Final report for WP4.3: Enhancement of design methods ... - Upwind

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UPWIND WP4: Offshore Support Structures and Foundations uf = fluid velocity perpendicular to element axis us = cable element’s own velocity perpendicular to element axis Cm = inertia coefficient A = effective cross-section area (for a chain which does not have a uniform cross-section, this is actually the volume of a unit length of cable) ρ = water density These hydrodynamic forces are combined with the other loads on the cable (inertial / gravitational / tension loading) and then forces on all the elements are used to model the overall dynamic behaviour of the cable. Figure 8.37 User interface window for the optional Coupled Cable Dynamics module in AQWA-NAUT. Key findings - AQWA The conclusion drawn from the above is that AQWA-NAUT, in combination with WAMIT or AQWA-LINE, would a suitable tool for a comparison exercise with the look-up table or quasi-static approach. It can model mooring lines using Morison elements, which means a useful comparison can be made. OrcaFlex OrcaFlex is a dedicated “marine dynamics” analysis package produced by Orcina Software. It covers moorings and risers, as well as towing systems. OrcaFlex can carry out full modal, static and dynamic analysis in the time-domain. It supports a wide range of wave models as well as drift forces, wind drag, currents etc. The software has a Windows UI which includes animated or static 3-D graphical displays, including some quite realistic rendering. OrcaFlex can also be run in non-interactive (batch) mode. There is an interactive click-and-drag type UI which allows the user to build up a model in a fairly intuitive way. Objects such as vessels, buoys, mooring lines etc. can be added from a library of predefined objects or custom-defined by the user. Environmental conditions (wind, waves, currents) can be similarly defined and added to the model. When a model has been completed a simulation is started. The behaviour of the model during the simulation can be visualised on the animated 3-D view window. Output quantities (load, motions, etc) can be sampled at user-defined intervals during the simulation and output to a file. Outputs can be easily imported to Excel, etc. for further processing. OrcaFlex also has its own graphical display function. Theoretical aspects The code supports a wide range of different wave models, including regular and irregular waves (four standard wave spectra are supported), and both linear and nonlinear waves. Wave drift forces are also available (in contrast to AQWA). Hydrodynamic forces on the mooring lines and the moored device are derived using an extended form of Morison’s equation. Mooring lines are modelled on a finite-element basis; each line is divided 126
UPWIND WP4: Offshore Support Structures and Foundations into a number of straight-line elements each with a clump weight, buoyancy and drag. Figure 8.38 shows the coordinate frame of a line element. Each element is treated as a stiff massless rod with a telescopic sliding joint in the centre, so that it can change in length (and can also twist around its own axis). The user is given the option of specifying both stiffness and damping coefficients for the following degrees of freedom: • Axial deflections (changes in the length of the rod element). • Torsional deflections about the rod element’s central axis. This means one end of the element twisting relative to the other end. • Bending deflections (changes in the relative angle between the rod element and its immediate neighbouring elements). N.B. The damping discussed above is only for the cable itself; external (hydrodynamic) damping is treated separately and is discussed below. Figure 8.38: Line element representation in Orcaflex, showing the element’s frame of reference. The tension in each element of the line is given by the relation T e ( dL / dt) = EA. ε + EA. e [8-15] L where: 0 Te = effective tension. EA = axial stiffness of line (i.e. Young’s modulus x effective cross-section area). ε = mean axial strain = (L-λL0)/(λL0). L = instantaneous length of segment. λ = expansion factor of segment. L0 = unstretched length of segment. e = numerical damping of the line, in seconds. Hydrodynamic drag forces on the line are found using a choice of three different relations, all based on Morison’s equation. Drag forces are applied both in water and optionally also in air (wind forces). The same relations are used for both water and air, with appropriate values for fluid density. The three available relations are as follows: • Standard formulation – the most commonly used; suited to general flow conditions. • Pode formulation – preferred by some modellers for situations where flow is nearly tangential to the line. • Eames formulation – sometimes preferred for bare (unsheathed) mooring cables. 127
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Project UpWind Contract No.: 019945
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Acknowledgement The presented work
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Summary The overall aim of the UpWi
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Table of Contents Acknowledgement..
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Task 4.1 Integration of support str
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Sequential coupling The sequential
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analysis. In the new multibody code
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Figure 2.4: 2nd global bending mode
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3.2 Comparison of deterministic loa
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Figure 3.5: Time series of axial fo
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• Time domain simulation in ADCoS
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• A supplementary load vector for
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The following results are found: Fi
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Figure 4.5: Output positions in the
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It is directly visible that there i
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ated eigenfrequency is shifted into
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Water levels For the calculation of
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guidelines for the inclusion of cli
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damaging if the frequency of the ex
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uncertain parameters carefully. Thr
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Table 5.3 shows annual reliability
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Steel substructure for offshore win
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Table 5.16 shows the required FDF v
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A Fracture Mechanical (FM) modellin
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Figure 5.4: Annual reliability indi
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Further, the effect of possible ins
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Rainflow evaluation The load cases
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For DLC 7.2 it has to be considered
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Guideline, DLC 1.5). Furthermore, t
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Table 5.28: Output locations for da
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From these results it can be clearl
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Figure 5.11: Normalised DELs with v
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Figure 5.14 presents normalized DEL
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Figure 5.16: Output locations for e
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UPWIND WP4: Offshore Support Struct
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Final report for WP4.3: Enhancement of design methods ... - Upwind

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