Hostname: page-component-84b7d79bbc-tsvsl Total loading time: 0 Render date: 2024-07-29T13:17:11.273Z Has data issue: false hasContentIssue false
  • English
  • Français

Near-tip correction functions for the actuator line method to improve the predicted lift and drag distributions

Published online by Cambridge University Press:  29 July 2024

Francois Trigaux Open the ORCID record for Francois Trigaux [Opens in a new window] ,
Thierry Villeneuve Open the ORCID record for Thierry Villeneuve [Opens in a new window] ,
Guy Dumas Open the ORCID record for Guy Dumas [Opens in a new window]  and
Grégoire Winckelmans Open the ORCID record for Grégoire Winckelmans [Opens in a new window]
Francois Trigaux*
Affiliation:
Institute of Mechanics, Materials and Civil Engineering (iMMC), Université catholique de Louvain (UCLouvain), 1348 Louvain-la-Neuve, Belgium
Thierry Villeneuve
Affiliation:
CFD Laboratory LMFN, Département de Génie Mécanique, Université Laval, Québec, QC, G1V 0A6, Canada
Guy Dumas
Affiliation:
CFD Laboratory LMFN, Département de Génie Mécanique, Université Laval, Québec, QC, G1V 0A6, Canada
Grégoire Winckelmans
Affiliation:
Institute of Mechanics, Materials and Civil Engineering (iMMC), Université catholique de Louvain (UCLouvain), 1348 Louvain-la-Neuve, Belgium
*
†Email address for correspondence: francois.trigaux@uclouvain.be
Get access Rights & Permissions [Opens in a new window]

Abstract

The actuator line method (ALM) is a commonly used technique to simulate slender lifting and dragging bodies such as wings or blades. However, the accuracy of the method is significantly reduced near the tip. To quantify the loss of accuracy, translating wings with various aspect and taper ratios are simulated using several methods: wall-resolved Reynolds-averaged Navier–Stokes (RANS) simulations, an advanced ALM with two-dimensional (2-D) mollification of the force, a lifting line method, a mollified lifting line method and a vortex lattice method. Significant differences in the lift and drag distributions are found on the part of the wing where the distance to the tip is smaller than approximately 3 chords and are identified to arise from both the forces mollification and the uneven induced velocity along the chord. Correction functions acting on the lift coefficient and effective angle of attack near the wing tip are then derived for rectangular wings of various aspect ratios. They are then also applied to wings of various taper ratios using the ‘effective dimensionless distance to the tip’ as the main parameter. The application of the correction not only leads to a much improved lift distribution, but also to a more consistent drag distribution. The correction functions are also obtained for various mollification sizes, as well as for ALM with three-dimensional (3-D) mollification. These changes mostly impact the correction for the effective angle of attack. Finally, the correction is applied to simulations of the NREL Phase VI wind turbine, leading to an enhanced agreement with the experimental data.

JFM classification

Mathematical Foundations: Computational methods Vortex Flows: Vortex shedding
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 989 , 25 June 2024 , A1
Check for updates
Copyright
© The Author(s), 2024. Published by Cambridge University Press

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.)

References

Branlard, E., Dixon, K. & Gaunaa, M. 2013 Vortex methods to answer the need for improved understanding and modelling of tip-loss factors. IET Renew. Power Gener. 7 (4), 311–320.CrossRefGoogle Scholar
Breton, S.-P., Sumner, J., Sørensen, J.N., Hansen, K.S., Sarmast, S. & Ivanell, S. 2017 A survey of modelling methods for high-fidelity wind farm simulations using large eddy simulation. Phil. Trans. R. Soc. A: Math. Phys. Engng Sci. 375 (2091), 20160097.CrossRefGoogle ScholarPubMed
Bühler, M., Weihing, P., Klein, L., Lutz, T. & Krämer, E. 2018 Actuator line method simulations for the analysis of wind turbine wakes acting on helicopters. J. Phys.: Conf. Ser. 1037, 062004.Google Scholar
Caprace, D.-G., Chatelain, P. & Winckelmans, G. 2019 Lifting line with various mollifications: theory and application to an elliptical wing. AIAA J. 57 (1), 17–28.CrossRefGoogle Scholar
Chow, J.S. 1994 Turbulence Measurements in the Near-Field of a Wingtip Vortex. Stanford University.Google Scholar
Chow, J.S., Zilliac, G.G. & Bradshaw, P. 1997 Mean and turbulence measurements in the near field of a wingtip vortex. AIAA J. 35 (10), 1561–1567.CrossRefGoogle Scholar
Churchfield, M.J. & Blaisdell, G.A. 2013 Reynolds stress relaxation turbulence modeling applied to a wingtip vortex flow. AIAA J. 51 (11), 2643–2655.CrossRefGoogle Scholar
Churchfield, M.J., Schreck, S.J., Martinez, L.A., Meneveau, C. & Spalart, P.R. 2017 An advanced actuator line method for wind energy applications and beyond. AIAA Paper 2017-1998.CrossRefGoogle Scholar
Dag, K.O. & Sørensen, J.N. 2020 A new tip correction for actuator line computations. Wind Energy 23 (2), 148–160.CrossRefGoogle Scholar
Duponcheel, M., Bricteux, L., Manconi, M., Winckelmans, G. & Bartosiewicz, Y. 2014 Assessment of RANS and improved near-wall modeling for forced convection at low prandtl numbers based on LES up to $re_{\tau }=2000$. Intl J. Heat Mass Transfer 75, 470–482.CrossRefGoogle Scholar
Glauert, H. 1935 Airplane Propellers, pp. 169–360. Springer.CrossRefGoogle Scholar
Hand, M.M., Simms, D., Fingersh, L., Jager, D., Cotrell, J., Schreck, S. & Larwood, S. 2001 Unsteady aerodynamics experiment phase VI: wind tunnel test configurations and available data campaigns. Tech. Rep. National Renewable Energy Laboratory.CrossRefGoogle Scholar
Jeanmart, H. & Winckelmans, G. 2007 Investigation of eddy-viscosity models modified using discrete filters: A simplified ‘regularized variational multiscale model’ and an ‘enhanced field model’. Phys. Fluids 19 (5), 055110.Google Scholar
Jha, P.K., Churchfield, M.J., Moriarty, P.J. & Schmitz, S. 2014 Guidelines for volume force distributions within actuator line modeling of wind turbines on large-eddy simulation-type grids. Trans. ASME: J. Sol. Energy Engng 136 (3), 031003.Google Scholar
Jha, P.K. & Schmitz, S. 2018 Actuator curve embedding – an advanced actuator line model. J. Fluid Mech. 834, R2.CrossRefGoogle Scholar
Jonkman, J.M. 2003 Modeling of the uae wind turbine for refinement of FAST_AD. Tech. Rep. National Renewable Energy Laboratory (NREL).CrossRefGoogle Scholar
Katz, J. & Plotkin, A. 2001 Low-Speed Aerodynamics. Cambridge University Press.CrossRefGoogle Scholar
Kleine, V.G., Hanifi, A. & Henningson, D.S. 2023 a Non-iterative vortex-based smearing correction for the actuator line method. J. Fluid Mech. 961, A29.CrossRefGoogle Scholar
Kleine, V.G., Hanifi, A. & Henningson, D.S. 2023 b Simulating airplane aerodynamics with body forces: actuator line method for nonplanar wings. AIAA J. 61 (5), 2048–2059.CrossRefGoogle Scholar
Li, A., Gaunaa, M., Pirrung, G.R., Meyer Forsting, A. & Horcas, S.G. 2022 How should the lift and drag forces be calculated from 2-d airfoil data for dihedral or coned wind turbine blades? Wind Energy Sci. 7 (4), 1341–1365.CrossRefGoogle Scholar
Maniaci, D. & Schmitz, S. 2016 Extended glauert tip correction to include vortex rollup effects. J. Phys.: Conf. Ser. 753, 022051.Google Scholar
Martinez, L., Leonardi, S., Churchfield, M. & Moriarty, P. 2012 A comparison of actuator disk and actuator line wind turbine models and best practices for their use. AIAA Paper 2012-0900.CrossRefGoogle Scholar
Martínez-Tossas, L.A., Churchfield, M.J. & Meneveau, C. 2017 Optimal smoothing length scale for actuator line models of wind turbine blades based on gaussian body force distribution. Wind Energy 20 (6), 1083–1096.CrossRefGoogle Scholar
Martínez-Tossas, L.A. & Meneveau, C. 2019 Filtered lifting line theory and application to the actuator line model. J. Fluid Mech. 863, 269–292.CrossRefGoogle Scholar
Melani, P., Balduzzi, F. & Bianchini, A. 2022 Simulating tip effects in vertical-axis wind turbines with the actuator line method. J. Phys.: Conf. Ser. 2265 (3), 032028.Google Scholar
Melani, P.F., Balduzzi, F., Ferrara, G. & Bianchini, A. 2021 Tailoring the actuator line theory to the simulation of vertical-axis wind turbines. Energy Convers. Manage. 243, 114422.CrossRefGoogle Scholar
Mendoza, V., Bachant, P., Ferreira, C. & Goude, A. 2018 Near-wake flow simulation of a vertical axis turbine using an actuator line model. Wind Energy 22 (2), 171–188.CrossRefGoogle Scholar
Merabet, R. & Laurendeau, E. 2022 Hovering helicopter rotors modeling using the actuator line method. J. Aircraft 59 (3), 774–787.CrossRefGoogle Scholar
Meyer Forsting, A.R., Pirrung, G.R. & Ramos-García, N. 2019 A vortex-based tip/smearing correction for the actuator line. Wind Energy Sci. 4 (2), 369–383.CrossRefGoogle Scholar
Mikkelsen, R.F. 2004 Actuator disk methods applied to wind turbines. PhD thesis, Technical University of Denmark.Google Scholar
Moens, M., Duponcheel, M., Winckelmans, G. & Chatelain, P. 2018 An actuator disk method with tip-loss correction based on local effective upstream velocities. Wind Energy 21 (9), 766–782.CrossRefGoogle Scholar
Pirrung, G.R., Van der Laan, M.P., Ramos-García, N. & Meyer Forsting, A.R. 2020 A simple improvement of a tip loss model for actuator disc simulations. Wind Energy 23 (4), 1154–1163.CrossRefGoogle Scholar
Shamsoddin, S. & Porté-Agel, F. 2014 Large eddy simulation of vertical axis wind turbine wakes. Energies 7 (2), 890–912.CrossRefGoogle Scholar
Shen, W.Z., Mikkelsen, R., Sørensen, J.N. & Bak, C. 2005 a Tip loss corrections for wind turbine computations. Wind Energy 8 (4), 457–475.CrossRefGoogle Scholar
Shen, W.Z., Sørensen, J.N. & Mikkelsen, R. 2005 b Tip loss correction for actuator/Navier–Stokes computations. Trans. ASME: J. Sol. Energy Engng 127 (2), 209–213.Google Scholar
Shives, M. & Crawford, C. 2013 Mesh and load distribution requirements for actuator line CFD simulations. Wind Energy 16 (8), 1183–1196.CrossRefGoogle Scholar
Siemens 2019 STAR-CCM+ User Guide, version 14.02.012. Available at: https://mdx.plm.automation.siemens.com/star-ccm-plus.Google Scholar
Sørensen, J.N., Dag, K.O. & Ramos-García, N. 2016 A refined tip correction based on decambering. Wind Energy 19 (5), 787–802.CrossRefGoogle Scholar
Sorensen, J.N. & Shen, W.Z. 2002 Numerical modeling of wind turbine wakes. Trans. ASME J. Fluids Engng 124 (2), 393–399.CrossRefGoogle Scholar
Stanly, R., Martinez-Tossas, L.A., Frankel, S.H. & Delorme, Y. 2022 Large-eddy simulation of a wind turbine using a filtered actuator line model. J. Wind Engng Ind. Aerodyn. 222, 104868.CrossRefGoogle Scholar
Stokkermans, T.C., Van Arnhem, N., Sinnige, T. & Veldhuis, L.L. 2019 Validation and comparison of rans propeller modeling methods for tip-mounted applications. AIAA J. 57 (2), 566–580.CrossRefGoogle Scholar
Troldborg, N. 2008 Actuator line modelling of wind turbine wakes. PhD thesis, Technical University of Denmark.Google Scholar
Villeneuve, T., Boudreau, M. & Dumas, G. 2019 Lift enhancement and drag reduction of lifting blades through the use of end-plates and detached end-plates. J. Wind Engng Ind. Aerodyn. 184, 391–404.CrossRefGoogle Scholar
Villeneuve, T., Winckelmans, G. & Dumas, G. 2021 Increasing the efficiency of vertical-axis turbines through improved blade support structures. Renew. Energy 169, 1386–1401.CrossRefGoogle Scholar
Wimshurst, A. & Willden, R. 2017 Analysis of a tip correction factor for horizontal axis turbines. Wind Energy 20 (9), 1515–1528.CrossRefGoogle Scholar
Supplementary material: File

Trigaux et al. supplementary material 1

Trigaux et al. supplementary material
Download Trigaux et al. supplementary material 1(File)
File 15.8 KB