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Research Papers

Composed Fluid–Structure Interaction Interface for Horizontal Axis Wind Turbine Rotor

[+] Author and Article Information
Dubravko Matijašević

Department of Aeronautical Engineering,
Faculty of Mechanical Engineering
and Naval Architecture,
University of Zagreb,
Ivana Lučića 5,
Zagreb 10000, Croatia
e-mail: dubravko.matijasevic@fsb.hr

Zdravko Terze

Professor
Department of Aeronautical Engineering,
Faculty of Mechanical Engineering
and Naval Architecture,
University of Zagreb,
Ivana Lučića 5,
Zagreb 10000, Croatia
e-mail: zdravko.terze@fsb.hr

Milan Vrdoljak

Associate Professor
Department of Aeronautical Engineering,
Faculty of Mechanical Engineering
and Naval Architecture,
University of Zagreb,
Ivana Lučića 5,
Zagreb 10000, Croatia
e-mail: milan.vrdoljak@fsb.hr

More specifically, Λ denotes sites with generalized displacements and loads. As we are considering CCCFVM for the fluid domain, X denotes points with spatial displacements (without rotations) and forces (without moments).

We are considering only one blade and part of hub assigned to that blade, thus Γ = Γh ∪ Γb. For multiple blades, each blade has its own recovery assigned to it.

Note that the distinction between Ri and a submatrix form equation (22) is that the arguments of the skew-symmetric linear operator A(⋅) in Eq. (22) are mesh vertices, and in Eq. (27) is a boundary polygon area centres, see Fig. 9.

FSI interface with CCCFVM is only approximately conservative as points at which the pressure is known differ from the mesh vertices at which boundary displacement is prescribed, see Figure 9. The displacement is transferred from the structure to the fluid side by HbΛT, see Eq. (23). But now, for the conservative transfer the load should be known in the fluid mesh vertices. Instead of distributing the load from the face centres to the mesh vertices by some new interpolation, in Ref. [17] the following solution to the problem was proposed for CCCFVM. Different displacement transfer matrices are calculated, one that formally transfers displacement to the face centres, and then its transpose is used for the load transfer in the conservative spatial interface. Regardless of the fact, the two matrices slightly differ, as they project the same interpolation to different set of evaluation points, we use the same symbol for both.

Composed interface can be closed, i.e., Γ = Ωs, or just a part of a closed surface. Generalization to any number of blades is straightforward.

1Corresponding author.

Contributed by the Design Engineering Division of ASME for publication in the JOURNAL OF COMPUTATIONAL AND NONLINEAR DYNAMICS. Manuscript received February 14, 2014; final manuscript received February 4, 2015; published online April 2, 2015. Assoc. Editor: Carlo L. Bottasso.

J. Comput. Nonlinear Dynam 10(4), 041009 (Jul 01, 2015) (10 pages) Paper No: CND-14-1044; doi: 10.1115/1.4029749 History: Received February 14, 2014; Revised February 04, 2015; Online April 02, 2015

In this paper, we propose a technique for high-fidelity fluid–structure interaction (FSI) spatial interface reconstruction of a horizontal axis wind turbine (HAWT) rotor model composed of an elastic blade mounted on a rigid hub. The technique is aimed at enabling re-usage of existing blade finite element method (FEM) models, now with high-fidelity fluid subdomain methods relying on boundary-fitted mesh. The technique is based on the partition of unity (PU) method and it enables fluid subdomain FSI interface mesh of different components to be smoothly connected. In this paper, we use it to connect a beam FEM model to a rigid body, but the proposed technique is by no means restricted to any specific choice of numerical models for the structure components or methods of their surface recoveries. To stress-test robustness of the connection technique, we recover elastic blade surface from collinear mesh and remark on repercussions of such a choice. For the HAWT blade recovery method itself, we use generalized Hermite radial basis function interpolation (GHRBFI) which utilizes the interpolation of small rotations in addition to displacement data. Finally, for the composed structure we discuss consistent and conservative approaches to FSI spatial interface formulations.

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References

Figures

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Fig. 1

Schematic representation of aeroelastic domain Ω¯. Fluid domain is denoted with Ωf, while Ωs represents the structure domain. Dashed region represents patches of the PU for a single blade, while darker dashed region is where PU patches overlap.

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Fig. 2

FEM discretization of elastic blade with 13 DOF 1D beam elements. Axis z defines blade span.

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Fig. 3

FSI boundary of fluid domain mesh

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Fig. 4

Deformed blade on rigid hub

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Fig. 5

Edgewise displacement error, flapwise displacement error, and displacement error magnitude

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Fig. 6

Comparison of the reconstructed displacement error without and with the PU method

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Fig. 7

Error of reconstruction when using the PU method

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Fig. 8

The process of connecting the elastic mesh to the rigid one. Depicted mesh points are from the blade surface intersection with the x = const plane passing through rotor rotation axis, at blades forward facing position. Any mesh vertex depicted in the figure is in the overlapping region, and the dashed line represents the GHRBFI recovery in the region. Error from RBFI recovery of the mesh is depicted with circles, and for the ease of correlation to displaced mesh the exact recovery is depicted with squares. Final mesh, after utilizing PU, is depicted with stars.

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Fig. 9

Detail of fluid domain CCCFVM mesh boundary, in region where blade wet surface Γb (represented by dashed region) is connected to hub wet surface Γh. Dots represent mesh vertices at which displacement is prescribed. Circles represent area centers of boundary polygons, the points at which pressure is known.

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Fig. 10

Schematic representation of nodal load lumping on two element FEM mesh. FEM nodes are represented by dots, and dashed regions represent nodes tributary regions. FSI interface Γ is now composed of rigid hub boundary Γh, and elastic blade boundary Γb, which is itself composed of k tributary regions Γbk, i.e., Γ = Γh∪Γb = Γh∪(∪kΓbk).

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