«J. Mar. Sci. Eng. 2015, 3, 1362-1381; doi:10.3390/jmse3041362 OPEN ACCESS Journal of Marine Science and Engineering ISSN 2077-1312 ...»
J. Mar. Sci. Eng. 2015, 3, 1362-1381; doi:10.3390/jmse3041362
Design Optimization for a Truncated Catenary Mooring System
for Scale Model Test
Climent Molins 1,*, Pau Trubat 1, Xavi Gironella 2 and Alexis Campos 1
Department of Civil and Environmental Engineering, Universitat Politècnica de Catalunya—BarcelonaTech, Jordi Girona 1-3, Campus Nord C1-206, 08018 Barcelona, Spain;
E-Mails: email@example.com (P.T.); firstname.lastname@example.org (A.C.) 2 Department of Civil and Environmental Engineering, Universitat Politècnica de Catalunya—BarcelonaTech, Jordi Girona 1-3, Campus Nord D1- 111A, 08018 Barcelona, Spain;
E-Mail: email@example.com * Author to whom correspondence should be addressed; E-Mail: firstname.lastname@example.org;
Academic Editor: Bjoern Elsaesser Received: 29 July 2015 / Accepted: 2 November 2015 / Published: 6 November 2015 Abstract: One of the main aspects when testing floating offshore platforms is the scaled mooring system, particularly with the increased depths where such platforms are intended.
The paper proposes the use of truncated mooring systems to emulate the real mooring system by solving an optimization problem. This approach could be an interesting option when the existing testing facilities do not have enough available space. As part of the development of a new spar platform made of concrete for Floating Offshore Wind Turbines (FOWTs), called Windcrete, a station keeping system with catenary shaped lines was selected. The test facility available for the planned experiments had an important width constraint. Then, an algorithm to optimize the design of the scaled truncated mooring system using different weights of lines was developed. The optimization process adjusts the quasi-static behavior of the scaled mooring system as much as possible to the real mooring system within its expected maximum displacement range, where the catenary line provides the restoring forces by its suspended line length.
J. Mar. Sci. Eng. 2015, 3 1363 Keywords: scale moorings; scale tests; wind turbines; floating offshore platform; optimization
1. Introduction Floating offshore wind energy research is focused on developing new platform concepts that fit the necessary requirements of the stability for a wind turbine design and also present competitive construction and operational costs.
As in the Oil and Gas (O&G) Industry, into the design stage of the new platform concepts, the motion and loads of the platform have to be assessed and well predicted in several load combinations to ensure the reliability of the structure and the mooring system. The main approaches to predict the whole platform behavior are the numerical simulation and the physical scale models. However, it is still widely accepted in the offshore industry that model testing is the most reliable procedure to validate the results and to be the final benchmark for the design of a platform.
The physical model testing is mainly performed in the ocean engineering basins, where the environmental conditions such as waves, currents and wind can be reproduced [1,2]. Furthermore, there are others facilities that can reproduce the ocean situations like wave flumes that are not commonly used due to their highly restrictive dimensions. On the other hand, the usage of these installations would help the development of the offshore wind technology allowing the performance of the model tests in more places and reducing costs in that research field.
Some wind offshore platforms model tests have been performed in wave flumes despite their limited width dimension. One example is a Tension Leg Platform (TLP) prototype tested in the CEHINAV (Canal de Ensayos Hidrodinámicos) . In this particular case, a flume is a suitable place for testing because of the inner configuration of a TLP, a buoyant platform moored with vertical tethers. Even a spread mooring system does not seem to fit well in a wave flume; Krawkosky et al  tested a spar scale model with a four line mooring system in a flume. The azimuthal angles between two adjacent mooring lines were of 90 degrees. The lines were scaled in two different ways, the lines placed in the longitudinal direction of the tank are well-scaled using proper tethers, while in the transverse direction the mooring lines are modeled as two constant forces. The forces were applied by two ropes hanging on both sides of the flume with weights on their extremes. However, this simplification does not allow changing the waves relative direction to the platform position because the scaled mooring system only works in the longitudinal direction. Furthermore, a three line mooring system could not be scaled in the same way because the different symmetry between the mooring system and the wave flume. Then, in order to perform tests with different wave directions using the same scaled mooring system, an equivalent system with shorter radius to anchor should be designed. In such a mooring system, the line length should be truncated to allow placing all mooring lines in the wave flume. Other scale models have been tested in bigger basins,  uses truncated mooring lines attached to springs because the depth of the basin does not match the model in the selected scale. Another solution to overcome the width basin constraint was adopted by , where the mooring line segment, constantly resting on the seabed during the tests, was removed. This lead to a shorter radius to anchor using the well scaled prototype mooring system.
J. Mar. Sci. Eng. 2015, 3 1364 Truncated mooring systems are a common scale method used in the O&G industry [7–10]. Since the tank basins sizes do not allow performing tests in the common scales for the upcoming ultra-deep waters, new systems have to be conceived to manage this challenge. The truncated passive system is the most widely used and feasible method of the hybrid model testing methods, which uses a combination of physical model tests and numerical modeling. In the passive method, all the model characteristics like platform properties, wave height, current velocity, etc., are well scaled except the working depth and the mooring shape. This method uses an equivalent truncated mooring system for the scale tests and the results are used to interpret and adjust the model in order to perform a full depth numerical model.
Stansberg  states the challenges for the development of the truncated passive methods. The new truncated mooring system set-up has to guarantee the following aspects: (1) the motion response should have the same behavior as the results of the full-depth mooring system and (2) the truncated mooring system should present the most similar physical properties as the full-depth system. To achieve the correct design of the truncated mooring system, Stansberg presents the following rules ordered by priority.
Model the total horizontal restoring force Model the quasi-static coupling between vessel responses Model a “representative” level of mooring and riser system damping, and current force Model a “representative” single line tension characteristics (at least quasi-static) In the field of the truncated mooring system design, optimization models to better adjust the truncated system approach to the real one commonly solve the problem. Zhang  proposed an annealing simulation algorithm for hybrid discrete variables (ASFHDV) to optimize the static response of a single catenary and the whole catenary system static response in one direction. Further investigations propose an optimization model that accounts for the mooring-induced damping generated by the transverse motion of the mooring line due to the low-frequency surge oscillation using a genetic algorithm .
In order to improve the behavior of the truncated mooring line, Qiao  proposes the connection of viscous dampers joined to the mooring line to simulate the whole damping of the real mooring line.
These models have been validated and widely used, but the quasi-static approach could underestimate the tension in the mooring lines due to dynamics when those are important . On the other hand, new methods have recently been developed to take into account the line dynamics and obtain a more realistic system behavior using the real scaled mooring line in the upper sections, where the line dynamics are more important, and using external actuators that replicate the truncated line segments behavior .
The main contribution of this paper is the design of a truncated mooring system to replace the prototype mooring system, which cannot be installed due to basin constraints. The truncated mooring system is designed as a simple mooring line composed of two materials without any other external systems as springs. This new mooring system allows the study of several wave approaching directions to the whole structure, float and moorings. Tests results and the comparison with numerical simulations are also presented.
First, the real model and the scale model due to the basin constrains are presented. Then, the calculation of the static mooring forces and the optimization problem are described. Finally, the optimization and the experimental results, with the comparison with numerical simulations, are discussed.
J. Mar. Sci. Eng. 2015, 3 1365
2. Real Model
The monolithic concrete spar, the so-called Windcrete , is a prototype floating platform for wind turbines developed in AFOSP (Alternative Floating Platform Designs for Offshore Wind Turbines using Low Cost Materials) within a KIC-InnoEnergy innovation project [14–16].
The spar prototype is designed as a monolithic concrete structure from the top of the tower to the bottom of the buoy, thus joints are avoided to ensure water-tightness and a good fatigue behavior.
The structure, for a 5 MW wind turbine, is composed of three parts: first, the buoy, composed of a cylinder with a diameter of 13 m and a height of 120 m; second, the transition segment, which is a cone of 10 m high, these two parts are the submerged ones, therefore the total draft of the structure is 130 m. The third part is the emerged tower that reaches 87.6 m above the SWL. A sketch of the concept and its hydrodynamic characteristics are shown in Figure 1 and Table 1. The moorings system is connected to the platform at the fairleads located 60 m above the bottom with a draft of 70 m, near the Centre of Gravity (COG) to reduce the coupling motions between the surge and pitch.
In this study, the Windcrete is considered to be placed in a 265 m depth sea location. The mooring system is configured to provide enough restoring force to maintain the platform motion in a relative offset and to prevail over the wave and wind loads. In order to achieve simplicity in the model, the prototype mooring system is composed of three equispaced chain mooring lines with the same cross section.
The main characteristics of the line are defined in the Table 2.
3. Scale Model
Model tests were performed in the ICTS-CIEM (Investigation flume and offshore experimentation) inside LIM (Maritime Engineering Laboratory) at the UPC (Universitat Politècnica de Catalunya—BarcelonaTech). The flume is equipped with a wave generator that can generate waves from 10 cm up to 160 cm height. The flume is 100 meters long with a cross section 3.5 m wide and 5 m high. The flume and the wave paddle are shown in Figures 2 and 3, respectively.
According to the prototype’s sizes and the flume height, the selected scale is 1:100. Then, the scaled depth would be 2.65 m. The flume width does not allow the direct scaling of the catenary lines because the common anchor radius should be between two and four times the total depth, requiring a 10 m wide channel. Furthermore, if several wave directions are studied, the mooring system should be able to rotate in z direction allowing the wave to impact on the platform from different relative direction with the mooring system. Then, the mooring system should not be connected through the flume wall. For these reasons, a truncated mooring system is used in the model scale test, reducing the radius to anchor distance, and therefore the total length of the lines. Figure 4 shows the cross section of the wave flume with both the scale prototype mooring system and the truncated one.
J. Mar. Sci. Eng. 2015, 3 1366
The truncated mooring system is defined by the radius to anchor, the line length and the materials that compose the different segments of the mooring line. The radius to anchor is previously defined as the maximum radius allowed by the channel width taking account the margins for a proper installation operation of the mooring system. Furthermore, if the truncated mooring line were composed of a unique cross section, the necessary weight to achieve the restoring forces of the prototype system would cause huge vertical forces on the floating platform. For this reason, two different chain sections are chosen to design the mooring line. The heaviest line section is positioned at the bottom, connected to the anchor, providing the restoring horizontal force. The upper section, a light segment connected to the platform, J. Mar. Sci. Eng. 2015, 3 1368 reduces the total line payload due to its light weight. The exact properties of the lines are obtained through an optimization problem to fit the responses between the prototype mooring system and the truncated one, which is presented in next sections.
To solve Equations (1) and (2), the mooring line is discretized in n + 1 nodes forming n line elements.
The nodes are described as N [N1, N2,...,Ni,..., Nn 1 ] and the segments as S [ S1, S2,..., Si,...,Sn ].
The properties that define each element are the weight per unit length i, its length li and the longitudinal stiffness EAi. Figure 6 shows a sketch of the mooring line composed by n segments.
function is expressed as the difference between the response of the prototype mooring system and the truncated one. This distance has to be minimized as a function of the mooring variables.