This paper presents the numerical models underlying the implementation of a novel harmonic balance compressible Navier-Stokes solver with low-speed preconditioning for wind turbine unsteady aerodynamics. The numerical integration of the harmonic balance equations is based on a multigrid iteration, and, for the first time, a numerical instability associated with the use of such an explicit approach in this context is discussed and resolved. The harmonic balance solver with low-speed preconditioning is well suited for the analyses of several unsteady periodic low-speed flows, such as those encountered in horizontal axis wind turbines. The computational performance and the accuracy of the technology being developed are assessed by computing the flow field past two sections of a wind turbine blade in yawed wind with both the time-and frequency-domain solvers. Results highlight that the harmonic balance solver can compute these periodic flows more than 10 times faster than its time-domain counterpart, and with an accuracy comparable to that of the time-domain solver.
Issue Section:
Research Papers
References
1.
Hansen
, M.
, Sorensen
, J.
, Voutsinas
, S.
, Sorensen
, N.
, and Madsen
, H.
, 2006, “State of the Art in Wind Turbine Aerodynamics and Aeroelasticity
,” Prog. Aerosp. Sci.
, 42
, pp. 285
–330
.2.
Gomez-Iradi
, S.
, Steijl
, R.
, and Barakos
, G.
, 2009, “Development and Validation of a CFD Technique for the Aerodynamic Analysis of HAWT
,” J. Sol. Energy Eng.
, 31
(8
), p. 031009
.3.
Le Pape
, A.
, and Gleize
, V.
, 2006, “Improved Navier-Stokes Computations of a Stall-regulated Wind Turbine Using Low Mach Number Preconditioning
,” Proceedings of the 44th AIAA Aerospace Sciences Meeting and Exhibit
, Reno, NV, AIAA Paper No. 2006-1502.4.
Sorensen
, N.
, Michelsen
, J.
, and Schreck
, S.
, 2002, “Navier-Stokes Predictions of the NREL Phase VI Rotor in the NASA Aimes 80 ft × 120 ft Wind Tunnel
,” Wind Energy
, 5
, pp. 151
–169
.5.
Madsen
, H.
, Sorensen
, N.
, and Schreck
, S.
, 2003, “Yaw Aerodynamics Analyzed with Three Codes In Comparison with Experiment
,” Proceedings of the 41st AIAA Aerospace Sciences Meeting and Exhibit
, Reno, NV, AIAA Paper No. 2003–0519.6.
Hall
, K.
, Thomas
, J.
, and Clark
, W.
, 2002, “Computations of Unsteady Nonlinear Flows in Cascades Using a Harmonic Balance Technique
,” AIAA J.
, 40
(5
), pp. 879
–886
.7.
Su
, X.
, and Yuan
, X.
, 2010, “Implicit Solution of Time-Spectral Method for Periodic Unsteady Flows
,” Int. J. Numer. Methods Fluids
, 63
(7
), pp. 860
–876
.8.
van der Weide
, E.
, Gopinath
, A.
, and Jameson
, A.
, 2005, “Turbomachinery Applications With the Time Spectral Method
,” Proceedings of the 17th AIAA Computational Fluid Dynamics Conference
, Toronto, Ontario, Canada, AIAA Paper No. 2005-4905.9.
Da Ronch
, A.
, Choreyshi
, M.
, Badcock
, K.
, Goertz
, S.
, Widhalm
, M.
, Dwight
, R.
, and Campobasso
, M.
, 2010, “Linear Frequency Domain and Harmonic Balance Predictions of Dynamic Derivatives
,” Proceedings of the 28th AIAA Applied Aerodynamics Conference
, Chicago, IL, AIAA Paper No. 2010-4699.10.
Sicot
, F.
, Puigt
, G.
, and Montagnac
, M.
, 2008, “Block-Jacobi Implicit Algorithms for the Time Spectral Method
,” AIAA J.
, 46
(12
), pp. 3080
–3089
.11.
Woodgate
, M. A.
, and Badcock
, K. J.
, 2009, “Implicit Harmonic Balance Solver for Transonic Flows With Forced Motions
,” AIAA J.
, 47
(4
), pp. 893
–901
.12.
McMullen
, M.
, and Jameson
, A.
, 2006, “The Computational Efficiency of Non-Linear Frequency Domain Methods
,” J., Comput. Phys.
, 212
(2
), pp. 637
–661
.13.
McMullen
, M.
, Jameson
, A.
, and Alonso
, J.
, 2002, “Application of a Non-linear Frequency-domain Solver to the Euler and Navier-Stokes Equations
,” Proceedings of the 40th AIAA Aerospace Sciences Meeting and Exhibit
, Reno, NV, AIAA Paper No. 2002-0120.14.
McMullen
, M.
, Jameson
, A.
, and Alonso
, J.
, 2001, “Acceleration of Convergence to a Periodic Steady State in Turbomachinery Flows
,” Proceedings of the 39th AIAA Aerospace Sciences Meeting and Exhibit
, Reno, NV, AIAA Paper No. 2001-0152.15.
Kumar
, M.
, and Murthy
, V.
, 2006, “Rotor Blade Response Based on CFD in the Frequency Domain
,” Proceedings of the 44th AIAA Aerospace Sciences Meeting and Exhibit
, Reno, NV, AIAA Paper No. 2006-438.16.
He
, L.
, 2008, “Harmonic Solution of Unsteady Flow around Blades With Separation
,” AIAA J.
, 46
(6
), pp. 1299
–1307
.17.
Venkateswaran
, S.
, and Merkle
, C.
, 1999, “Analysis of Preconditioning Methods for the Euler and Navier-Stokes Equations
,” 30th VKI Lecture Series on Computational Fluid Dynamics
, von Karman Institute for Fluid Dynamics, Sint-Genesius-Rode
, Belgium
.18.
Campobasso
, M.
, Bonfiglioli
, A.
, and Baba-Ahmadi
, M.
, 2009, “Development of Efficient and Accurate CFD Technologies for Wind Turbine Unsteady Aerodynamics
,” Proceedings of the Conference on Modeling Fluid Flow
, J.
Vad
, ed., 14th Event of International Conference Series on Fluid Flow Technologies held in Budapest,
Department of Fluid Mechanics, Budapest University of Technology and Economics
, Vol. 2
, pp. 879
–886
.19.
Liu
, L.
, Thomas
, J.
, Dowell
, E.
, Attar
, P.
, and Hall
, K.
, 2006, “A Comparison of Classical and High Dimensional Harmonic Balance Approaches for a Duffing Oscillator
,” J. Comput.Phys.
, 215
(1
), pp. 298
–320
.20.
Campobasso
, M.
, and Baba-Ahmadi
, M.
, 2011, “Ad-Hoc Boundary Conditions for CFD Analyses of Turbomachinery Problems With Strong Flow Gradients at Farfield Boundaries
,” ASME Journal of Turbomachinery
, 133
(4
).21.
Jackson
, A.
, Campobasso
, M.
, and Baba-Ahmadi
, M.
, 2011, “On the Parallelization of a Harmonic Balance Compressible Navier-Stokes Solver for Wind Turbine Aerodynamics
,” ASME Paper No. GT2011-45306.22.
Jameson
, A.
, 1991, “Time Dependent Calculations Using Multigrid, With Application to Unsteady Flows Past airfoils and Wings
,” Proceedings of the 10th Computational Fluid Dynamics Conference
, Honolulu, HI, AIAA Paper No. 91–1596.23.
Arnone
, A.
, Liou
, M.-S.
, and Povinelli
, L.
, 1993, “Multigrid Time-Accurate Integration of Navier-Stokes Equations
,” Technical Memorandum No. NASA TM 106373, ICOMP-93-37, Lewis Research Center, Cleveland, OH.24.
Melson
, N.
, Sanetrik
, D.
, and Atkins
, H.
, 1993, “Time-Accurate Navier-Stokes Calculations With Multigrid Acceleration
,” Proceedings of the 6th Copper Mountain Conference on Multigrid Methods
, pp. II423
-II437
.25.
Briggs
, W.
, Henson
, V.
, and McCormick
, S.
, 2000, A Multigrid Tutorial
, 2nd ed., SIAM
, Philadelphia, PA
.26.
Threfethen
, L.
, and Embree
, M.
, 2005, Spectra and Pseudospactra
, Princeton University Press
, Princeton, NJ
.27.
Thomas
, J.
, Duster
, C.
, Dowell
, E.
, and Hall
, K.
, 2009, “Unsteady Flow Computation Using a Harmonic Balance Approach Implemented About the OVERFLOW 2 Flow Solver
,” Proceedings of the 19th AIAA Computational Fluid Dynamics Conference
, San Antonio, TX, AIAA Paper No. 2009-4270.28.
Weiss
, J.
, Maruszewski
, J.
, and Smith
, W.
, 1999, “Implicit Solution of Preconditioned Navier-Stokes Equations Using Algebraic Multigrid
,” AIAA J.
, 37
(1
), pp. 29
–36
.29.
Darmofal
, D.
, and Siu
, K.
, 1999, “A Robust Multigrid Algorithm for the Euler Equations With Local Preconditioning and Semi-Coarsening
,” J. Comput. Phys.
, 151
, pp. 728
–756
.30.
Buelow
, P.
, 1995, “Convergence Enhancement of Euler and Navier-Stokes Algorithms
,” Ph.D. thesis, Pennsylvania State University, PA.31.
Pandya
, S.
, Venkateswaran
, S.
, and Pulliam
, T.
, 2003, “Implementation of Dual-Time Procedures in Overflow
,” Proceedings of the 41st AIAA Aerospace Sciences Meeting and Exhibit
, Reno, NV, AIAA Paper No. 2003-0072.32.
Bonfiglioli
, A.
, Campobasso
, M.
, and Carpentieri
, B.
, 2009, “Parallel Unstructured Three-dimensional Turbulent Flow Analyses Using Efficiently Preconditioned Newton-Krylov Solver
,” Proceedings of the 19th AIAA Computational Fluid Dynamics Conference
, San Antonio, TX, AIAA Paper No. 2009-4137.33.
Theodorsen
, T.
, 1935, “General Theory of Aerodynamic Instability and the Mechanism of Flutter
,” Tech Report No. NACA Report 496.34.
Le Pape
, A.
, and Lecanu
, J.
, 2004, “3D Navier-Stokes Computations of a Stall-Regulated Wind Turbine
,” Wind Energy
, 7
, pp. 309
–324
.Copyright © 2012
by American Society of Mechanical Engineers
You do not currently have access to this content.
