author:

Kevin R. Moore

bibliography:

ac_sources.bib

title: Offshore Wind Energy Simulator (OWENS) Glue Code Basic Theory, Frames of Reference, and Inter-Module Coupling Methods –-

Introduction

The Offshore Wind Energy Simulator (OWENS) Code is a floating turbine-platform code capable of steady, unsteady, and modal analysis. It is comprised of, or coupled to many modules for aerodynamics, hydrodynamics, mooring dynamics, and finite element formulations.

How many of these items are used is not straightforward or a-priori and can easily lead to confusion or mistake (like how the aerodynamics uses inflow data; is it just simple based on the mean hub velocity, or in the rotating blade frame of reference? If the latter, what is that frame of reference so that we make sure we don't incorrectly map the vectors?) This document is intended as a developers guide for the intent of clearing up the relative ambiguity between the many moving and modular pieces. It is not a full theory document or users guide. For theory and use, please see the theory and user guides respectively. Within this document, we give enough detail about the operations of the \"glue\" code, the frames of reference, and coupling methods to aid further development.

Contributing

Please make all feature changes and bug fixes as branches and then create pull requests against the dev branch. The dev branch will be periodically pulled into master.

Glue Code Basic Theory

Due to the nonlinearity and non-closed-form nature of the floating turbine problem in both the design and temporal space, OWENS uses many types of iterative solution methods, specific to the physics involved. Loose or Gauss-Seidel iteration is used for the coupling between the modules. gives an overview of the general code structure for transient analysis, with the main equations being solved and the relative location of the iteration loops.

::: algorithm ::: spacing 1.18

::: algorithmic Initialize simulation (all module parameters, meshing, composite properties, etc) Initialize displacements and forces as 0

Get driveshaft displacement from generator torque Get rotor speed, rotational displacement from generator torque, aero torque, and turbine inertia Get aero forces from rotor speed, position Get structural displacements and reaction forces from aero forces Update displacements$_\text{guess}$ with the calculated displacements ::: :::

[]{#alg:Transient label="alg:Transient"} :::

Global Frame of Reference

Thanks to some legacy VAWT frames of reference where wind was originally coming from the top down, and then from the left right, the convention was to simply rotate the axes instead of properly redefining the global frame of reference to match standard math convention again. Therefore, an azimuth angle of 0, or yaw angle for standard VAWT frame of reference is top dead center. Therefore, blade 1 of a vawt should also be top dead center, i.e. aligned with the y+ axis as shown below.

{#fig:ac_velocities width="60%"}

InflowWind and TurbSim Velocity Inflow

This is how it is defined in the manual, despite inverting the positive direction of rotation compared to standard notation.

Wind frame of reference is the same as global. However, the angle follows TurbSim and [InflowWind](https://github.com/old-NWTC/InflowWind) notation Wind propagation angle is zero when aligned with the positive X-axis and clockwise positive, in the direction of the negative negative Y-axis. {#fig:ac_velocities width="50%"}

OWENSAero Aerodynamics (AC and DMS)

$VAWT 2D section looking downwards with induced velocity \$w\$ vector broken into \$u\$ and \$v\$ components depicted by arrows. Airfoils show example blade locations with dots aligning to the circumferential discretization. Aero frame of reference is the same as global, however a blade is at 0 degrees azimuth when it is aligned with the Y-axis. If an aero module is 2D, it is made quasi-3D by stacking slices from lower to higher in the Z-axis.$ {#fig:ac_velocities width="50%"}

Note: CACTUS, does not fully follow this scheme and differs from the global frame of reference by switching the Y and Z axes for a VAWT. Also, be careful with the geometry inputs; if the blade 1 starts out at the \"south\" position, as opposed to the north, then it will behave as though it were a north starting blade rotating clockwise, and a symmetric gust velocity will match (if the simple iec uniform gust is used). All else for CACTUS follows the description above.

Aerodynamics forces are radial inward positive and tangential in direction of rotation positive. So, the blade local accelerations in the radial will be outward positive and in the tangential will be in the opposite direction of rotation for a CCW rotor. CW rotors are still in work and would need to have the local frame of reference rotation verified. Therefor, for the added mass equations, the forces should be negated.

OWENSFEA Structures

Yaw is equivalent to the global azimuth angle as above, and is denoted in the code as Psi. Zero is top dead center, right hand rule positive rotation. The subscript D indicates degrees. Theta is the element slope, or delta, and

The rotation sequence is a Roll (Rx) - Pitch (Ry) - Yaw (Rz) sequence in OWENSFEA (R = Rz * Ry *Rx in multiplication order). This corresponds to Twist - Theta - Psi angle ordering. In the matrix multiplication this is R = $R_{psi}$ * $R_{theta}$ * $R_{twist}$, which is a [3,2,1] matrix ordering.

::: center Name Rotation Axis OWENS Angle Names –––- –––––––- –––––––––- Roll about X Twist Pitch about Y Theta Yaw about Z Psi

: Module Level of Detail in This Document :::

We apply these in order of Roll, then Pitch, then Yaw, which is R = Rz * Ry * Rx (application is from right to left in rotations) for a rotation of vector x by R. i.e R(x) = Rz * Ry * Rx * x.

In the code I now have ang = [ort.Psid[idx], ort.Thetad[idx],ort.Twistd[idx]+180,-90]; DCM = CH2G * createGeneralTransformationMatrix(ang,[3,2,1,2]); Where I have an additional rotation by -90 about the Y axis to align Z with X before applying the other rotation sequences. This is due to AD15 using the IEC conventions with +Z along the blade, but the beam solver using the more typical beam formulation of +X along the beam.

This is almost consistent between blades and struts (have a +90 rotation on struts for some reason that I haven't sorted out yet).

Rotating Frame of Reference, 6 DOF where 1 = turbine vertical force, 2 = turbine 2D slice tangential force, 3 = turbine 2D slice normal force, 4 = blade M25 twisting moment, 5 = blade curvature twisting moment, 6 = blade sweep moment.

The Mesh matches the global frame of reference of x, y, and z. Element length is the length along the element.

The mesh itself is comprised only of components. For example, a tower, two blades, and four struts. The element number is sequential. There are overlapping points where each component connects. The mesh has a connectivity vector, which has rows corresponding to each element, column 1 corresponds to the \"master\" node, and column 2 corresponds to the \"slave\" node. The element connection in the mesh is only intra-component. I.e. there is no connectivity between components - that is defined in the joint matrix, which has columns for: Joint Number, Joint Master Node, Joint Slave Node, Joint Type, Joint Mass, Not Used, PsiD, ThetaD. The D indicates angle in degrees. Joint types are: (0 = weld(fixed), 1=pinned, 2 = hinge joint with axis about slave node element's e2 axis, 3 = hinge joint axis about slave node element's e1 axis, 4 = hinge joint axis about slave node element's e3 axis). The Psi and Theta are of the slave node (or its closest neighbor of the same component due to the gaps in element mesh connectivity). The not used column is just filled with zeros. The \"flapwise\" normal vector of an element is forced to be away from the machine for consistency. During the meshing process, the component type need to be known in order to get this right: Mesh Type: 0-blade 1-tower 2-strut.

Composites

Hydrodynamics

Hydrodynamics are applied into OWENS using the HydroDyn module native to OpenFAST, but applied here through a standalone library linked to OWENS. The physics contained in the HydroDyn standalone library is virtually unchanged from its native application in OpenFAST. HydroDyn user documentation can be found here.

Platform Structure

To enable capturing the hydrodynamics in OWENS for floating turbines, a second mesh is created to represent the platform. OWENS assumes the platform is a rigid body, so the mesh is composed of a single element with effectively infinite stiffness. The two nodes forming this element are:

The platform reference point (i.e., the platform at the still water level along the vertical centerline of its center of gravity) is the bottom node
The tower base point is the top node

The structures composing the platform mesh itself are the same as the OWENSFEA structures documented above, though most of the definitions to define the mesh can be set to zero or are very simple. There are two main exceptions:

The platform center of gravity must be defined, since neither node is at this location. This is defined in the zcm parameter in the SectionPropsArray for the platform mesh.
The 6x6 rigid body mass matrix is defined as a concentrated input at the platform reference point node

A full example of these definitions can be found in the floating platform example notebook (TODO).

Solve Procedure

When applying hydrodynamics, OWENS adds additional Gauss-Seidel loops to solve for the structural motions of both the platform mesh and the "topside" mesh (i.e. everything above the platform) in a way that generates global convergence. This process is:

Solve via a Gauss-Seidel loop for the topside mesh using platform motions from the previous time step

Setting platform motions to zero is how OWENS runs for land-based turbines

Solve via an outer Gauss-Seidel loop and an inner Newton-Raphson loop for the platform mesh, using updated external hydrodynamic loads from HydroDyn and tower base loads from step 1

The Newton-Raphson loop is contained in Unsteady.OWENS_HD_Coupled_Solve, and is necessary to properly account for added mass impacting both HydroDyn and OWENS in a tightly coupled manner.

This solve process is complex, but is documented in detail in Section 2.4.1 of Devin et al. (2022) here. This is a very similar procedure used to coupled HydroDyn to the ElastoDyn module in OpenFAST.

Solve via a Gauss-Seidel loop for the topside mesh using platform motions from the current time step, i.e. the motions calculated in step 2.

This flow chart visualizes this solve procedure, and which step corresponds to which modules connecting to the core OWENS glue code: Hydrodynamics Solve Procedure Flowchart

Reference Frame Conversions

Since HydroDyn operates in the global reference frame, the hydrodynamics capabilities in OWENS deviate from the general convention in OWENS of operating in the hub reference frame. As a result, operations manipulating the platform mesh (e.g. running OWENSFEA.structuralDynamicsTransient) are also applied in the global reference frame. Functionally, this means that the rbData vector input is set to zero when using the platform mesh in OWENSFEA.structuralDynamicsTransient. Care must be taken for I/O procedures between the platform and topside meshes! The Unsteady_utilities.frame_convert function is intended to make this process simpler.

Mooring

Mooring dynamics for floating platforms in OWENS are calculated using a standalone library linking to MoorDyn, another module native to OpenFAST. The mooring loads calculated in MoorDyn are applied as an external load to the same platform mesh as the hydrodynamics, as described above. Since the mooring dynamics do not need to account for added mass, the coupling between MoorDyn and OWENS is much simpler, and the mooring dynamics are applied in the Gauss-Seidel solve procedure without being modified by the additional Newton-Raphson solve in Unsteady.OWENS_HD_Coupled_Solve. Note that MoorDyn operates in the global reference frame, so be careful with reference frame conversions for MoorDyn I/O.

Coupling Methods

Inflow - Aero

Direct: Aero module supplies an x-y-z and time coordinate, inflow returns x-y-z velocity. This is repeated for all blade discrete points as per the aero formulation.

Aero - Turbine Structure

Loose Iteration: Structure provides blade local radius, twist, sweep, and 6 DOF velocities, aero returns forces, moments. This is iterated on until convergence. It is preferred to change this to a N-dimensional root solver and pass gradients to the root solver to increase performance.

Specifically, from the meshing process, the starting and ending node numbers for the blades are known and the aerodynamic loads mapped to the elements between those nodes.