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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

## Abstract

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

Hsu, M. C., and Bazilevs, Y., 2012, “Fluid–Structure Interaction Modeling of Wind Turbines: Simulating the Full Machine,” Comput. Mech., 50(6), pp. 821–833.
Heinz, J. C., 2013, “Partitioned Fluid–Structure Interaction for Full Rotor Computations Using CFD,” Ph.D. thesis, DTU Wind Energy, Lyngby, Denmark.
Farhat, C., Lesoinne, M., and Tallec, P., 1998, “Load and Motion Transfer Algorithms for Fluid–Structure Interaction Problems With Non-Matching Discrete Interfaces: Momentum and Energy Conservation, Optimal Discretisation and Application to Aeroelasticity,” Comput. Methods Appl. Mech. Eng., 157(1–2), pp. 95–114.
Boer, A. D., van Zuijlen, A., and Bijl, H., 2008, “Comparison of Conservative and Consistent Approaches for the Coupling of Non-Matching Meshes,” Comput. Methods Appl. Mech. Eng., 197(49), pp. 4284–4297.
Quaranta, G., Masarati, P., and Mantegazza, P., 2005, “A Conservative Mesh-Free Approach for Fluid–Structure Interface Problems,” International Conference on Computational Methods for Coupled Problems in Science and Engineering, M. Papadrakakis, E. Õnate and B. Schreer (Eds), Barcelona, pp. 1–23.
Ahrem, R., Beckert, A., and Wendland, H., 2007, “Recovering Rotations in Aeroelasticity,” J. Fluid Struct., 23(6), pp. 874–884.
Matijašević, D., and Terze, Z., 2013, “An Approach for the Spatial Coupling of Multibody System Chain in a Partitioned Algorithm,” ECCOMAS Conference Proceedings on Multibody Dynamics 2013, pp. 883–892.
Malcolm, D., and Laird, D., 2007, “Extraction of Equivalent Beam Properties From Blade Models,” Wind Energy, 10(2), pp. 135–157.
Hardy, R. L., 1971, “Multiquadric Equations of Topography and Other Irregular Surfaces,” J. Geophys. Res., 176, pp. 1905–1915.
Ahrem, A., Beckert, A., and Wendland, H., 2005, “A New Multivariate Interpolation Method for Large-Scale Spatial Coupling Problems in Aeroelasticity,” IFADS Conference Proceedings 2005.
Narcowich, F. J., and Ward, J. D., 1994, “Generalized Hermite Interpolation Via Matrix-Valued Conditionally Positive Definite Functions,” Math. Comput., 63(208), pp. 661–687.
Wendland, H., 2010, Scattered Data Approximation, Cambridge University Press, Cambridge, UK.
Schaback, R., 1995, “Optimal Recovery in Translation-Invariant Spaces of Functions,” Ann. Numer. Math., 4(1–4), pp. 547–556.
Tobor, I., Reuter, P., and Schlick, C., 2003, “Efficient Reconstruction of Large Scattered Geometric Datasets Using the Partition of Unity and Radial Basis Functions,” LaBRI, Bordeaux, France, Technical Report No. 130103.
Resor, B., and Paquette, J., 2012, “A Numad Model of the SANDIA CX-100 Blade,” Sandia National Laboratories, Albuquerque, NM, Technical Report No. SAND2012-9273.
Sideroff, C., Carrigan, T., and Matus, R., 2011, “Hybrid Meshing for a Horizontal Axis Wind Turbine,”
Lombardi, M., Parolini, N., and Quarteroni, A., 2013, “Radial Basis Functions for Inter-Grid Interpolation and Mesh Motion in FSI Problems,” Appl. Mech. Eng., 256, pp. 117–131.
Boer, A. D., van Zuijlen, A., and Bijl, H., 2007, “Review of Coupling Methods for Non-Matching Meshes,” Comput. Methods Appl. Mech. Eng., 196(8), pp. 1515–1525.

## Figures

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.

Fig. 2

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

Fig. 5

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

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.

Fig. 3

FSI boundary of fluid domain mesh

Fig. 4

Fig. 6

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

Fig. 7

Error of reconstruction when using the PU method

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.

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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