Hostname: page-component-669899f699-qzcqf Total loading time: 0 Render date: 2025-04-28T12:51:18.305Z Has data issue: false hasContentIssue false
  • English
  • Français

Numerical improvement to Glauert correction for the flow around a wind turbine

Published online by Cambridge University Press:  29 June 2023

J.B.V. Wanderley Open the ORCID record for J.B.V. Wanderley [Opens in a new window]  and
C. Levi Open the ORCID record for C. Levi [Opens in a new window]
J.B.V. Wanderley*
Affiliation:
COPPE/UFRJ, Rio de Janeiro, Brasil
C. Levi
Affiliation:
COPPE/UFRJ, Rio de Janeiro, Brasil
*
Corresponding author: J. B. V. Wanderley; Email: juanw@oceanica.ufrj.br
Get access Rights & Permissions [Opens in a new window]

Abstract

Accurate and reliable computation of the aerodynamic characteristics of wind turbines is very important for the development of new efficient designs. The flow around a wind turbine is modeled by a permeable disc (PD), solved through the Unsteady Reynolds-Averaged Navier–Stokes equations (URANS), here named PD/URANS method. The finite volume method and a total variation diminishing (TVD) scheme solve numerically the flow governing equations. The turbulent flow in the wake of the wind turbine is simulated utilising a one-equation turbulence model. The Glauert correction calculation considers a uniform normal force distribution (CT) on the virtual permeable disc applied to the flow, while the axial induction factor is obtained directly from the numerical solution of the URANS equations. The numerical axial induction factor obtained agrees fairly well with Glauert correction, except if the flow behind the turbine is highly unsteady and Reynolds number dependent.

Keywords

Wind turbineComputational fluid mechanicsFinite volumeTVD scheme
Type
Research Article
Information
The Aeronautical Journal , Volume 128 , Issue 1320 , February 2024 , pp. 230 - 244
Check for updates
Copyright
© The Author(s), 2023. Published by Cambridge University Press on behalf of Royal Aeronautical Society

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Article purchase

Temporarily unavailable

References

Zhong, W., Wang, G.T., Zhu, W.J. and Shen, W.Z. Evaluation of tip loss corrections to AD/NS simulations of wind turbine aerodynamic performance, Appl. Sci., November 2019, 9, (4919).Google Scholar
Roe, P.L. Generalized formulation of TVD Lax-Wendroff scheme, ICASE Report, pp 84–53, 1984.Google Scholar
Sweby, P.K. High resolution scheme using flux limiter for hyperbolic conservation law, SIAM J. Numer. Anal., 1984, 21, pp 995–1011.CrossRefGoogle Scholar
Spalart, P.R. and Allmaras, S.R.A. One-equation turbulence model for aerodynamic flows, Recherche Aerospatiale, 1994, 1, pp 5–21.Google Scholar
Glauert, H. Airplane propeller, in Durand, W.F. (ed.) Aerodynamic Theory, vol 4, Division L, Julius Springer, Berlin, pp 169–360, 1936.Google Scholar
Mikkelsen, R., Sorensen, J.N. and Shen, W.Z. Modeling and analysis of the flow field around a coned rotor, Wind Energy, 2001, 4, pp 121–135.CrossRefGoogle Scholar
Menter, F.R. Two-equation eddy viscosity turbulence model for engineering applications, AIAA J., 1994, 32, pp 1598–1605.CrossRefGoogle Scholar
Sharp, D.J. A general momentum theory applied to an energy-extracting actuator disc, Wind Energy, 2004, 7, pp 177–188.CrossRefGoogle Scholar
Moens, M., Duponcheel, M., Winckelmans, G. and Chatelain, P. An actuator disc method with tip-loss correction based on Local effective upstream velocities, Wind Energy, 2018, 21, pp 766–782.CrossRefGoogle Scholar
Simisiroglou, N., Polatidis, H. and Ivanell, S. Wind farm power production assessment: introduction of a new actuator disc method and comparison with existing models in the context of a case study, Appl. Sci., 2019, 9, (431).Google Scholar
Crasto, G. and Gravdahl, A.R. CFD wake modeling using a porous disc, Proceedings of the European Wind Energy Conference & Exhibition 2008, Brussels, Belgium, 31 March–3 April, 2008.Google Scholar
Simisiroglou, N., Sarmast, S., Breton, S.P. and Ivanell, S. Validation of the actuator disc approach in PHOENICS using small scale model wind turbines, J. Phys., 2016, 753, (032028).Google Scholar
Jensen, N.O.A. Note on Wind Generator Interaction, Technical University of Denmark, Kongens Lyngby, Denmark, 1983.Google Scholar
Larsen, G.C. A Simple Wake Calculation Procedure, Technical University of Denmark, Kongens Lyngby, Denmark, 1988.Google Scholar
Van Leer, B. Towards the ultimate conservative difference scheme, V: a second-order sequel to Godunov’s method, J. Computat. Phys., 1979, 32, pp 101–136.CrossRefGoogle Scholar
Boussinesq, J. Essai sur la théorie des eaux courantes, Memoirs of Presentes Academy of Science 23, 46, 1877.Google Scholar
Wilson, R.E. and Walker, S.N. Performance analysis of horizontal axis wind turbines, NASA Research Project NAG-3-278, Sept, 1984.Google Scholar
Favre, A. Equations des gaz turbulents compressibles: 1. Formes Générales, Journal of Mechanics, 1965, 4, pp 361–390.Google Scholar
Anderson, J.D. Fundamentals of Aerodynamics, Third Edition, McGraw-Hill, New York, USA, 2001.Google Scholar
Hansen, M.O.L. Aerodynamics of Wind Turbines, Second Edition, Earthscan, London, UK, 2008.Google Scholar