Full-scale, 3D, time-dependent aerodynamics modeling and simulation of a Darrieus-type vertical-axis wind turbine (VAWT) is presented. The simulations are performed using a moving-domain finite-element-based ALE-VMS technique augmented with a sliding-interface formulation to handle the rotor-stator interactions present. We simulate a single VAWT using a sequence of meshes with increased resolution to assess the computational requirements for this class of problems. The computational results are in good agreement with experimental data. We also perform a computation of two side-by-side counterrotating VAWTs to illustrate how the ALE-VMS technique may be used for the simulation of multiple turbines placed in arrays.
Issue Section:
Research Papers
References
1.
Hau
, E.
, 2006
, Wind Turbines: Fundamentals, Technologies, Application, Economics
, 2nd ed., Springer
, Berlin
.2.
Jonkman
, J.
, Butterfield
, S.
, Musial
, W.
, and Scott
, G.
, 2009
, “Definition of a 5-MW Reference Wind Turbine for Offshore System Development,” National Renewable Energy Laboratory, Golden, CO, Technical Report NREL/TP-500-38060.3.
Klimas
, P. C.
, 1982
, “Darrieus Rotor Aerodynamics
,” ASME J. Solar Energ. Eng.
, 104
, pp. 102
–105
.10.1115/1.32662804.
Dabiri
, J. O.
, 2011
, “Potential Order-of-Magnitude Enhancement of Wind Farm Power Density Via Counter-Rotating Vertical-Axis Wind Turbine Arrays
,” J. Renew. Sustain. Energ.
, 3
, p. 043104
.10.1063/1.36081705.
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. Meth. Eng.
, 19
, pp. 171
–225
.10.1007/s11831-012-9071-36.
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
.10.1142/S02182025123000257.
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. Num. Meth. Fluid.
, 65
, pp. 207
–235
.10.1002/fld.24008.
Hsu
, M.-C.
, Akkerman
, I.
, and Bazilevs
, Y.
, 2011
, “High-Performance Computing of Wind Turbine Aerodynamics Using Isogeometric Analysis
,” Comput. Fluid.
, 49
, pp. 93
–100
.10.1016/j.compfluid.2011.05.0029.
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
, (published online).10.1002/we.159910.
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
, pp. 499
–511
.10.1007/s00466-012-0686-x11.
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. Num. Meth.
, 65
, pp. 236
–253
.10.1002/fld.245412.
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. Meth. Appl. Mech. Eng.
, 249–252
, pp. 28
–41
.10.1016/j.cma.2012.03.02813.
Hsu
, M.-C.
, and Bazilevs
, Y.
, 2012
, “Fluid–Structure Interaction Modeling of Wind Turbines: Simulating the Full Machine
,” Comput. Mech.
, 50
, pp. 821
–833
.10.1007/s00466-012-0772-014.
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
, pp. 249
–272
.10.1142/S021820251340003415.
Bazilevs
, Y.
, and Hughes
, T. J. R.
, 2008
, “NURBS-Based Isogeometric Analysis for the Computation of Flows About Rotating Components
,” Comput. Mech.
, 43
, pp. 143
–150
.10.1007/s00466-008-0277-z16.
Bazilevs
, Y.
, and Hughes
, T. J. R.
, 2007
, “Weak Imposition of Dirichlet Boundary Conditions in Fluid Mechanics
,” Comput. Fluid.
, 36
, pp. 12
–26
.10.1016/j.compfluid.2005.07.01217.
Bazilevs
, Y.
, Michler
, C.
, Calo
, V. M.
, and Hughes
, T. J. R.
, 2007
, “Weak Dirichlet Boundary Conditions for Wall-Bounded Turbulent Flows
,” Comput. Meth. Appl. Mech. Eng.
, 196
, pp. 4853
–4862
.10.1016/j.cma.2007.06.02618.
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. Meth. Appl. Mech. Eng.
, 199
, pp. 780
–790
.10.1016/j.cma.2008.11.02019.
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. Meth. Appl. Mech. Eng.
, 213–216
, pp. 71
–83
.10.1016/j.cma.2011.11.00820.
Scheurich
, F.
, Fletcher
, T.
, and Brown
, R.
, 2011
, “Simulating the Aerodynamic Performance and Wake Dynamics of a Vertical-Axis Wind Turbine
,” Wind Energy
, 14
, pp. 159
–177
.10.1002/we.40921.
Scheurich
, F.
, and Brown
, R.
, 2013
, “Modelling the Aerodynamics of Vertical-Axis Wind Turbines in Unsteady Wind Conditions
,” Wind Energy
, 16
, pp. 91
–107
.10.1002/we.53222.
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
, pp. 349
–361
.10.1002/we.47223.
Bravo
, R.
, Tullis
, S.
, and Ziada
, S.
, 2007
, “Performance Testing of a Small Vertical-Axis Wind Turbine
,” Proceedings of the 21st Canadian Congress of Applied Mechanics
(CANCAM07), Toronto, Canada, June 3–7, pp. 470
–471
.24.
Hughes
, T. J. R.
, Liu
, W. K.
, and Zimmermann
, T. K.
, 1981
, “Lagrangian–Eulerian Finite Element Formulation for Incompressible Viscous Flows
,” Comput. Meth. Appl. Mech. Eng.
, 29
, pp. 329
–349
.10.1016/0045-7825(81)90049-925.
Bazilevs
, Y.
, Takizawa
, K.
, and Tezduyar
, T.
, 2013
, Computational Fluid–Structure Interaction: Methods and Applications
, Wiley
, Chichester
, UK.26.
Chung
, J.
, and Hulbert
, G. M.
, 1993
, “A Time Integration Algorithm for Structural Dynamics With Improved Numerical Dissipation: The Generalized-α Method
,” ASME J. Appl. Mech.
, 60
, pp. 371
–375
.10.1115/1.290080327.
Jansen
, K. E.
, Whiting
, C. H.
, and Hulbert
, G. M.
, 2000
, “A Generalized-α Method for Integrating the Filtered Navier–Stokes Equations With a Stabilized Finite Element Method
,” Comput. Meth. Appl. Mech. Eng.
, 190
, pp. 305
–319
.10.1016/S0045-7825(00)00203-628.
Bazilevs
, Y.
, Calo
, V. M.
, Hughes
, T. J. R.
, and Zhang
, Y.
, 2008
, “Isogeometric Fluid–Structure Interaction: Theory, Algorithms, and Computations
,” Comput. Mech.
, 43
, pp. 3
–37
.10.1007/s00466-008-0315-x29.
Tezduyar
, T. E.
, 1992
, “Stabilized Finite Element Formulations for Incompressible Flow Computations
,” Adv. Appl. Mech.
, 28
, pp. 1
–44
.10.1016/S0065-2156(08)70153-430.
Tezduyar
, T. E.
, Behr
, M.
, and Liou
, J.
, 1992
, “A New Strategy for Finite Element Computations Involving Moving Boundaries and Interfaces—The Deforming-Spatial-Domain/Space–Time Procedure: I. The Concept and the Preliminary Numerical Tests
,” Comput. Meth. Appl. Mech. Eng.
, 94
(3
), pp. 339
–351
.10.1016/0045-7825(92)90059-S31.
Tezduyar
, T. E.
, Behr
, M.
, Mittal
, S.
, and Liou
, J.
, 1992
, “A New Strategy for Finite Element Computations Involving Moving Boundaries and Interfaces—The Deforming-Spatial-Domain/Space–Time Procedure: II. Computation of Free-Surface Flows, Two-Liquid Flows, and Flows With Drifting Cylinders
,” Comput. Meth. Appl. Mech. Eng.
, 94
(3
), pp. 353
–371
.10.1016/0045-7825(92)90060-W32.
Tezduyar
, T. E.
, 2003
, “Computation of Moving Boundaries and Interfaces and Stabilization Parameters
,” Int. J. Num. Meth. Fluid.
, 43
, pp. 555
–575
.10.1002/fld.50533.
Tezduyar
, T. E.
, and Sathe
, S.
, 2007
, “Modeling of Fluid–Structure Interactions With the Space–Time Finite Elements: Solution Techniques
,” Int. J. Num. Meth. Fluid.
, 54
, pp. 855
–900
.10.1002/fld.143034.
Takizawa
, K.
, and Tezduyar
, T. E.
, 2011
, “Multiscale Space–Time Fluid–Structure Interaction Techniques
,” Comput. Mech.
, 48
, pp. 247
–267
.10.1007/s00466-011-0571-z35.
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
, pp. 333
–344
.10.1007/s00466-011-0589-236.
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
, pp. 647
–657
.10.1007/s00466-011-0614-537.
Takizawa
, K.
, and Tezduyar
, T. E.
, 2012
, “Space–Time Fluid–Structure Interaction Methods
,” Math. Models Methods Appl. Sci.
, 22
(Supp. 02
), p. 1230001
.10.1142/S021820251230001338.
Tezduyar
, T.
, Aliabadi
, S.
, Behr
, M.
, Johnson
, A.
, Kalro
, V.
, and Litke
, M.
, 1996
, “Flow Simulation and High Performance Computing
,” Comput. Mech.
, 18
, pp. 397
–412
.10.1007/BF0035024939.
Behr
, M.
, and Tezduyar
, T.
, 1999
, “The Shear-Slip Mesh Update Method
,” Comput. Meth. Appl. Mech. Eng.
, 174
, pp. 261
–274
.10.1016/S0045-7825(98)00299-040.
Behr
, M.
, and Tezduyar
, T.
, 2001
, “Shear-Slip Mesh Update in 3D Computation of Complex Flow Problems With Rotating Mechanical Components
,” Comput. Meth. Appl. Mech. Eng.
, 190
, pp. 3189
–3200
.10.1016/S0045-7825(00)00388-141.
Tezduyar
, T. E.
, 2001
, “Finite Element Methods for Flow Problems With Moving Boundaries and Interfaces
,” Arch. Comput. Meth. Eng.
, 8
, pp. 83
–130
.10.1007/BF0289787042.
Tezduyar
, T. E.
, 2007
, “Finite Elements in Fluids: Special Methods and Enhanced Solution Techniques
,” Comput. Fluid.
, 36
, pp. 207
–223
.10.1016/j.compfluid.2005.02.01043.
Karypis
, G.
, and Kumar
, V.
, 1999
, “A Fast and High Quality Multilevel Scheme for Partitioning Irregular Graphs
,” SIAM J. Sci. Comput.
, 20
, pp. 359
–392
.10.1137/S1064827595287997Copyright © 2014 by ASME
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