Hostname: page-component-586b7cd67f-t8hqh Total loading time: 0 Render date: 2024-11-28T04:17:38.807Z Has data issue: false hasContentIssue false
  • English
  • Français

On the relationship between turbine thrust and near-wake velocity and vorticity

Published online by Cambridge University Press:  29 September 2022

Eric J. Limacher Open the ORCID record for Eric J. Limacher [Opens in a new window] ,
Liuyang Ding Open the ORCID record for Liuyang Ding [Opens in a new window] ,
Alexander Piqué Open the ORCID record for Alexander Piqué [Opens in a new window] ,
Alexander J. Smits Open the ORCID record for Alexander J. Smits [Opens in a new window]  and
Marcus Hultmark
Eric J. Limacher*
Affiliation:
Department of Mechanical and Aerospace Engineering, Princeton University, Princeton, NJ 08544, USA
Liuyang Ding
Affiliation:
Department of Mechanical and Aerospace Engineering, Princeton University, Princeton, NJ 08544, USA
Alexander Piqué
Affiliation:
Department of Mechanical and Aerospace Engineering, Princeton University, Princeton, NJ 08544, USA
Alexander J. Smits
Affiliation:
Department of Mechanical and Aerospace Engineering, Princeton University, Princeton, NJ 08544, USA
Marcus Hultmark
Affiliation:
Department of Mechanical and Aerospace Engineering, Princeton University, Princeton, NJ 08544, USA
*
†Email address for correspondence: [email protected]
Get access Rights & Permissions [Opens in a new window]

Abstract

Vortical impulse theory is used to investigate the relationship between turbine thrust and the near-wake velocity and vorticity fields. Three different hypotheses regarding the near-wake structure allow the derivation of novel expressions for the thrust on a steadily rotating wind turbine, and these are tested using stereoscopic particle-image velocimetry (PIV) data acquired just behind a rotor in a water channel. When one assumes that vortex lines and streamlines are aligned in a rotor-fixed frame of reference, one obtains a PIV-based thrust estimate that fails even to capture the trend of the directly measured thrust, and this failure is attributed to an implicit assumption that most of the generated thrust does useful work. When one neglects the axial gradients of radial velocity, the PIV-based thrust estimate captures the measured thrust trend, but underpredicts its magnitude by approximately $33\,\%$. The third and most promising physical proposition treats the trailing vortices as purely ‘rolling’ structures that exhibit zero-strain rate in their cores, with the corresponding thrust estimates in close agreement with direct thrust measurements. This best-performing expression appears as a correction to the classical thrust expression from momentum theory, possessing additional squared-velocity terms that can account for the high-thrust regime of turbine operation that is typically addressed empirically.

JFM classification

Wakes/Jets: Wakes
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 949 , 25 October 2022 , A24
Check for updates
Copyright
© The Author(s), 2022. 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

REFERENCES

Bastankhah, M. & Porté-Agel, F. 2016 Experimental and theoretical study of wind turbine wakes in yawed conditions. J. Fluid Mech. 806, 506–541.CrossRefGoogle Scholar
Bontempo, R. & Manna, M. 2017 Highly accurate error estimate of the momentum theory as applied to wind turbines. Wind Energy 20 (8), 1405–1419.CrossRefGoogle Scholar
Buhl, M.L. Jr. 2005 New empirical relationship between thrust coefficient and induction factor for the turbulent windmill state. Tech. Rep. NREL/TP-500-36834. National Renewable Energy Lab. (NREL), Golden, CO, USA.CrossRefGoogle Scholar
Ebert, P.R. & Wood, D.H. 1997 The near wake of a model horizontal-axis wind turbine–I. Experimental arrangements and initial results. Renew. Energy 12 (3), 225–243.CrossRefGoogle Scholar
Gharali, K. & Johnson, D.A. 2014 PIV-based load investigation in dynamic stall for different reduced frequencies. Exp. Fluids 55 (8), 1803.CrossRefGoogle Scholar
Krogstad, P.-Å. & Adaramola, M.S. 2011 Performance and near wake measurements of a model horizontal axis wind turbine. Wind Energy 15 (5), 743–756.CrossRefGoogle Scholar
Krogstad, P.-Å. & Eriksen, P.E. 2013 “Blind test” calculations of the performance and wake development for a model wind turbine. Renew. Energy 50, 325–333.CrossRefGoogle Scholar
Kurtulus, D.F., Scarano, F. & David, L. 2007 Unsteady aerodynamic forces estimation on a square cylinder by TR-PIV. Exp. Fluids 42 (2), 185–196.CrossRefGoogle Scholar
Limacher, E., McClure, J., Yarusevych, S. & Morton, C. 2020 Comparison of momentum and impulse formulations for PIV-based force estimation. Meas. Sci. Technol. 31 (5), 054001.CrossRefGoogle Scholar
Limacher, E., Morton, C. & Wood, D. 2019 On the calculation of force from PIV data using the generalized added-mass and circulatory force decomposition. Exp. Fluids 60, 4.CrossRefGoogle Scholar
Limacher, E.J. & Wood, D.H. 2021 An impulse-based derivation of the Kutta–Joukowsky equation for wind turbine thrust. Wind Energy Sci. 6, 191–201.CrossRefGoogle Scholar
Lust, E.E., Flack, K.A. & Luznik, L. 2018 Survey of the near wake of an axial-flow hydrokinetic turbine in quiescent conditions. Renew. Energy 129, 92–101.CrossRefGoogle Scholar
Massouh, F. & Dobrev, I. 2007 Exploration of the vortex wake behind of wind turbine rotor. In Journal of Physics: Conference Series, vol. 75, p. 012036. IOP.CrossRefGoogle Scholar
McClure, J. & Yarusevych, S. 2019 Planar momentum balance in three-dimensional flows: applications to load estimation. Exp. Fluids 60 (3), 41.CrossRefGoogle Scholar
McCutchen, C.W. 1985 A theorem on swirl loss in propeller wakes. J. Aircraft 22, 344–346.CrossRefGoogle Scholar
McTavish, S., Feszty, D. & Nitzsche, F. 2014 An experimental and computational assessment of blockage effects on wind turbine wake development. Wind Energy 17 (10), 1515–1529.CrossRefGoogle Scholar
Meinhart, C.D., Wereley, S.T. & Santiago, J.G. 2000 A PIV algorithm for estimating time-averaged velocity fields. Trans. ASME J. Fluids Engng 122 (2), 285–289.CrossRefGoogle Scholar
Moffat, R.J. 1988 Describing the uncertainties in experimental results. Exp. Therm. Fluid Sci. 1 (1), 3–17.CrossRefGoogle Scholar
Mohebbian, A. & Rival, D.E. 2012 Assessment of the derivative-moment transformation method for unsteady-load estimation. Exp. Fluids 53 (2), 319–330.CrossRefGoogle Scholar
Noca, F. 1997 On the evaluation of time-dependent fluid-dynamic forces on bluff bodies. PhD thesis, California Institute of Technology.Google Scholar
Sørensen, J.N. 2016 General Momentum Theory for Horizontal Axis Wind Turbines, vol. 4. Springer.CrossRefGoogle Scholar
Steiros, K. & Hultmark, M. 2018 Drag on flat plates of arbitrary porosity. J. Fluid Mech. 853, R3.CrossRefGoogle Scholar
Westerweel, J. & Scarano, F. 2005 Universal outlier detection for PIV data. Exp. Fluids 39 (6), 1096–1100.CrossRefGoogle Scholar
Whale, J., Papadopoulos, K.H., Anderson, C.G., Helmis, C.G. & Skyner, D.J. 1996 A study of the near wake structure of a wind turbine comparing measurements from laboratory and full-scale experiments. Solar Energy 56 (6), 621–633.CrossRefGoogle Scholar
Wieneke, B. 2005 Stereo-PIV using self-calibration on particle images. Exp. Fluids 39 (2), 267–280.CrossRefGoogle Scholar
Wood, D.H. 2007 Including swirl in the actuator disk analysis of wind turbines. Wind Engng 31, 317–323.CrossRefGoogle Scholar
Wu, J.-Z., Ma, H.-Y. & Zhou, M.-D. 2015 Vortical Flows. Springer.CrossRefGoogle Scholar
Yang, Z., Sarkar, P. & Hu, H. 2011 An experimental investigation on the wake characteristics of a wind turbine in an atmospheric boundary layer wind. In 29th AIAA Applied Aerodynamics Conference, AIAA Paper 2011-3815.Google Scholar