SLOWLY VARYING DRIFT FORCES. Acronym: HYIII DHI 8 - DRIFT EC contract no.: HYDRALAB III (022441)

Transcription

1 SLOWLY VARYING DRIFT FORCES Acronym: HYIII DHI 8 - DRIFT EC contract no.: HYDRALAB III (022441) Status: draft Date: November

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3 Heading: Infrastructure Project Campaign Title DHI Water & Environment HYIII-DHI-8 DRIFT Drift forces Slowly varying drift forces Participants Instituto Superior Técnico (IST) ; Institut Francais de Recherche pour l Exploitation de la Mer (IFREMER); National Technical University of Athens (NTUA). Lead Author Contributors Nuno Fonseca João Pessoa Date Campaign 11 May 2009 to 3 July 2009 (?) Date final Completion 3 July

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5 INDEX 1 SCIENTIFIC AIM AND BACKGROUND SCIENTIFIC AIM BACKGROUND AND SCIENTIFIC CONTEXT DESCRIPTION GENERAL DESCRIPTION OF THE TESTS CHARACTERISTICS OF THE BODY DEFINITION OF THE COORDINATE SYSTEM USED SHALLOW WATER TESTS Body Restrained from Moving Freely Floating Model Still Water DEEP WATER TESTS Body Restrained from Moving Freely Floating Body Still Water No Body INERTIAL MOMENT TEST Definition of the coordinate system used Description Layout and list of instruments CHARACTERISTICS OF INSTRUMENTS USED DATA ORGANIZATION LIST OF TESTS

6 1 SCIENTIFIC AIM AND BACKGROUND 1.1 SCIENTIFIC AIM The objective of the experimental program is to obtain comprehensive data regarding the drift forces on a floating body of simple geometry. The aim is, firstly, to enhance the understanding of the physics of these second order forces and, secondly, to systematically assess the existing theoretical and numerical methods to calculate them. The complete second order solution for the slow drift forces is now implemented in a few codes around the world, as for example in Wamit V6.1s (or Hydrostar). The complete solution of the slowly varying drift forces results from the interaction between pairs of harmonic components with different frequencies. Each pair of incident harmonic waves will result on a harmonic drift force changing slowly in time. Presently there is no experimental data available to assess the computational methods. Since the problem is very complex, the investigation will be carried out on a step by step basis, from the simpler problem to the most complex. The general objective of the investigation is stated on the first paragraph. Specific objectives are: (a) Obtain new experimental data on the drift forces in bi-harmonic waves with the same incidence but different frequencies. (b) Obtain new experimental data on the drift forces in conditions represented by two systems of harmonic waves with the same frequency but different incidences. (c) Assess the influence of the waterdepth on the mean and slowly varying drift forces. The experimental data will be used to assess the existing codes based on the complete second order solution, establish the limits of application of the theory and verify the usual procedures to calculate the slow drift forces in irregular sea states and compare them with the complete solution. 1.2 BACKGROUND AND SCIENTIFIC CONTEXT Second order wave forces are important for different types of fixed and floating structures. Within a frequency domain approach, these forces can be decomposed into three components namely: a steady force, a difference frequency component and a sum frequency component. Sum and difference frequency effects are important for different problems. In the case of the difference frequency second order forces, they result on the slowly varying wave drift forces in irregular seas, which are important, for example, for floating moored structures. Usually the mooring system is compliant with the first order wave exciting forces since the natural period of the floater plus mooring is large compared to the wave period. However, the slowly varying drift forces have longer periods therefore they may excite the floater and mooring system at their natural frequency, resulting in large horizontal motions of the floater and tensions on the mooring lines. 6

7 Although the subject of slowly varying drift forces has been well studied in the past from the theoretical and numerical point of view, for both single and multi body configurations, little experimental data is available. On the other hand, experimental studies focusing on steady drift forces were conducted by several researchers. Huijsmans et al. [1] have published the results of the steady drift forces on a semi submersible from an experimental program at the Maritime Research Institute in the Netherlands (MARIN). Kashiwagi et. al [2] presented experimental results of the steady drift forces in a multi body configuration of a Wigley hull and a rectangular barge. The objective was to validate a new numerical method based on a far field approach for the calculation of the steady drift forces, however using a control surface around each body. Wichers [3] also conducted his experiments in MARIN, and studied the steady drift forces on a tanker while being towed, thus researching the steady drift forces with non zero forward speed. Regarding the slowly varying drift forces, some experimental work has been presented as well, but focusing mainly on irregular sea states. As examples, Lee et al. [4] have conducted experiments on the slowly varying drift forces for a container ship model in an irregular sea state, while Tomaki at al. [5] studied the same forces on a very large floating structure for an irregular bidirectional sea state. Irregular wave results of drift forces are certainly useful, however they are not the best type of results to validate second order hydrodynamic theories and their numerical implementation. The aim of the proposed experimental investigation is to obtain experimental data of the slowly varying drift forces on a body of simple geometry appropriate for the validation of theoretical and numerical methods. The tests will be carried out on a step by step basis, from the simpler problem of a restrained body in monochromatic waves to the most general problem of the free oscillating body in irregular waves. One of the important groups of tests to be carried out consists of bi-chromatic wave conditions. In fact, the origin of the slowly varying drift forces lies on second order interactions between pairs of harmonic waves with different frequencies. The usual procedure for calculation of slow drift forces is to simplify the quadratic transfer function by representing the difference frequency components in terms of the zero difference results (Newmans s approximation, Newman [6]). In this way the second order problem is much simplified as well as the computational effort. However this approximation has some limitations and in particular for the slow drift oscillations problem it may be important to consider correctly the difference frequency components (Fonseca et al. [7]). The experimental data in bi-chromatic waves will permit the assessment of the Newman s approximation and also the validation of computer codes based on second order theory (Wamit V6.1s, Hydrostar from Bureau Veritas). Such experimental data is not available at the moment. Tests in two systems of mono-chromatic waves with the same frequency but different incidence angles are also planned. The effects of water depth in the drift forces will also be investigated, since these effects are important (Fonseca et al. [7]). References : 7

8 [1]. R. H. M. Huijsmans and A. J. Hermans, 1988, The effect of the steady perturbation potential on the motion of a ship sailing in random seas. Proc. 5th Int. Conf. Num. Ship Hydrodyn., Hiroshima. [2]. Kashiwagi, M., Endo, K., Yamaguchi, H., 2005, Wave drift forces and moments on two ships arranged side by side in waves, Ocean Engineering,, Vol.32, pp [3]. J. E.W.Wichers, A Simulation Model for a Single Point Moored Tanker. PhD thesis, TU Delft (1988) 243 pp. [4]. S.K. Lee, H. Choi and S. Surendra, Experimental studies on the slowly varying drift motion of a berthed container ship model, Ocean Engineering, Vol. 33, Issues 17-18, December 2006, Pages [5]. Ikoma, Tomoki; Maeda, Hisaaki; Rheem, Chang-Kyu, Slowly varying wave drifting force on a very large floating structure in short crested waves, Oceans Conference Record (IEEE), v 1, 2000, p [6]. Newman, J.N., 1974, Second Order Slowly Varying Forces on Vessels in Irregular Waves, Symp. on Dyn. of Mar. Veh. and Struct. in Waves, London. [7]. Fonseca N., Pessoa J., Guedes Soares C., Calculation of second order drift forces on a FLNG accounting for difference frequency components, proceedings of OMAE, June 15-20, 2008, Estoril, Portugal 2 DESCRIPTION 2.1 GENERAL DESCRIPTION OF THE TESTS The aim of the experimental investigation is to obtain experimental data of the slowly varying drift forces on a body of simple geometry appropriate for the validation of theoretical and numerical methods. The tests were carried out on a step by step basis, from the simpler problem of a restrained body in monochromatic waves to the most general problem of the free oscillating body in irregular waves. An important part of the study is to access the depth effects on the slowly varying drift forces, so the tests were carried out for 3 different water depths: 40 cm and 55 cm which are considered to be of the shallow water type, and 3 m representing deep waters. The first two were performed in the shallow water basin, while the last was performed in the offshore basin. For each water depth, two different main types of experiments were performed. In the first type the body is held restrained from moving, subjected to incident waves and the loads are measured. The second type of experiments is performed with the body freely floating and held in its average position by a very soft mooring system. The body is subjected to incident waves and the resulting motions are recorded. A subtype of the freely floating body experiments that was also tested is the case where no incident waves are present, and an impulsive force is applied to the model. In this case the resulting decaying motions are recorded. 8

9 For the deep water program an additional type of experiments with no body present but with waves and current was tested and the free surface elevation on certain geographical points was recorded. Another two additional subtype of experiments performed for this water depth was the case with the body restrained from moving and subjected to waves and current or to only current. In this case the forces acting on the body were measured. A schematic representation of these types of experiments can be seen on Figure 1. Shallow Water Basin Depths 40 cm and 55 cm Restrained body Freely floating body Incident waves Incident waves Still Water Deep Water Basin Depth 3 m Restrained body Freely floating body No body Incident waves Incident Waves and current Incident current Incident waves Still Water Incident waves Figure 1 schematic plan of the experimental program Incident Waves and current Incident current Adding to these tests, a centre of gravity and inertial moment test of the pendulum type was performed on the body out of the water. 2.2 CHARACTERISTICS OF THE BODY The tested body is a cylinder with rounded bottom. The curve that originates the wetted surface of the geometry by means of a 360º revolution can be seen in Figure 2. The dimensions and the aimed mass properties for the cylinder can be seen in Table 1. Figure 2 curve whose 360 º revolution originates the wetted surface of the tested model 9

10 Table 1 dimensions and aimed mass properties of the axisymmetrical body Figure 3 on the left: model outside the water with a grid and the draught line drawn. On the right: the model fixed to a rig and subjected to an incident long crested wave 2.3 DEFINITION OF THE COORDINATE SYSTEM USED The origin of the orthogonal coordinate system used in these experiments is located in the centre of the model at the calm free surface level. X is positive in the direction contrary to the propagation of the waves (and in some cases the current flow) and Z is positive upwards. All of the quantities measured are compliant with this coordinate system. All of the units in the acquired data are those of the International System (m, s, N, ms -1, ms -2 ) 2.4 SHALLOW WATER TESTS The shallow water tests were carried for two different water depths 40 cm and 55 cm. The basin itself includes an 18 meter wide segmented 3D piston type wave maker which is equipped with an active wave absorption system to avoid that waves reflected in the model are inputted again into to the basin. The controlling of the wave maker is done by using DHI Wave Synthesizer Software. A dissipation beach is placed around 20 m away from the wave maker. The model was located 8 meter away from the wave maker and at the centre of the wave makers width. A schematic representation of this set up can be seen in Figure 4. 10

11 Figure 4 Shallow water basin particulars and model location For this set of experiments, the model was attached to a triangular shaped rig, which was fixed to the bottom of the basin (an image of this rig with the model attached can be seen in Figure 5). The side of the rig to which the model was attached to is perpendicular to the propagation direction of the incident waves, and the remaining sides are placed downstream in order to minimize the hydrodynamic interference of the rigs fixing poles with the model (see Figure 5). The rigs fixing poles were prepared so that the set up would fit both water depths, fixing the model at exactly the correct draught. A 3D force transducer was placed between the rig and the model to measure the loads caused by wave-body interaction. A 3D accelerometer was placed on the model as well to ensure that no vibrations were being sent by the rig that might contaminate the results. Wave gauges were placed in front and on the side of the model to measure the free surface elevation. Another wave gauge was also attached to the model, in the symmetry axis which is in the direction of the wave propagation to measure the run up, and a grid of 1cm wide squares was attached on the model for visual measurement of the run up. A data acquisition system was installed in a platform downstream from where the model was placed. Some of the experiments were filmed with a high definition camera. Figure 5 on the left: Triangular rig with the model attached. On the right: schematic representation of the triangular rig 11

12 The tests itself consists in running the wave maker during a certain amount of time, and measuring the loads in the model. In this case, monochromatic waves 1 to 10 and bichromatic waves 1 to 23 (see Table 2 to Table 5) were tested in both water depths. Test duration varied between 2 min for monochromatic waves and 5 min for bichromatic waves. Between each test the basins free surface is allowed to settle Body Restrained from Moving Incident Waves The waves selected for testing were chosen so that they would be in the relevant range of periods for the chosen geometry. They are restricted in wave height to avoid either the body to hit the bottom or the wave to break. Both monochromatic and bi-chromatic waves were tested, as well as some irregular seastates. For monochromatic waves a set of 10 waves was selected. In the case of bi-chromatic waves, three different set of waves were chosen so that the difference between the harmonics (dw) would be 0.5 (rad/s), 1.5 (rad/s) and 4 (rad/s), holding the first two sets 9 waves and the last set 5 waves. In addition to this, 3 2D Jonswap spectra irregular sea states were considered. On all the tests involving incident waves, and unless specified otherwise, the waves to be tested are the following (Table 2, Table 3, Table 4, Table 5 and Table 6): Table 2 characteristics of the tested monochromatic waves monochromatic waves wave index T (s) A (cm) Table 3 characteristics of the tested bichromatic waves with dw=0.5 rad/s bichromatic waves - dw=0.5 (rad/s) wave index T1 (s) T2 (s) A1 (cm) A2 (cm)

13 Table 4 characteristics of the tested bichromatic waves with dw=1.5 rad/s bichromatic waves - dw=1.5 (rad/s) wave index T1 (s) T2 (s) A1 (cm) A2 (cm) Table 5 characteristics of the tested bichromatic waves with dw=4 rad/s bichromatic waves - dw=4 (rad/s) wave index T1 (s) T2 (s) A1 (cm) A2 (cm) Table 6 characteristics of the tested Jonswap irregular seastates Irregular waves - Jonswap Spectra wave index T0(s) Hs (cm) Beta1 (deg) Beta2 (deg) Irregular seastate 2 is in fact the superposition of two 2D irregular seastates with different directions, thus creating a 3D seastate List and Layout of Instruments The following instruments were used: 8 Wave Gauges Type 202 Amplifier Type 102E Accelerometer of the Setra type 141A Force transducer Type 205/3C Amplifier Type 106E 1 computer equipped with DHI Wave Synthesizer software for data acquisition Connecting cables The 8 wave gauges were connected to the Amplifier Type 102E and both the Accelerometer and force transducers were connected to the strain amplifier type 106E. Both the amplifiers were then connected to the computer which acquired all the data at an 80 Hz sample rate. A schematic representation of this set up can be seen in Figure 1. 13

14 Type 205/3C Force Transducer Type 141A accelerometer Type 102 Wave gauge 1 Type 106E Amplifier Type 102E Amplifier Computer with data logging software Type 102 Wave gauge 2... Type 102 Wave gauge 8 Figure 6 Schematic representation of the instrumentation set up Both the accelerometers and the force transducers were installed in the model. Six of the wave gauges were placed in front of the model, in the flow symmetry line, and one was placed 4 meters to the side of the centre of the model. The last wave gauge was fixed in front of the model to measure the run up. A schematic representation with the coordinates of the location of each wave gauge is shown on Figure 7. Figure 7 Schematic representation of the experiment set up (not to scale) Freely Floating Model In the freely floating case, the model was held at its average position with a very soft mooring system. Four lines were attached to each quadrant of the model in such way 14

15 that they would not touch the water, and with an inclination angle such that the mooring forces would pass approximately through the models centre of gravity (see Figure 8). This way the mooring systems effect on the dynamics of the model was minimized. Figure 8 mooring lines layout The lines were then connected to pulleys fixed on 4 poles at the necessary height to ensure the lines inclination angle. From there the lines were connected to another pulley, located further up the poles, and then to a chain resting in a bucket. The chains weight, kg / m, ensures the design stiffness of the mooring system. About 1.5 m of each chain was left hanging to issue a certain pre tension to the mooring lines. A force transducer was placed between the lines and the chain to measure the tension. A schematic representation of this system can be seen in Figure 9. The model was equipped with an optic motion detection system composed of two detecting cameras and 5 small and very light infrared light reflecting balls (called active markers) placed over the model (see 15

16 Figure 10). A dedicated Pc stores the position of the markers for each time step at a sample rate of 80 Hz, and calculates the motions of the model in the 6 degree of freedom. Figure 9 mooring system and pole layouts 16

17 Figure 10 Motion detection system, composed by two detecting cameras and five active markers placed in the model A similar set up of 7 wave gauges was placed in the water, but with slightly different positions than in the case of the fixed model (see Figure 12). The wave run up gauge was removed from the model to avoid interference with the dynamics of the system. The data acquisition was installed in the same platform as that of the restrained model experiments. Some of the experiments were filmed with a high definition video camera Incident Waves These sets of tests are very similar to the ones performed for the restrained model. Starting from its resting position, the model is subjected to incident waves generated by the wave maker during a period of time and the motions are recorded. The tests lasted between 3.5 min and 10 min, since in some of the tests it took a long time for the flow to reach a steady state. For the 55 cm water depth, monochromatic waves 1 to 10 and bichromatic waves 1 to 23 were tested. In addition to that, surge decay tests with incident monochromatic waves 1 to 10 were performed to access the slow drift damping. The difference between this test and the last ones is that instead of having the model resting in its average location, an initial displacement in the surge motion mode is forced. After the generated monochromatic waves reach the model, it is released and the decaying motions are recorded. When the model reaches a steady state the test ends. In the 40 cm water depth, the combination of the restricted water depth to the large motions of the model increased the risk that the model would touch the bottom of the basin. Due to this, it was necessary to reduce the amplitude in some of the tested waves. The following table presents the waves that endured changes in its amplitude. All of the remaining monochromatic and bichromatic tested waves were left unchanged. 17

18 Table 7 characteristics of the alternative monochromatic wave for the 40 cm water depth monochromatic waves wave index T (s) A (cm) 10 ' Table 8 characteristics of the alternative bichromatic waves for the 40 cm water depth bichromatic waves wave index T1 (s) T2 (s) A1 (cm) A2 (cm) 4 ' ' ' ' ' ' ' ' List and Layout of Instruments The following instruments were used: 7 Wave Gauge Type 202 Amplifier Type 102E 4 Force transducer type 211/50 Amplifier Type 106E 2 infrared detecting cameras 5 active marker light sources Dedicated Pc for the MarineTrak motion sensing System 1 computer equipped with DHI Wave Synthesizer software for data acquisition Connecting cables The 7 wave gauges were connected to the Amplifier Type 102E which was connected to the computer that acquired all the data at an 80 Hz sample rate. The force transducers were connected to the type 106 E amplifier, which was the connected to the data acquiring computer. The two cameras capture the position of the active makers and send it to the dedicated computer which calculates the motions on the 6 degree of freedom of the model. This information is then sent to the computer equipped with the data acquisition software. A schematic representation can be seen in Figure

19 Type 211/50 froce transducer 1 Type 211/50 froce transducer 2... Type 211/50 froce transducer 4 Type 106E Amplifier Infrared detecting camera 1 Dedicated PC Infrared detecting camera 2 Type 102 Wave gauge 1 Type 102E Amplifier Computer with data logging software Type 102 Wave gauge 2... Type 102 Wave gauge 7 Figure 11 Schematic representation of the instrumentation set up The infrared detecting cameras were placed one on each side of the wave maker facing the model. The wave gauges were distributed in a very similar configuration as the previous set of tests, although the five gauges close to the model were moved in the wave maker direction to allow the model move freely. A schematic drawing with the coordinates of each of these equipments can be seen in Figure

20 2.4.3 Still Water Description Figure 12 Schematic representation of the experiment set up (not to scale) In still water both free decay tests and metacentric height tests were done. Surge, pitch and heave decay tests were performed for both water depths. These are done by forcing a displacement in each of the motion modes (but only one mode per test), then releasing the model and measuring the decaying motions. Metacentric height tests are performed by placing a weight in the top edge of the model and measuring the heel angle. In this case a 1 kg weight was placed in x=0.31 m, y=0 m and z=0.2 m, so that only the pitch rotational mode would be affected, and the resulting angle was measured. This procedure was repeated both with and without the mooring lines attached to allow accessing the interference of the mooring system in this parameter List and Layout of Instruments The instrumentation used in this set of experiments is: 2 infrared detecting cameras 5 active marker light sources Dedicated Pc for the MarineTrak motion sensing System 1 computer equipped with DHI Wave Synthesizer software for data acquisition 20

21 Connecting cables 1 weight with 1 Kg The instrumentation layout is the same as shown before. See Figure DEEP WATER TESTS The deep water tests were carried out on the offshore basin, which has a water depth of 3 m. This basin is 20 m long and 30 m wide, and includes a hydraulic flap wave maker controlled by DHI Wave Synthesizer software. A parabolic beech with holes and wave absorbs is included in the tank to drawback the energy given by the reflection, and it s located in the opposite side to the wave maker at a distance of 11.6 m. A set of portable noodles connected to hoses and a hydraulic pump that can be used to generate current in the tank is part of the equipment available in this basin. A large crane which can move in the y direction is used to fix the model, wave gauges and other types of equipment in the basin and creates a stable platform for people to work on. A smaller crane is also present and was used to fix the motion detection cameras. The model was located at a distance of 7.6 m away from the wave maker, and at the centre of the basins width. A representation of this is shown on Figure 13. Figure 13 Deep water or offshore basin particulars and model location Body Restrained from Moving 21

22 For this set of experiments, the model was attached to a triangular shaped rig, which was fixed to the large movable crane (an image of this rig with the model attached can be seen in Figure 14). Figure 14 model fixed to the rig in the deep water basin A 3D force transducer was placed between the rig and the model to measure the loads caused by wave-body interaction. A 3D accelerometer was placed on the model as well to ensure that no vibrations were being sent by the rig that might contaminate the results. Wave gauges were placed in front and on the side of the model to measure the free surface elevation. Another wave gauge was also attached to the model, in the symmetry axis which is in the direction of the wave propagation to measure the run up, and a grid of 1cm wide squares was attached on the model for visual measurement of the run up. A data acquisition system was installed on the side of the tank. Some of the experiments were filmed with a high definition camera Incident Waves Description The procedure for tests involving incident waves is the same as in shallow waters. See For this situation, monochromatic waves 1 to 10, bichromatic waves 1 to 23 and irregular seastates 1 to 3 were tested during periods of time that varied between 2 min for monochromatic waves and 5 min for bi-chromatic waves. In the case of the irregular seastates, 15 min runs were considered. 22

23 Table 9 characteristics of the monochromatic waves created to evaluate the wave amplitude effect on drift forces Wave amp effect wave index T (s) A (cm) In addition to these, a new set of waves was created to evaluate the influence of the wave amplitude on the drift forces. These are basically a set of monochromatic waves with the same period but different amplitudes. Two different periods with nine different amplitudes each were created. Its characteristics can be seen in the Table Layout and list of instruments The instrumentation and layout of the set up is the same as the ones used in the analogous experimentations in the shallow water basin. See Current Description For this case the current portable noodles were placed about 1 m in front of the wave maker, which was not used. A close to uniform flow is achieved in the middle of the tank, where two circular flows meet (see Figure 15). 23

24 Figure 15 Current flow representation in the deep water tank Two current velocities were tested 0.06 m/s and 0.12 m/s. The test consists in creating a current, heading in the negative x direction that reaches the model as close to a uniform flow as it was possible. No wave gauges were used, but a current meter was placed in the position where the model would be during a calibration run, 10 cm below the free surface. The forces acting on the model were measured with a force transducer placed between the model and the rig Layout and list of instruments The following instruments were used: 1 MINILAB ultrasonic current meter system Force transducer Type 205/3C Amplifier Type 106E 1 computer equipped with DHI Wave Synthesizer software for data acquisition Connecting cables The force transducer was connected to the strain amplifier type 106E. Both the amplifier and the current meter system were then connected to the computer which acquired all the data at an 80 Hz sample rate. A schematic representation can be seen in Figure

25 Current meter system Computer with data logging software Force transducer Type 205/3C Amplifier Figure 16 Schematic representation of the instrumentation set up The force transducer was placed between the model and the rig, and the current meter was placed at x = m, y = 0 m and z = -10 m during a calibration run Incident Waves and current Description This set of experiments is a combination of the previous two set of experiments. The procedure is simply to submit the model to the action of the current combined with incident waves. Both current speeds of 0.06 m/s and 0.12 m/s were tested, and each of the current speeds were combined with monochromatic waves 1, 3, 5, 7 and 9, and bichromatic waves 1, 3, 6, 8, 10, 13, 15 and 17. The forces acting on the model and the wave height in particular places were measured Layout and list of instruments The same as in previous fixed body and incident waves experiments, but with the addition of the current meter system. See and Freely Floating Body In the freely floating case, the model was held at its average position with a very soft mooring system, designed in such way that it would have the same stiffness and pretension as in the shallow water case. The system layout is therefore very similar to the one presented before. The deepness of the tank made it impossible to have the poles installed inside the tank so they were installed in different geographical locations. The same inclination angle and the same spreading of the mooring lines were achieved by moving pulley n1 to a higher position (see Figure 9). Since the system is not symmetrical in respect to x axis, this position in the poles that are in the beach side is different to those that are in the wavemaker side. 25

26 Figure 17 Layout of the mooring system and camera positioning The two cameras for the motion detection system were placed in a small crane in one of the sides of the tank, in a different layout than that of the shallow water case. This was due to the same reason that obligated to change the position of the mooring poles. The layout of both the mooring system and camera positioning can be seen in Figure Incident waves Description Both monochromatic waves 1 to 10 and bichromatic waves 1 to 23 were tested in this case. In addition to that, the monochromatic waves created for the wave amplitude effect experiments 1 to 18 were tested as well. The procedure is the same as in the fixed body case, although the body is left free to move and motions are recorded instead of forces. Also the surge decay test with monochromatic waves 1 to 10 was completed. The procedure for this was been explained in Layout and list of instruments The instrumentation and layout is the same as in the shallow water case, except for the position of the motion detection cameras. See and Still Water Description In this case both decay and metacentric height tests were performed. The procedure was the same as in the shallow water case for the decay tests. For the metacentric height tests, instead of using just one 1 kg weight, 3 different weights were used. A 0.1 kg, 0.2 kg and 0.5 kg weight were sequentially placed at x=0.31 m, y=0 m and z=0.2 m, and the resulting heel angle was measured. This test was done without the mooring system attached. 26

27 Layout and list of instruments The instrumentation used in this set of experiments is: 2 infrared detecting cameras 5 active marker light sources Dedicated Pc for the MarineTrak motion sensing System 1 computer equipped with DHI Wave Synthesizer software for data acquisition Connecting cables Weights of 0.1, 0.2 and 0.5 Kg, one of each The layout is the same as shown before. See No Body Description This set of tests focused in the interaction between the waves and current, and targeted to describe their interference. No body is present, so only wave heights were measured for several combinations of waves, both regular and irregular, with and without an uniform current coming from the opposite direction to that of the propagation of the waves. The method to create this current is the same as used in , although the current flumes were placed in the opposite side of the tank thus creating a symmetrical flow to the one shown on Figure 15. The test itself consist in creating a certain wave and current condition, and measure the wave heights with a configuration of seven wave gauges and the current velocity with a current meter. During the tests real seastates were scaled down to basin dimensions by a factor of l = 50. The conditions to be tested were a set of regular waves (Table 10), the same set of regular waves plus 3 current conditions (Table 11), a set of irregular Jonswap seastates (Table 12) and the combination of this set with the 3 current conditions (Table 13), a set of double peak spectra obtained by the superposition of two Jonswap spectra (Table 14) and the combination of these with a current condition (Table 15), and finally a Jonswap spectra with 2 different directional spreading of 2 and 10 degrees (Table 16) and the 27

28 combination of these with the current conditions (Table 17). The duration of the tests varied from 3 min for regular waves to 30 min in some of the irregular seastates. Table 10 totable 17 present the main characteristics of the performed experiments. Table 10 characteristics of the tested monochromatic waves and duration of the tests monochromatic waves T (s) A (cm) duration (min) Table 11 characteristics of the tested monochromatic waves and currents and duration of the tests monochromatic waves + current T (s) A (cm) U (ms -1 ) duration (min)

29 Table 12 characteristics of the tested irregular seastates and duration of the tests Irregular Waves (Jonswap) Tp (s) Hs (cm) duration (min) Table 13 characteristics of the tested irregular seastates and current and duration of the tests Irregular Waves (Jonswap) + current Tp (s) Hs (cm) U (ms -1 ) duration (min) Table 14 characteristics of the tested double peak irregular seastates and duration of the tests Double peak spectra (Jonswap) Tp1 (s) Hs1 (cm) Tp2 (s) Hs2 (cm) duration (min)

30 Table 15 characteristics of the tested double peak irregular seastates and current and duration of the tests Double peak spectra (Jonswap) + current Tp1 (s) Hs1 (cm) Tp2 (s) Hs2 (cm) U (ms -1 ) duration (min) Table 16 characteristics of the irregular seastates with directional spreading and duration of the tests Jonswap with directional spreading Tp (s) Hs (cm) spreading (º) duration (min) Table 17 characteristics of the irregular seastates with directional spreading and currents and duration of the tests Tp (s) Hs (cm) spreading (º) U (ms -1 ) duration (min) Layout and list of instruments Jonswap with directional spreading + current The following instruments were used: 7 Wave Gauge Type 202 Amplifier Type 102E 1 MINILAB ultrasonic current meter system Amplifier Type 106E 1 computer equipped with DHI Wave Synthesizer software for data acquisition Connecting cables The 7 type 202 wave gauges are connected to the type 102E amplifier, and the current meter system was connected to the type 106E amplifier. Both the amplifiers were 30

31 connected to the computer equipped with data logging software. A schematic representation of this set up can be seen in Figure 18. MINILAB ultrasonic current meter system Type 102 Wave gauge 1 Type 106E Amplifier Type 102E Amplifier Computer with data logging software Type 102 Wave gauge 2... Type 102 Wave gauge 7 Figure 18 Schematic representation of the instrumentation set up The wave gauges were placed in a straight line aligned with both the wave direction and current flow. The current meter was positioned next to the middle wave gauge at a depth of 10 cm. A representation of this layout is shown in Figure 19. Figure 19 Schematic representation of the experiment set up (not to scale) 2.6 INERTIAL MOMENT TEST Definition of the coordinate system used The orthogonal coordinate system used for this set of experiments is fixed with the body and placed at its symmetry axis, and at the mid height. Z is pointing upwards. The tension is measured in N. 31

32 2.6.2 Description An inertial moment test of the pendulum type was conducted in this experiment. The model is hanging from a structure by a line. There is a force transducer attached to the line to measure the tension. The model is given an initial displacement and is left to oscillate in a slowly decaying motion in the direction to which the inertial moment is to be measured. The variation in the measured tension is associated with the variation of the angular acceleration, so it is possible to measure the natural oscillation period, which is related with the inertial moment. Two different line lengths L were used m and 1.31 m and both the inertial moment in the x and y directions were assessed. Figure 20 shows a schematic representation of this set up. Figure 20 Schematic representation of the experiment set up Layout and list of instruments The following instruments were used: Force transducer Type 205/3C Amplifier Type 106E 1 computer equipped with DHI Wave Synthesizer software for data acquisition Connecting cables m line 1.31 m line 32

33 The force transducer was connected to the amplifier which was connected to the data logging computer. A schematic representation can be seen in Figure 21. Type 211/50 froce transducer 1 Type 106E Amplifier Computer with data logging software Figure 21 Schematic representation of the instrumentation set up 2.7 CHARACTERISTICS OF INSTRUMENTS USED Name, type and description Name of instrument Gauge Type 202 Quantity measured Free surface elevation Basis of measurement Conductivity between two parallel electrodes partly immersed in water General description Wave gauge Range, accuracy and calibration Range of measurement up to 96 cm Accuracy of measurement <1mm How often it should be calibrated every day Calibration procedure applying a known voltage to a known elevation of the F.S. by adjusting a gain Instalation, power and data Type of connector 4-pole LEMO Dimensions Length (mm) 250 to 1000 (custumer specified) Name, type and description Name of instrument Wave Amplifier Module Type 102E General description Signal amplifier / filter Instalation, power and data Power supply/supplies required VDC/+- 16mA Type of connector 6-pole LEMO (gauge) / BNC on front (signal out) Details of data acquisition system Linearity better than 0.2% F.S. Dimensions Length (mm) 50.6 Width (mm) 129 Height (mm) 160 Weight (kg) 0.56 Name, type and description Name of instrument Transducer type 211/50 Quantity measured Tension (N) General description Force tranducer Range, accuracy and calibration Range of measurement 50 N Accuracy of measurement < 0.05% Instalation, power and data Type of connector 6-pole LEMO Name, type and description Name of instrument Strain Amplifier Type 106E General description High-Performance DC transducer amplifier for static / dynamic measurements Name, type and description Name of instrument General description Instalation, power and data Type of connector Details of data acquisition system DHI Wave Synthesizer Data acquisition software using a I/O board analogue/digital I/O board 12 bits input/output resolution, 2 output channels, ±5 V range 16, 32 or 64 input channels per board, built-in quartz clock 33

34 Name, type and description Name of instrument Minilab current meter Quantity measured Flow velocity General description 2D Ultrasonic current meter Range, accuracy and calibration Range of measurement m / s Resolution m / s 3 DATA ORGANIZATION The data collected in these experiments is recorded in an ASCII file format of the *.txt type. Each file includes: a header line that contains the information relative to the performed test, such as wave period and amplitude, or water depth; a second line in which the measured quantity for each column of the subsequent data is presented; a third line that should be disregarded; the actual data presented in columns the number of columns is dependent of the type of test to which the data refers to. An example representing the first five lines of the monochromatic wave 1 in the 55 cm water depth test file is shown next: First Line: Test no 97: H55 - monochromatic wave 1 - T1=0,7 A=1,1 Second Line: Time WG1 WG2 WG3 WG4 WG5 WG6 WG7 wave run up. Fx Fy Fz Third Line : Unit Fourth Line: E Fifth Line: E E It should be noted that in the fixed model tests on the deep water basin, a small problem with calibration factor of the Surge forces has occurred. Because of that, the surge force in all of the monochromatic waves for that depth and up until the 7th wave (DeepDw05RestrainedT7.txt) in the bichromatic waves should be multiplied by a correction factor of -2. A similar problem occurred in bichromatic waves 12 to 23, for the freely floating body tests in the water depth of 55 cm with surge and heave motions. These quantities should be multiplied by a factor of 2. The files containing this data are organized by test type and water depth and are stored in a main folder called tests ascii files. The organization of this and all the subsequent folders is presented next: 1. tests ascii files 1.1. calibration H40 40 cm water depth tests bichromatic waves 34

35 monochromatic waves H55 55 cm water depth tests bichromatic waves monochromatic waves Hoo 3 m water depth tests bichromatic waves current irregular waves monochromatic waves wave amp effect 1.2. COG and inertial moment tests (out of the water - pendulum test) 1.3. Fixed body results H bichromatic waves monochromatic waves H bichromatic waves monochromatic waves Hoo bichromatic waves irregular waves monochromatic waves wave amp effect waves and current 1.4. freely floating body results H bichromatic waves COG tests Decay tests monochromatic waves H bichromatic waves 35

36 Decay tests irregular seastates monochromatic waves Slow drift damping tests Hoo 1.5. No Body bichromatic waves COG tests decay tests no mooring with mooring irregular waves monochromatic waves Slow drift damping tests wave amp effect current monochromatic irregular jonswap two peak jonswap directional spreading no current monochromatic irregular jonswap 4 LIST OF TESTS two peak jonswap directional spreading What follows is a list of all the tests performed with the correspondent main particulars and the names of the ascii files where the data is stored. Still water tests Deep water File name 36

37 Test nº 1 Determination of CG test DeepCOGTest1 - No mooring 2 Free decay test in heave 1 DeepFreeDecayHeave1 - no mooring 3 Free decay test in heave 2 DeepFreeDecayHeave2 4 Free decay test in heave 3 DeepFreeDecayHeave3 5 Free decay test in pitch 1 DeepFreeDecayPitch1 - no mooring 6 Free decay test in pitch 2 DeepFreeDecayPitch2 - no mooring 7 Free decay test in pitch 3 DeepFreeDecayPitch1 - with mooring 8 Free decay test in surge 1 DeepFreeDecaySurge1 9 Free decay test in surge 2 DeepFreeDecaySurge2 10 Free decay test in surge 3 DeepFreeDecaySurge3 H=0.40 Test nº 327 Determination of CG test H40COGTest1 328 Determination of CG test H40COGTest2 11 Free decay test in heave 1 H40FreeDecayHeave1 12 Free decay test in heave 2 H40FreeDecayHeave2 13 Free decay test in heave 3 H40FreeDecayHeave3 329 Free decay test in heave 4 H40FreeDecayHeave4 330 Free decay test in heave 5 H40FreeDecayHeave5 14 Free decay test in pitch 1 H40FreeDecayPitch1 15 Free decay test in pitch 2 H40FreeDecayPitch2 16 Free decay test in pitch 3 H40FreeDecayPitch3 331 Free decay test in pitch 4 H40FreeDecayPitch4 17 Free decay test in surge 1 H40FreeDecaySurge1 18 Free decay test in surge 2 H40FreeDecaySurge2 19 Free decay test in surge 3 H40FreeDecaySurge3 332 Free decay test in surge 4 H40FreeDecaySurge4 333 Free decay test in surge 5 H40FreeDecaySurge5 334 Free decay test in roll 1 H40FreeDecayRoll1 335 Free decay test in roll 2 H40FreeDecayRoll2 H=0.55 Test nº 20 Free decay test in heave 1 H55FreeDecayHeave1 21 Free decay test in heave 2 H55FreeDecayHeave2 22 Free decay test in heave 3 H55FreeDecayHeave3 336 Free decay test in heave 4 H55FreeDecayHeave4 37

38 23 Free decay test in pitch 1 H55FreeDecayPitch1 24 Free decay test in pitch 2 H55FreeDecayPitch2 25 Free decay test in pitch 3 H55FreeDecayPitch3 26 Free decay test in surge 1 H55FreeDecaySurge1 27 Free decay test in surge 2 H55FreeDecaySurge2 28 Free decay test in surge 3 H55FreeDecaySurge3 336 Free decay test in surge 4 H55FreeDecaySurge4 Out of the water - pendulum test Test nº 319 Inertia about xx axis - lenght 1 COG and Ixx test 1 L1 320 Inertia about xx axis - lenght 2 COG and Ixx test 1 L2 321 Inertia about xx axis - lenght 2 COG and Ixx test 2 L2 322 Inertia about yy axis - lenght 1 COG and Ixx test 1 L1 323 Inertia about yy axis - lenght 1 COG and Ixx test 2 L1 324 Inertia about yy axis - lenght 1 COG and Ixx test 1 L2 325 Inertia about yy axis - lenght 2 COG and Ixx test 2 L2 326 Inertia about yy axis - lenght 2 COG and Ixx test 3 L2 RESTRAINED BODY - depth = 0.40m Test nº Condition T1 (s) T2 (s) A1 (cm) A2 (cm) Tm(s) dw(rad/s) File name calibration File dw(rad/s)= Restrained H40Dw00RestrainedT1 calh40dw00t1 63 Restrained H40Dw00RestrainedT2 calh40dw00t2 64 Restrained H40Dw00RestrainedT3 calh40dw00t3 65 Restrained H40Dw00RestrainedT4 calh40dw00t4 66 Restrained H40Dw00RestrainedT5 calh40dw00t5 67 Restrained H40Dw00RestrainedT6 calh40dw00t6 38