4.6.5. Modeling Considerations
SubDyn was designed as a flexible tool for modeling a wide range of substructures for both land-based and offshore applications. This section provides some general guidance to help construct models that are compatible with SubDyn.
Please refer to the theory in Section 6 for detailed information about SubDyn’s coordinate systems, and the theoretical approach we have followed in SubDyn.
4.6.5.1. Model Discretization
SubDyn allows for the specification of arbitrary multimember structure geometries. The user defines the geometry of a structure in SubDyn using joints and members. Specifically, the user specifies a list of joints that represent the endpoints of beams, and the connectivity between one or more members at each joint. Members and their cross-sectional properties are then defined between two joints. Members can be further subdivided into multiple (NDiv) elements to increase the model resolution. Nodes, where the numerical calculations take place, are located at the endpoints of each element. To keep the mesh as uniform as possible when using NDiv, the initial member definition should also have a roughly uniform mesh. For tapered members, we recommend setting NDiv > 1. Improper discretization of the members may decrease the accuracy of the model.
When SubDyn is coupled to FAST, the joints and members need not match between HydroDyn and SubDyn—FAST’s mesh-mapping utility handles the transfer of motion and loads across meshes in a physically relevant manner [MJJ14], but consistency between the joints and members in HydroDyn and SubDyn is advised.
For offshore applications, because of the exponential decay of hydrodynamic loads with depth, HydroDyn requires higher resolution near the water free surface to properly capture loads as waves oscillate about the still water level (SWL). We recommend that the HydroDyn discretization not exceed element lengths of 0.5 m in the region of the free surface (5 to 10 m above and below SWL), 1.0 m between 25- and 50-m depth, and 2.0 m in deeper waters.
When SubDyn is hydro-elastically coupled to HydroDyn through FAST for the analysis of fixed-bottom offshore systems, we recommend that the length ratio between elements of SubDyn and HydroDyn not exceed 10 to 1. As such, we recommend that the SubDyn discretization not exceed element lengths of 5 m in the region of the free surface, 10 m down to 25- to 50-m depth, and 20 m in deeper waters. These are not absolute rules, but rather a good starting point that will likely require refinement for a given substructure. Additional considerations for SubDyn discretization include aspects that will impact structural accuracy, such as member weight, substructure modes and/or natural frequencies, load transfer, tapered members, and so on.
Members in SubDyn are assumed to be straight circular (and possibly tapered) cylinders. The use of more generic cross-sectional shapes will be considered in a future release.
4.6.5.2. Foundations
There are two methods that can be used to model foundation flexibility or soil-structure interaction in SubDyn. The first method makes us of the SSI stiffness and mass matrices at the partially restrained bottom joints as described in Sections 3.3.4, 3.4, and 6. The second method mimics the flexibility of the foundation through the apparent (or effective) fixity (AF) length approach, which idealizes a pile as a cantilever beam that has properties that are different above and below the mudline. The beam above the mudline should have the real properties (i.e., diameter, thickness, and material) of the pile. The beam below the mudline is specified with effective properties and a fictive length (i.e., the distance from the mudline to the cantilevered base) that are tuned to ensure that the overall response of the pile above the mudline is the same as the reality. The response can only be identical under a particular set of conditions; however, it is common for the properties of the fictive beam to be tuned so that the mudline displacement and rotation would be realistic when loaded by a mudline shear force and bending moment that are representative of the loading that exists when the offshore wind turbine is operating under normal conditions.
Note that in HydroDyn, all members that are embedded into the seabed (e.g., through piles or suction buckets) must have a joint that is located below the water depth. In SubDyn, the bottom joint(s) will be considered clamped or partially restrained and therefore need not be located below the seabed when not applying the AF approach. For example, if the water depth is set to 20 m, and the user is modeling a fixed-bottom monopile with a rigid foundation, then the bottom-most joint in SubDyn can be set at Z = -20 m; HydroDyn, however, needs to have a Z-coordinate such that Z < -20 m. This configuration avoids HydroDyn applying static and dynamic pressure loads from the water on the bottom of the structure. When the AF approach is applied, the bottom-most joint in SubDyn should be set at Z < -20 m.
4.6.5.3. Member Overlap
As mentioned earlier, the current version of SubDyn is incapable of treating the overlap of members at the joints, resulting in an overestimate of the mass and potentially of the structure stiffness. One strategy to overcome this shortcoming employs virtual members to simulate the portion of each member within the overlap at a joint. The virtual members should be characterized by low self-mass and high stiffness. This can be achieved by introducing virtual joints at the approximate intersection of the finite-sized members, and then specifying additional members from these new joints to the original (centerline) joints. The new virtual members then use reduced material density and increased Young’s and shear moduli. Care is advised in the choice of these parameters as they may render the system matrix singular. Inspection of the eigenvalue results in the summary file should confirm whether acceptable approximations have been achieved.
4.6.5.4. Substructure Tower/Turbine Coupling
When SubDyn is coupled to FAST, the 6 DOFs of the platform in ElastoDyn must be enabled to couple loads and displacements between the turbine and the substructure. The platform reference-point coordinates in ElastoDyn should also be set equal to the TP reference-point’s coordinates (commonly indicating either the tower-base flange location, or TP centroid, or TP center of mass) that the user may have set in the stand-alone mode for checking the SubDyn model. A rigid connection between the SubDyn interface joints and TP reference point (\({\equiv}\) platform reference point) is assumed.
For full lattice support structures or other structures with no transition piece, the entire support structure up to the yaw bearing may be modeled within SubDyn. Modeling the tower in SubDyn as opposed to ElastoDyn, for example, allows the ability to include more than the first two fore-aft and side-to-side bending modes, thus accounting for more general flexibility of the tower and its segments; however, for tubular towers, the structural model in ElastoDyn tends to be more accurate because ElastoDyn considers geometric nonlinearities not treated in SubDyn. When modeling full-lattice towers using SubDyn, the platform reference point in ElastoDyn can be located at the yaw bearing; in this case, the tower-bending DOFs in ElastoDyn should be disabled.
If FAST is run with SubDyn but not HydroDyn, the water depth will be automatically set to 0 m. This will influence the calculation of the reaction loads. Reactions are always provided at the assumed mudline, therefore, they would not be correctly located for an offshore turbine as a result. Thus, it is recommended that HydroDyn always be enabled when modeling bottom-fixed offshore wind turbines.
ElastoDyn also needs tower mode shapes specified (coefficients of best-fit sixth-order polynomials), derived using appropriate tower-base boundary conditions. They can be derived with an appropriate software (finite-element analysis, energy methods, or analytically) and by making use of the SubDyn-derived equivalent substructure stiffness and mass matrices (the KBBt and MBBt matrices found in the SubDyn summary file) to prescribe the boundary conditions at the base of the tower.
For instance, using NREL’s BModes software, the SubDyn-obtained matrices can be used in place of the hydrodynamic stiffness (hydro_K) and mass matrices (hydro_M) (mooring_K can be set to zero). By setting the hub_conn boundary condition to two (free-free), BModes will calculate the mode shapes of the tower when tower cross-sectional properties are supplied. To obtain eigenmodes that are compatible with the FAST modal treatment of the tower (i.e., no axial or torsional modes and no distributed rotational-inertia contribution to the eigenmodes), the tower-distributed properties should be modified accordingly in BModes (e.g., by reducing mass moments of inertia towards zero and by increasing torsional and axial stiffness while assuring convergence of the results; see also https://wind.nrel.gov/forum/wind/viewtopic.php?f=4&t=742).
The rotational inertia of the undeflected tower about its centerline is not currently accounted for in ElastoDyn. Thus, when the nacelle-yaw DOF is enabled in ElastoDyn there will not be any rotational inertia of the platform-yaw DOF (which rotates the tower about its centerline) when both the platform-yaw inertia in ElastoDyn is zero and the tower is undeflected. To avoid a potential division-by-zero error in ElastoDyn when coupled to SubDyn, we recommend setting the platform-yaw inertia (PtfmYIner) in ElastoDyn equal to the total rotational inertia of the undeflected tower about its centerline. Note that the platform mass and inertia in ElastoDyn can be used to model heavy and rigid transition pieces that one would not want to model as a flexible body in either the ElastoDyn tower or SubDyn substructure models.
*Damping of the Guyan modes:*
There are three ways to specify the damping associated with the motion of the interface node.
SubDyn Guyan damping matrix using Rayleigh damping
SubDyn Guyan damping matrix using user defined 6x6 matrix
HydroDyn additional linear damping matrix (AddBLin)
The specificaiton of the Guyan damping matrix in SubDyn is discussed in Section 4.6.6.6.5.
Old:
The C-B method assumes no damping for the interface modes. This is equivalent to having six undamped rigid-body DOFs at the TP reference point in the absence of aerodynamic or hydrodynamic damping. Experience has shown that negligible platform-heave damping can cause numerical problems when SubDyn is coupled to FAST. One way to overcome this problem is to augment overall system damping with an additional linear damping for the platform-heave DOF. This augmentation can be achieved quite easily by calculating the damping from Eq. (4.104) and specifying this as the (3,3) element of HydroDyn’s additional linear damping matrix, AddBLin. Experience has shown that a damping ratio of 1% of critical (\({\zeta=0.01}\)) is sufficient. In Eq. (4.104), \({K_{33}^{(SD)}}\) is the equivalent heave stiffness of the substructure (the (3,3) element of the KBBt (i.e., \({\tilde{K}_{BB}}\)) matrix found in the SubDyn summary file, see also Section 6), \({M_{33}^{(SD)}}\) is the equivalent heave mass of the substructure (the (3,3) element of the MBBt (i.e., \({\tilde{M}_{BB}}\)) matrix found in the SubDyn summary file, see also Section 6), and \({M^{(ED)}}\) is the total mass of the rotor, nacelle, tower, and TP (found in the ElastoDyn summary file).
To minimize extraneous excitation of the platform-heave DOF, it is useful to set the initial platform-heave displacement to its natural static-equilibrium position, which can be approximated by Eq. (4.105), where is the magnitude of gravity. PtfmHeave from Eq. (4.105) should be specified in the initial conditions section of the ElastoDyn input file.
4.6.5.5. Self-Weight Calculations
SubDyn will calculate the self-weight of the members and apply appropriate forces and moments at the element nodes. Lumped masses will also be considered as concentrated gravity loads at prescribed joints. The array of self-weight forces can be seen in the summary file if the code is compiled with DEBUG compiler directives. In general, SubDyn assumes that structural motions of the substructure are small, such that (1) small-angle assumptions apply to structural rotations and (2) the so-called P- \({\Delta}\) effect is negligible, and therefore undeflected node locations are used for self-weight calculations.
4.6.5.6. Note On Other Load Calculations
When SubDyn is coupled to HydroDyn through FAST, the hydrodynamic loads, which include buoyancy, marine-growth weight, and wave and current loads, will be applied to the effective, deflected location of the nodes by the mesh-mapping routines in the glue code. Those loads, however, are based on wave kinematics at the undeflected position (see Jonkman et al. 2014 for more information).
4.6.5.7. Craig-Bampton Guidelines
When SubDyn is coupled with FAST, it is important to choose a sufficient number of C-B modes, ensuring that the vibrational modes of the coupled system are properly captured by the coupled model. We recommend that all modes up to at least 2-3 Hz be captured; wind, wave, and turbine excitations are important for frequencies up to 2-3 Hz. Eigenanalysis of the linearized, coupled system will make checking this condition possible and aid in the selection of the number of retained modes; however, the linearization process has yet to be implemented in FAST v8. Until full-system linearization is made available, experience has shown that it is sufficient to enable all C-B modes up to 10 Hz (the natural frequencies of the C-B modes are written to the SubDyn summary file). If SIM (see Section Section 4.6.6.6.6) is not enabled, in addition to capturing physical modes up to a given frequency, the highest C-B mode must include the substructure axial modes so that gravity loading from self-weight is properly accounted for within SubDyn. This inclusion likely requires enabling a high number of C-B modes, reducing the benefit of the C-B reduction. Thus, we recommend employing the C-B reduction with SIM enabled. Because of the fixed-fixed treatment of the substructure boundary conditions in the C-B reduction, the C-B modes will always have higher natural frequencies than the physical modes.
4.6.5.8. Integration Time Step Guidelines
Another consideration when creating SubDyn input files is the time step size. SubDyn offers three explicit time-integrators — the fourth-order Runge-Kutta (RK4), fourth-order Adams-Bashforth (AB4), fourth-order Adams-Bashforth-Moulton (ABM4) methods — and the implicit second-order Adams-Moulton (AM2) method. Users have the option of using the global time step from the glue code or an alternative SubDyn-unique time step that is an integer multiple smaller than the glue-code time step. It is essential that a small enough time step is used to ensure solution accuracy (by providing a sufficient sampling rate to characterize all key frequencies of the system), numerical stability of the selected explicit time-integrator, and that the coupling with FAST is numerically stable.
For the RK4 and ABM4 methods, we recommend that the SubDyn time step follow the relationship shown in Eq. (4.106), where \({f_{max}}\) is the higher of (1) the highest natural frequency of the retained C-B modes and (2) the highest natural frequency of the physical modes when coupled to FAST. Although the former can be obtained from the SubDyn summary file, the latter is hard to estimate before the full-system linearization of the coupled FAST model is realized. Until then, experience has shown that the highest physical mode when SubDyn is coupled to FAST is often the platform-heave mode of ElastoDyn, with a frequency given by Eq. (4.107), where the variables are defined in Section 5.3.
For the AB4 method, the recommended time step is half the value given by Eq. (4.106).
For AM2, being implicit, the required time step is not driven by natural frequencies within SubDyn, but should still be chosen to ensure solution accuracy and that the coupling to FAST is numerically stable.