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Research Papers

Fluid–Structure Interaction Modeling of Vertical-Axis Wind Turbines

[+] Author and Article Information
Y. Bazilevs

Department of Structural Engineering,
University of California–San Diego,
La Jolla, CA 92093
e-mail: yuri@ucsd.edu

A. Korobenko, X. Deng, J. Yan

Department of Structural Engineering,
University of California–San Diego,
La Jolla, CA 92093

M. Kinzel, J. O. Dabiri

Department of Aerospace Engineering,
Division of Engineering and Applied Science,
California Institute of Technology,
Pasadena, CA 91125

Manuscript received March 25, 2014; final manuscript received April 14, 2014; accepted manuscript posted April 22, 2014; published online May 7, 2014. Assoc. Editor: Kenji Takizawa.

J. Appl. Mech 81(8), 081006 (May 07, 2014) (8 pages) Paper No: JAM-14-1135; doi: 10.1115/1.4027466 History: Received March 25, 2014; Revised April 14, 2014; Accepted April 22, 2014

Full-scale, 3D, time-dependent aerodynamics and fluid–structure interaction (FSI) simulations of a Darrieus-type vertical-axis wind turbine (VAWT) are presented. A structural model of the Windspire VAWT (Windspire energy, http://www.windspireenergy.com/) is developed, which makes use of the recently proposed rotation-free Kirchhoff–Love shell and beam/cable formulations. A moving-domain finite-element-based ALE-VMS (arbitrary Lagrangian–Eulerian-variational-multiscale) formulation is employed for the aerodynamics in combination with the sliding-interface formulation to handle the VAWT mechanical components in relative motion. The sliding-interface formulation is augmented to handle nonstationary cylindrical sliding interfaces, which are needed for the FSI modeling of VAWTs. The computational results presented show good agreement with the field-test data. Additionally, several scenarios are considered to investigate the transient VAWT response and the issues related to self-starting.

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References

“Windspire Vertical Wind Turbine,” 2014, Ark Alloy, LLC, Reedsburg, WI, http://www.windspireenergy.com/
Vita, L., Paulsen, U. S., and Pedersen, T. F., 2010, “A Novel Floating Offshore Wind Turbine Concept: New Developments,” European Wind Energy Conference & Exhibition (EWEC 2010), Warsaw, Poland, April 20–23.
Vita, L., Paulsen, U. S., Madsen, H. A., Nielsen, H. P., Berthelsen, P. A., and Cartsensen, S., 2012, “Design and Aero-Elastic Simulation of a 5 MW Floating Vertical Axis Wind Turbine,” ASME Paper No. OMAE2012-83470. [CrossRef]
Hau, E., 2006, Wind Turbines: Fundamentals, Technologies, Application, Economics, 2nd ed., Springer, Berlin.
Kirke, B., and Lazauskas, L., 1991, “Enhancing the Performance of a Vertical Axis Wind Turbine Using a Simple Variable Pitch System,” Wind Eng., 15(4), pp. 187–195.
Dominy, R., Lunt, P., Bickerdyke, A., and Dominy, J., 2007, “Self-Starting Capability of a Darrieus Turbine,” Proc. Inst. Mech. Eng., Part A, 221(1), pp. 111–120. [CrossRef]
Hill, N., Dominy, R., Ingram, G., and Dominy, J., 2009, “Darrieus Turbines: The Physics of Self-Starting,” Proc. Inst. Mech. Eng., Part A, 223(1), pp. 21–29. [CrossRef]
Baker, J. R., 1983, “Features to Aid or Enable Self Starting of Fixed Pitch Low Solidity Vertical Axis Wind Turbines,” J. Wind Eng. Ind. Aerodyn., 15(1–3), pp. 369–380. [CrossRef]
Bazilevs, Y., Hsu, M.-C., Akkerman, I., Wright, S., Takizawa, K., Henicke, B., Spielman, T., and Tezduyar, T. E., 2011, “3D Simulation of Wind Turbine Rotors at Full Scale. Part I: Geometry Modeling and Aerodynamics,” Int. J. Numer. Methods Fluids, 65(1–3), pp. 207–235. [CrossRef]
Bazilevs, Y., Hsu, M.-C., Kiendl, J., Wüchner, R., and Bletzinger, K.-U., 2011, “3D Simulation of Wind Turbine Rotors at Full Scale. Part II: Fluid–Structure Interaction Modeling With Composite Blades,” Int. J. Numer. Methods Fluids, 65(1–3), pp. 236–253. [CrossRef]
Chow, R., and van Dam, C. P., 2012, “Verification of Computational Simulations of the NREL 5 MW Rotor With a Focus on Inboard Flow Separation,” Wind Energy, 15(8), pp. 967–981. [CrossRef]
Bechmann, A., Sørensen, N. N., and Zahle, F., 2011, “CFD Simulations of the MEXICO Rotor,” Wind Energy, 14(5), pp. 677–689. [CrossRef]
Takizawa, K., Henicke, B., Tezduyar, T. E., Hsu, M.-C., and Bazilevs, Y., 2011, “Stabilized Space–Time Computation of Wind-Turbine Rotor Aerodynamics,” Comput. Mech., 48(3), pp. 333–344. [CrossRef]
Takizawa, K., Henicke, B., Montes, D., Tezduyar, T. E., Hsu, M.-C., and Bazilevs, Y., 2011, “Numerical-Performance Studies for the Stabilized Space–Time Computation of Wind-Turbine Rotor Aerodynamics,” Comput. Mech., 48(6), pp. 647–657. [CrossRef]
Sørensen, N. N., and Schreck, S., 2012, “Computation of the National Renewable Energy Laboratory Phase-VI Rotor in Pitch Motion During Standstill,” Wind Energy, 15(3), pp. 425–442. [CrossRef]
Hsu, M.-C., Akkerman, I., and Bazilevs, Y., 2013, “Finite Element Simulation of Wind Turbine Aerodynamics: Validation Study Using NREL Phase VI Experiment,” Wind Energy, 17(3), pp. 461–481. [CrossRef]
Takizawa, K., Tezduyar, T. E., McIntyre, S., Kostov, N., Kolesar, R., and Habluetzel, C., 2014, “Space–Time VMS Computation of Wind-Turbine Rotor and Tower Aerodynamics,” Comput. Mech., 53(1), pp. 1–15. [CrossRef]
Korobenko, A., Hsu, M., Akkerman, I., Tippmann, J., and Bazilevs, Y., 2013, “Structural Mechanics Modeling and FSI Simulation of Wind Turbines,” Math. Models Methods Appl. Sci., 23(2), pp. 249–272. [CrossRef]
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. [CrossRef]
Stein, P., Hsu, M.-C., Bazilevs, Y., and Beucke, K., 2012, “Operator- and Template-Based Modeling of Solid Geometry for Isogeometric Analysis With Application to Vertical Axis Wind Turbine Simulation,” Comput. Methods Appl. Mech. Eng., 213–216, pp. 71–83. [CrossRef]
Scheurich, F., Fletcher, T., and Brown, R., 2011, “Simulating the Aerodynamic Performance and Wake Dynamics of a Vertical-Axis Wind Turbine,” Wind Energy, 14(2), pp. 159–177. [CrossRef]
Scheurich, F., and Brown, R., 2012, “Modelling the Aerodynamics of Vertical-Axis Wind Turbines in Unsteady Wind Conditions”. Wind Energy., 16(1), pp. 91–107. [CrossRef]
McLaren, K., Tullis, S., and Ziada, S., 2012, “Computational Fluid Dynamics Simulation of the Aerodynamics of a High Solidity, Small-Scale Vertical Axis Wind Turbine,” Wind Energy, 15(3), pp. 349–361. [CrossRef]
Korobenko, A., Hsu, M.-C., Akkerman, I., and Bazilevs, Y., 2013, “Aerodynamic Simulation of Vertical-Axis Wind Turbines,” ASME J. Appl. Mech., 81(2), p. 021011. [CrossRef]
Huskey, A., Bowen, A., and Jager, D., 2009, “Wind Turbine Generator System Power Performance Test Report for the Mariah Windspire 1-kW Wind Turbine,” National Renewable Energy Laboratory, Golden, CO, Technical Report No. NREL/TP-500-46192.
Dabiri, J. O., 2011, “Potential Order-of-Magnitude Enhancement of Wind Farm Power Density Via Counter-Rotating Vertical-Axis Wind Turbine Arrays,” J. Renewable Sustainable Energy, 3(4), p. 043104. [CrossRef]
“Biological Propulsion Laboratory at CALTECH (Wind Energy Research),” 2012, California Institute of Technology, Pasadena, CA, http://dabiri.caltech.edu/research/wind-energy.html
Bazilevs, Y., Hsu, M.-C., and Scott, M. A., 2012, “Isogeometric Fluid–Structure Interaction Analysis With Emphasis on Non-Matching Discretizations, and With Application to Wind Turbines,” Comput. Methods Appl. Mech. Eng., 249–252, pp. 28–41. [CrossRef]
Hughes, T. J. R., Liu, W. K., and Zimmermann, T. K., 1981, “Lagrangian–Eulerian Finite Element Formulation for Incompressible Viscous Flows,” Comput. Methods Appl. Mech. Eng., 29(3), pp. 329–349. [CrossRef]
Belytschko, T., Liu, W. K., and Moran, B., 2000, Nonlinear Finite Elements for Continua and Structures, Wiley, New York.
Bazilevs, Y., Takizawa, K., and Tezduyar, T. E., 2013, Computational Fluid–Structure Interaction: Methods and Applications, Wiley, New York.
Takizawa, K., Bazilevs, Y., and Tezduyar, T. E., 2012, “Space–Time and ALE-VMS Techniques for Patient-Specific Cardiovascular Fluid–Structure Interaction Modeling,” Arch. Comput. Methods Eng., 19(2), pp. 171–225. [CrossRef]
Bazilevs, Y., Hsu, M.-C., Takizawa, K., and Tezduyar, T. E., 2012, “ALE-VMS and ST-VMS Methods for Computer Modeling of Wind-Turbine Rotor Aerodynamics and Fluid–Structure Interaction,” Math. Models Methods Appl. Sci., 22(Supp 02), p. 1230002. [CrossRef]
Bazilevs, Y., and Hughes, T. J. R., 2007, “Weak Imposition of Dirichlet Boundary Conditions in Fluid Mechanics,” Comput. Fluids, 36(1), pp. 12–26. [CrossRef]
Bazilevs, Y., Michler, C., Calo, V. M., and Hughes, T. J. R., 2007, “Weak Dirichlet Boundary Conditions for Wall-Bounded Turbulent Flows,” Comput. Methods Appl. Mech. Eng., 196(49–52), pp. 4853–4862. [CrossRef]
Bazilevs, Y., Michler, C., Calo, V. M., and Hughes, T. J. R., 2010, “Isogeometric Variational Multiscale Modeling of Wall-Bounded Turbulent Flows With Weakly Enforced Boundary Conditions on Unstretched Meshes,” Comput. Methods Appl. Mech. Eng., 199(13–16), pp. 780–790. [CrossRef]
Hsu, M.-C., Akkerman, I., and Bazilevs, Y., 2011, “High-Performance Computing of Wind Turbine Aerodynamics Using Isogeometric Analysis,” Comput. Fluids, 49(1), pp. 93–100. [CrossRef]
Hsu, M.-C., Akkerman, I., and Bazilevs, Y., 2012, “Wind Turbine Aerodynamics Using ALE–VMS: Validation and the Role of Weakly Enforced Boundary Conditions,” Comput. Mech., 50(4), pp. 499–511. [CrossRef]
Kiendl, J., Bletzinger, K.-U., Linhard, J., and Wüchner, R., 2009, “Isogeometric Shell Analysis With Kirchhoff–Love Elements,” Comput. Methods Appl. Mech. Eng., 198(49–52), pp. 3902–3914. [CrossRef]
Raknes, S., Deng, X., Bazilevs, Y., Benson, D., Mathisen, K., and Kvamsdal, T., 2013, “Isogeometric Rotation-Free Bending-Stabilized Cables: Statics, Dynamics, Bending Strips and Coupling With Shells,” Comput. Methods Appl. Mech. Eng., 263, pp. 127–143. [CrossRef]
Hughes, T. J. R., Cottrell, J. A., and Bazilevs, Y., 2005, “Isogeometric Analysis: CAD, Finite Elements, NURBS, Exact Geometry, and Mesh Refinement,” Comput. Methods Appl. Mech. Eng., 194(39–41), pp. 4135–4195. [CrossRef]
Cottrell, J. A., Hughes, T. J. R., and Bazilevs, Y., 2009, Isogeometric Analysis: Toward Integration of CAD and FEA, Wiley, Chichester, UK.
Tezduyar, T. E., and Sathe, S., 2007, “Modeling of Fluid–Structure Interactions With the Space–Time Finite Elements: Solution Techniques,” Int. J. Numer. Methods Fluids, 54(6–8), pp. 855–900. [CrossRef]
Tezduyar, T. E., Sathe, S., Pausewang, J., Schwaab, M., Christopher, J., and Crabtree, J., 2008, “Interface Projection Techniques for Fluid–Structure Interaction Modeling With Moving-Mesh Methods,” Comput. Mech., 43(1), pp. 39–49. [CrossRef]
Tezduyar, T. E., Schwaab, M., and Sathe, S., 2009, “Sequentially-Coupled Arterial Fluid–Structure Interaction (SCAFSI) Technique,” Comput. Methods Appl. Mech. Eng., 198(45–46), pp. 3524–3533. [CrossRef]
Takizawa, K., Christopher, J., Tezduyar, T. E., and Sathe, S., 2010, “Space–Time Finite Element Computation of Arterial Fluid–Structure Interactions With Patient-Specific Data,” Int. J. Numerical Methods Biomed. Eng., 26(1), pp. 101–116. [CrossRef]
Tezduyar, T. E., Takizawa, K., Moorman, C., Wright, S., and Christopher, J., 2010, “Multiscale Sequentially-Coupled Arterial FSI Technique,” Comput. Mech., 46(1), pp. 17–29. [CrossRef]
Tezduyar, T. E., Takizawa, K., Moorman, C., Wright, S., and Christopher, J., 2010, “Space–Time Finite Element Computation of Complex Fluid–Structure Interactions,” Int. J. Numer. Methods Fluids, 64(10–12), pp. 1201–1218. [CrossRef]
Takizawa, K., Moorman, C., Wright, S., Purdue, J., McPhail, T., Chen, P. R., Warren, J., and Tezduyar, T. E., 2011, “Patient-Specific Arterial Fluid–Structure Interaction Modeling of Cerebral Aneurysms,” Int. J. Numer. Methods Fluids, 65(1–3), pp. 308–323. [CrossRef]
Takizawa, K., and Tezduyar, T. E., 2011, “Multiscale Space–Time Fluid–Structure Interaction Techniques,” Comput. Mech., 48(3), pp. 247–267. [CrossRef]
Tezduyar, T. E., Takizawa, K., Brummer, T., and Chen, P. R., 2011, “Space–Time Fluid–Structure Interaction Modeling of Patient-Specific Cerebral Aneurysms,” Int. J. Numer. Methods Biomed. Eng., 27(11), pp. 1665–1710. [CrossRef]
Takizawa, K., and Tezduyar, T. E., 2012, “Space–Time Fluid–Structure Interaction Methods,” Math. Models Methods Appl. Sci., 22(Supp 02), p. 1230001. [CrossRef]
Bazilevs, Y., and Hughes, T. J. R., 2008, “NURBS-Based Isogeometric Analysis for the Computation of Flows About Rotating Components,” Comput. Mech., 43(1), pp. 143–150. [CrossRef]
Tezduyar, T., Aliabadi, S., Behr, M., Johnson, A., Kalro, V., and Litke, M., 1996, “Flow Simulation and High Performance Computing,” Comput. Mech., 18(6), pp. 397–412. [CrossRef]
Behr, M., and Tezduyar, T., 1999, “The Shear-Slip Mesh Update Method,” Comput. Methods Appl. Mech. Eng., 174(3–4), pp. 261–274. [CrossRef]
Behr, M., and Tezduyar, T., 2001, “Shear-Slip Mesh Update in 3D Computation of Complex Flow Problems With Rotating Mechanical Components,” Comput. Methods Appl. Mech. Eng., 190(24–25), pp. 3189–3200. [CrossRef]
Tezduyar, T. E., 2001, “Finite Element Methods for Flow Problems With Moving Boundaries and Interfaces,” Arch. Comput. Methods Eng., 8(2), pp. 83–130. [CrossRef]
Tezduyar, T. E., 2007, “Finite Elements in Fluids: Special Methods and Enhanced Solution Techniques,” Comput. Fluids, 36(2), pp. 207–223. [CrossRef]
Takizawa, K., Tezduyar, T. E., and Kostov, N., 2014, “Sequentially-Coupled Space-Time FSI Analysis of Bio-Inspired Flapping-Wing Aerodynamics of an MAV,” Comput. Mech., February (published online). [CrossRef]
Takizawa, K., 2014, “Computational Engineering Analysis With the New-Generation Space-Time Methods,” Comput. Mech., March (published online). [CrossRef]
Takizawa, K., Tezduyar, T. E., Buscher, A., and Asada, S., 2014, “Space-Time Interface-Tracking With Topology Change (ST-TC),” Comput. Mech., October (published online). [CrossRef]
Takizawa, K., and Tezduyar, T. E., 2014, “Space–Time Computation Techniques With Continuous Representation in Time (ST-C),” Comput. Mech., 53(1), pp. 91–99. [CrossRef]
Takizawa, K., Tezduyar, T. E., Boben, J., Kostov, N., Boswell, C., and Buscher, A., 2013, “Fluid–Structure Interaction Modeling of Clusters of Spacecraft Parachutes With Modified Geometric Porosity,” Comput. Mech., 52(6), pp. 1351–1364. [CrossRef]
Tezduyar, T. E., Behr, M., Mittal, S., and Johnson, A. A., 1992, “Computation of Unsteady Incompressible Flows With the Finite Element Methods—Space–Time Formulations, Iterative Strategies and Massively Parallel Implementations,” New Methods in Transient Analysis, PVP-Vol. 246/AMD-Vol. 143, ASME, pp. 7–24.
Tezduyar, T., Aliabadi, S., Behr, M., Johnson, A., and Mittal, S., 1993, “Parallel Finite-Element Computation of 3D Flows,” Computer, 26(10), pp. 27–36. [CrossRef]
Johnson, A. A., and Tezduyar, T. E., 1994, “Mesh Update Strategies in Parallel Finite Element Computations of Flow Problems With Moving Boundaries and Interfaces,” Comput. Methods Appl. Mech. Eng., 119(1–2), pp. 73–94. [CrossRef]
Stein, K., Tezduyar, T., and Benney, R., 2003, “Mesh Moving Techniques for Fluid–Structure Interactions With Large Displacements,” ASME J. Appl. Mech., 70(1), pp. 58–63. [CrossRef]
Karypis, G., and Kumar, V., 1999, “A Fast and High Quality Multilevel Scheme for Partitioning Irregular Graphs,” SIAM J. Sci. Comput., 20(1), pp. 359–392. [CrossRef]
Bazilevs, Y., Hsu, M. C., and Bement, M. T., 2013, “Adjoint-Based Control of Fluid–Structure Interaction for Computational Steering Applications,” Proc. Comput. Sci., 18, pp. 1989–1998. [CrossRef]
Texas Advanced Computing Center (TACC) 2013, University of Texas, Austin, TX, http://www.tacc.utexas.edu

Figures

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Fig. 1

Windspire VAWT structural model with dimensions included: (a) full model using isogeometric NURBS-based rotation-free shells and beams; (b) model cross section 1 showing attachment of the struts to the blades and tower shell; (c) model cross section 2 showing attachment of the struts and tower shell

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Fig. 2

The VAWT aerodynamics computational domain in the reference configuration, including the inner cylindrical region, outer region, and sliding interface that is now allowed to move in space as a rigid object

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Fig. 3

A 2D cross section of the computational mesh along the rotor axis. The view is from the top of the turbine, and the blades are numbered counterclockwise, which is the expected direction of rotation. The sliding interface may be seen along a circular curve where the mesh appears to be nonconforming.

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Fig. 4

A 2D cross section of the blade boundary-layer mesh consisting of triangular prisms

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Fig. 5

Time history of the aerodynamic torque for the pure aerodynamics simulations. (a) 8.0 m/s wind with experimental data from Ref. [25] and (b) 6.0 m/s wind with experimental data from Refs. [26,27].

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Fig. 6

Time history of the rotor speed starting from 0 rad/s

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Fig. 7

Time history of the rotor speed starting from 4 rad/s

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Fig. 8

Time history of the rotor speed starting from 12 rad/s

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Fig. 9

Vorticity isosurfaces at a time instant colored by velocity magnitude for the 4 rad/s case

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Fig. 10

Vorticity isosurfaces of vorticity colored by velocity magnitude for the 4 rad/s case. Zoom on the rotor. From left to right: vorticity at 1.12 s, 1.24 s, 1.40 s, and 1.50 s.

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Fig. 11

Turbine current configuration at two time instances for the 4 rad/s case. The tower centerline in the reference configuration is shown using the dashed line to illustrate the range of turbine motion during the cycle. The range of the tower tip displacement during the cycle is about 0.10–0.12 m.

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