Extending the Capabilities of the Mooring Analysis Program: A Survey of Dynamic Mooring Line Theories for Integration Into FAST

Abstract

Techniques to model dynamic mooring lines take various forms. The most widely used models include a heuristic representation of the physics (such as a lumped-mass system), a finite-element analysis discretization of the lines (discretized in space), or a finite-difference model (which is discretized in both space and time). In this paper, the authors explore the features of the various models, weigh the advantages of each, and propose a plan for implementing one dynamic mooring line model into the open-source Mooring Analysis Program (MAP). MAP is currently used as a module for the FAST offshore wind turbine computer-aided engineering (CAE) tool to model mooring systems quasi-statically, although dynamic mooring capabilities are desired. Based on the exploration in this paper, the lumped-mass representation is selected for implementation in MAP based on its simplicity, low computational cost, and ability to provide physics similar to those captured by higher-order models. To begin, the underlying theories defining the three classes of dynamic mooring line models are identified and explored. This leads to insight into the capabilities of each representation. These capabilities are weighed against the current needs of the FAST wind turbine CAE tool, to which MAP will be coupled. Based on the assessment, a plan for integrating the dynamic mooring line theory into the current MAP structure is developed. Common problems arising from the determination of the model static equilibrium and known issues with numerical stability are addressed. Because MAP is a module that FAST can call, a plan consistent with the FAST modularization framework principles is described. Adding dynamic mooring line capabilities extends the features in MAP and also allows uncoupled analysis to be performed through MAP’s native Python bindings.

Offshore Wind Turbines – Research and Development

“…More sophisticated models capable of describing dynamics of mooring lines are further developed based on experience from the oil and gas industry. These models incorporate inertial and damping forces due to surrounding sea water, as well as loads caused by waves acting directly on mooring lines, [21] and [22].…”

Dynamic analysis of a floating spherical buoy fastened by mooring cables

“…The demand for accuracy promotes the dynamics of the cable being considered in the development of the numerical models. National renewable energy laboratory also planned to analyze the floating wind turbines using dynamic model of the cable, as shown by Masciola et al (2014). The system of a spherical buoy moored by cables is often used for meteorology monitoring and navigation (Idris et al, 1997).…”

Mathematical Modelling of Mooring Systems for Wave Energy Converters—A Review

“…By applying the equations of dynamic equilibrium and continuity (stress/strain) to each mass, a set of discrete equations of motion is derived. The lumped mass method is shown to have the advantage of a strictly diagonal mass matrix, eliminating the requirement of added computation for matrix inversion [100]. Detailed descriptions of example usage of lumped mass MMs can be found in [81,89,[101][102][103][104] and, for the specific case of WEC moorings, in Vissio et al [19].…”

“…The lumped mass method and other spatial discretisation approaches, such as finite differences and finite element methods (FEMs), are outlined in this subsection. A comparison of these different spatial discretisation approaches is given by Mascoila et al [100], who explore the features of the various models and weigh the advantages of each.…”

“…Whilst lumped mass models must place all masses at discrete nodes, FEMs can derive the governing equations with an integration of the mass over the entire element, leading to a "consistent" mass formulation [80]. Although the resulting mass matrix achieves an upper and lower bandwidth of two, compared to the more computationally efficient strictly diagonal matrix for the lumped mass formulation [100], the FEM is able to produce accurate results with a smaller number of elements compared to the lumped mass formulation. Examples of different solution methods include: collocation [14], Galerkin [88,108,109], and discontinous Galerkin [110] methods.…”