from 1.2 sec through 2.5 sec. For smaller periods the waves that were generated by the wave maker had very high slope leading to breaking waves. Figs 5~12 depict comparative measurements of wave elevation for four periods and for both the free-moving and the fixed model. The time histories concern row 2 because that was the location in which the highest elevation was visually observed and subsequently was confirmed through measurements’ processing. The horizontal lines in all figures denote the upper and the lower limit of the incident monochromatic wave. Apparently, the wave run-up is more important for the fixed platform (Figs 6, 8, 10 and 12). Although the wave elevation is decreased as the wave approaches the wall, the wave that eventually hits the structure is higher than the corresponding incident harmonic wave. The larger crests that were measured by the

The wave properties that were used for performing the tests, are given in Table 2.

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outer wave probes are caused because of the reflected waves which in turn amplify the heights of the incoming waves.

Table 1: Particulars of the TLP 154.1 kgr

Mass of platform Total vertical force from tendons

294 N

Draft

40 cm

Centre to centre distance between columns

72.52 cm

Diameter of columns

29 cm

Height of pontoons

14.5 cm

Width of pontoons

29 cm

Longitudinal Inertia

22.1 kgr⋅m2

GM

11.5 cm

Weight of tendons per unit length

0.0002 kgr/cm

Diameter of tendons

Equivalent spring constant of tendons

2 mm #1

2.33 kgr/cm

#2

2.43 kgr/cm

#3

2.41 kgr/cm

#4

2.19 kgr/cm

Fig. 4 Fixed model subjected to monochromatic waves H=0.16 m, T=1.3 sec

Furthermore, all of the output signals depicted in Figs 6, 8, 10 and 12 incorporate a higher-order nonlinear superharmonic, which is more noticeable close to the wall. This can be traced back to the fact that the extreme nonlinearity is confined to a region of close proximity to the wall. According to Nielsen (2003), this distance is much less than one column radius. The measurements presented herein show occurrences of nonlinear impacts that begin from a distance approximately equal to one column radius, while the wave height in this point is double the incident wave height. The phenomenon is extremely nonlinear and it cannot be predicted using the linear diffraction-radiation solution.

Table 2: Regular wave conditions Wave height (m)

Wave period (sec)

0.046

0.8-2.5 sec (0.1 sec spacing)

0.16

1.2-2.5 sec (0.1 sec spacing)

0.28

1.5 sec

0.31

2.0 sec

On the other hand, the wave elevation appears to be smaller on the free moving platform (Figs 5, 7, 9 and 11). The periods for which the measurements are shown, have been deliberately selected close to natural period for the heaving motions of the platform: Teig = 2π

m + A33

ρ gAwL + k s

≈ 1.25 sec

where m is the mass of the platform, A33 is the hydrodynamic mass of the horizontal pontoons in heave direction, AwL is the still waterline area of all four vertical columns, ρ=1000 kg/m3 is the water density, g is the acceleration due to gravity and ks is the equivalent spring constant provided by the tendons. The reduced impact of run-up is associated with the extreme heaving motions of the structure for periods that lie in the vicinity of the natural period (Figs 5, 7 and 9). For higher wave periods, the wave run-up grows accordingly, while the shape of the free surface just in front of the structure is almost identical to that of the fixed platform (Figs 11 and 12). The slight differences are related to the small surging motions of the platform.

Fig. 3 Free-moving model subjected to monochromatic waves H=0.16 m, T=1.3 sec

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Fig. 5 Wave elev. around A (free moving model), T=1.2 sec

Fig. 6 Wave elev. around A (fixed model), T=1.2 sec







385

Fig. 13 Max wave elevation along row 1, H=0.16 m (fixed model)




Fig. 17 Max wave elev. ζ(r,θ), H=0.16 m, T=1.7 sec (fixed model)




386


Fig. 22 RMS values for surging and heaving motions of the floater (H=0.046 m)

Although the wave probes were installed in one of the front columns, the experiments showed that the wave run-up is much more important for the back columns. In the present contribution this can be observed only visually for both the free moving and the fixed structure (Figs 3 and 4 respectively), while it is evident that for the fixed platform the specific phenomenon is extremely influential. Fig. 4 shows that in left column which is in the wake of the right column, there is no air-gap as the water surface reaches the underneath surface of the deck. It should be stated that the importance of the wave run-up on a leg directly in the wake of another leg was also reported by Niedzwecki and Huston (1992b). Run-up around cylindrical legs The wave run-up around the cylindrical columns of the platform is examined with the aid of Figs 13~21. All experimental data concern the fixed structure. Figs 13~16 depict the maximum values of the free surface elevation along rows 1 through 4 respectively (see Fig. 2) for H=0.16 m. The measurements show that the maximum run-up occurs in the middle of the outer quarter, i.e., along row 2 (Fig. 14) and not in the point in which the wave hits on the structure, i.e., along row 4. The wave elevation is increased for higher frequencies of the incident waves. According to Figs 13~16, the wave crests just in front of the structure’s hull (D periphery) are approximately equal to 1.2 the amplitude of the incident wave H/2, while run-up exceeds the double of H/2 in the middle of the D periphery. Generally, the values presented in this paper are comparable with the values reported by Nielsen (2003). The occurrence of local peaks of wave elevations in Figs 13~16 can be traced back to the hydrodynamic interaction between front and back columns.

Fig. 23 RMS values for surging and heaving motions of the floater (H=0.16 m)

The 3D plots in Figs 17~21 show in a more descriptive fashion, the wave crest elevation around the platform’s legs. These figures confirm that the free surface elevation is greater in the periphery A. Furthermore, the free surface climbs the cylinder as the orientation angle reaches the middle of the outer quarter, i.e., 45 degrees from the origin. Subsequently, the wave crests decay as the orientation angle increases up to 90 degrees (row 1). Fig. 24 Dynamic tension measured in port tension sensor (H=0.16 m)

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The wave run-up is less influential for smaller frequencies of the incoming waves (Fig. 20), while the heights of the crests hitting the cylinder’s wall (periphery D) for equal wave periods are of the same order of magnitude (Figs 18, 19 and 21). Fig 21 shows that even for smaller wave heights H=0.046 m in which the phenomenon is not so nonlinear, there is a significant surface elevation in the radial distance of the outer wave probes. It is expected that the wave height within a distance, approximately equal to one column radius, is also the double the incident wave height.

in a radial distance approximately equal to one cylinder’s radius, while extreme nonlinear phenomena occur just in front of the wall. The wave run-up is less important for the free moving structure especially in the vicinity of the structure’s natural frequency for heave. This region however, is governed by the large heaving motions which induce severe disturbances of the water surface due to waves radiated by the structure. The wave run-up is extremely influential for a leg which is located in the wake of another leg. As far as the dynamic behavior of the free-moving moored platform is concerned, it was reported that the extreme motions induced in the vicinity of the structure’s natural frequency for heave, reduce the corresponding horizontal displacements as the restoring characteristics are enhanced. The specific behavior is also associated with the so called snap-loading of tendons.

Dynamics of the free moving structure The features of the dynamic behavior of the free-moving structure, are examined with the aid of Figs 22~24. In this case, the motions of the floater are restrained using the high tension tendons. Figs 22 and 23 depict the RMS values of heaving and surging motions of the platform for H=0.046 m and H=0.16 m respectively. Fig. 24 describes the variation of dynamic tension for two different wave frequencies.

ACKNOWLEDGEMENTS The access to the El Pardo Model Basin was financially supported by the EC FP5 program: “Transnational Access to Research Infrastructures”. The construction of the model was sponsored by the available funds of the postgraduate program of the School of Naval Architecture and Marine Engineering in NTUA. The authors would like to thank Mr. Cesar Gutierrez and Mr. Dionissis Synetos for their help during the experiments and Mrs. Rena Tzoraki, for the elaboration of measurements.

For small wave frequencies, the TLP exhibits large surging motions, which are approximately equal to H/2. In this region the corresponding vertical displacements are insignificant. As the wave frequency approaches the natural frequency for heave, the horizontal displacement decreases progressively. This can be traced back to the fact that for relatively large vertical displacements, the restoring characteristics provided by the tendons are enhanced significantly. It is important to note that the frequency of the maximum heaving motion is in favorable agreement with the value which was determined using the physical properties of the structure (0.8 Hz). On the other hand, no resonance in surging occurs in the reported frequency range, i.e., 0.3-1.0 Hz, as for the specific model the natural frequency for surging motion is equal to 0.061 Hz. The resonance which is obtained in the vicinity of the natural frequency for heaving motion, is associated also with the large disturbances of the free surface recorded for wave periods T=1.2 sec, T=1.3 sec and T=1.5 sec (Figs 5, 7 and 9 respectively).

REFERENCES Abul-Azm, AG, Willimams, AN (1989). "Second-order Diffraction Loads on Arrays of Semi-immersed Circular Cylinders," J Fluids Structures, 3, pp 365 – 387. Buchmann, B, Skourp, J, Cheung, KF (1998). "Run-up on a Structure Due to Second Order Waves and a Current in a Numerical Wave Tank," Applied Ocean Research, 20, pp 297-308. Eatock Taylor, R, Hung, SM (1987). "Second-Order Diffraction Forces on a Vertical Cylinder in Regular Waves." Applied Ocean Research, 9, pp 19 – 30. Eatock Taylor, R, Huang, JB (1997). "Semi-Analytical Formulation for Second-Order Diffraction by a Vertical Cylinder in Bi-Chromatic Waves," J Fluids Structures, 11(5), pp 465-484. Huang, JB, Eatock Taylor, R (1996). "Semi-Analytical Solution for the Second-Order Diffraction by a Truncated Circular Cylinder in Monochromatic Waves," J Fluid Mech, 319, pp 171-196. ISSC (2000). Report from the 14th International Ship and Offshore Structures Congress, technical Committee I.2: Loads, Nagasaki, Japan. Kim, MH and Yue, DKP (1989). "The Complete Second-Order Diffraction Solution for an Axisymmetric Body. Part I: Monochromatic Incident Waves," J Fluid Mech, 200, pp 235 – 264. Kim, MH and Yue, DKP (1990). "The Complete Second-Order Diffraction Solution for an Axisymmetric Body. Part II: Bichromatic Incident Waves and Body Motions," J Fluid Mech, 201, pp 557 – 593. Kriebel, DL (1992). "Nonlinear Wave Interaction With a Vertical Circular Cylinder. Part 2: Wave Run-Up," Ocean Eng, 19(1), 77 – 99. Lee, C-H, Newman, JN (1994). "Second-Order Wave Effects on Offshore Structures," Proc 7th Int Behavior Offshore Structures Symp (BOSS’94), MIT, Boston, Vol. 2, pp 133-146. Loken, AE (1986). "Three-Dimensional Second-Order Hydrodynamic Effects on Ocean Structures in Waves. Report UR-86-54, University of Trondheim, Dept. of Marine Technology. Liu, YH, Kim, MH, Kim, CH (1995). "The Computation of SecondOrder Mean and Double-Frequency Wave Loads on a Compliant TLP

The specific behavior is also related with the effects that are originated from the dynamic behavior of the tendons. The large heaving motions induce the stretching of tendons and consequently the amplification of dynamic tension. When the dynamic component of tension exceeds the static value there are instances in which the total tension (and consequently the vertical holding force) is completely vanished. This is due to the fact that tendons cannot undertake bending moments. During the tension cancellation intervals the tendons become slack and subsequently they experience a severe impact loading, the so called snap-loading. The preceding discussion is confirmed with the aid of Fig. 24. According to this figure, the value of the dynamic tension for which the total tension is vanished is equal to 73 N. The specific value coincides favorably with the static pretension of each tendon which according to Table 1 is equal to one quarter of the total vertical force in static position, i.e., 73.5 N.

CONCLUSIONS A TLP model was tested experimentally. Measurements were taken for both the fixed and the free-moving platform. In the later case the model was connected to the floor using high tension tendons. Results concerning the wave run-up, the motions of the structure and the tension of the tendons in the point of their connection with the TLP’s hull are presented. The measurements show the significant impact of wave run-up on the wall. It was shown that the wave elevation is higher

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Nielsen, FG, Herfjord, K, Hunstad, G, and Olsen, G (1994). "Dynamic Characteristics of a Large Catenary Moored Production Platform," Proc 7th Behaviour Offshore Structures Symp, BOSS’94, MIT, Boston, Massachusetts, Vol. 2, pp 113-131. Rahman, M, Bora, SN and Satish, MG (1999). "A Note on SecondOrder Wave Forces on a Circular Cylinder in Finite Water Depth," Applied Mathematics Letters, 12(1), pp 63-70. Swan, C, Taylor, PH, Van Langen, H (1997). "Observations of wavestructure interaction for a multi-legged concrete platform," Applied Ocean Research, 19(5-6), pp 309 – 327. Teng, B, Kato, S (1999). "A Method for Second Order Diffraction Potential from an Axisymmetric Body," Ocean Engineering, 26(12), pp 1359-1387. Williams, AN, Abul-Azm, AG, Ghalayini, SA (1990). "A Comparison of Complete and Approximate Solutions for Second-Order Diffraction Loads on Arrays of Vertical Circular Cylinders," Ocean Eng, 17(4), pp 427 – 445. Williams, AN and Li, W (2000). "Water Wave Interaction with an Array of Bottom-Mounted Surface-Piercing Porous Cylinders," Ocean Eng, 27, pp 841-866.

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