Abstract
The instantaneous pressure fields and aerodynamic loads are obtained for rotating airfoils from time-resolved particle image velocimetry (TR-PIV) measurements. These allowed evaluating the contribution from the local acceleration (unsteady acceleration) to the instantaneous forces. Traditionally, this term has been neglected for wind turbines with quasi-steady flows, but results show that it is a dominant term in the wake where high temporal variations in the flow field are present due to vortex shedding. Briefly, time-resolved particle image velocimetry TR-PIV measurements are used to calculate flow velocity fields and corresponding spatial and temporal derivatives. These derivatives are then used in the Poisson equation to solve for the pressure field and later used in the integral momentum equation to solve for the instantaneous forces. The robustness of the measurements is analyzed by calculating the PIV uncertainty and the independence of the calculated forces. The experimental mean aerodynamic forces are compared with theoretical predictions from the blade element momentum theory showing good agreement. The instantaneous pressure field showed dependence with time in the wake due to vortex shedding. The contribution to the instantaneous forces from each term in the integral momentum equation is evaluated. The analysis shows that the larger contributions to the normal force coefficient are from the unsteady and the pressure terms, and the larger contribution to the tangential force coefficient is from the convective term.
Similar content being viewed by others
References
Abdallah S (1987) Numerical solutions for the pressure Poisson equation with Neumann boundary conditions using a non-staggered grid. I. J Comput Phys 70(1):182–192
Adrian RJ (2005) Twenty years of particle image velocimetry. Exp Fluids 39(2):159–169
Baur T, Köngeter J (1999) PIV with high temporal resolution for the determination of local pressure reductions from coherent turbulence phenomena. In: 3rd international workshop on particle image velocimetry, Santa Barbara, CA, USA
Bazilevs Y, Hsu MC, Akkerman I et al (2011a) 3D simulation of wind turbine rotors at full scale. Part I: geometry modeling and aerodynamics. Int J Numer Meth Fluids 65(1–3):207–235
Bazilevs Y, Hsu MC, Kiendl J et al (2011b) 3D simulation of wind turbine rotors at full scale. Part II: fluid–structure interaction modeling with composite blades. Int J Numer Meth Fluids 65(1–3):236–253
Betz A (1919) Schraubenpropeller mit geringstem Energieverlust. Gottinger Nachrichten, Delft
Bourgoyne DA, Ceccio SL, Dowling DR (2005) Vortex shedding from a hydrofoil at high Reynolds number. J Fluid Mech 531:293–324
Boutilier MSH, Yarusevych S (2012) Separated shear layer transition over an airfoil at a low Reynolds number. Phys Fluids 24(8):084105
Burton T, Jenkins N, Sharpe D et al (2011) Wind energy handbook. Wiley, New York
Charonko JJ et al (2010) Assessment of pressure field calculations from particle image velocimetry measurements. Meas Sci Technol 21:105401
De Kat R, van Oudheusden BW (2010) Instantaneous planar pressure from PIV: analytic and experimental test-cases. In Proceedings of the 15th international symposium on applications of laser techniques to fluid mechanics, Lisbon, Portugal
De Kat R, van Oudheusden BW (2011) Instantaneous planar pressure determination from PIV in turbulent flow. Exp Fluids 52(5):1089–1106
Fujisawa N, Tanahashi S, Srinivas K (2005) Evaluation of pressure field and fluid forces on a circular cylinder with and without rotational oscillation using velocity data from PIV measurement. Meas Sci Technol 16:989
Glauert H (1935) Airplane propellers. Aerodyn Theory 4:169–360
Gurka R et al (1999) Computation of pressure distribution using PIV velocity data. In: Workshop on particle image velocimetry
Hand MM et al (2001) Unsteady aerodynamics experiment phase VI: wind tunnel test configurations and available data campaigns. NREL/TP-500-29955, National Renewable Energy Lab., Golden
Hansen MOL et al (2006) State of the art in wind turbine aerodynamics and aeroelasticity. Prog Aerosp Sci 42(4):285–330
Hart DP (2000) PIV error correction. Exp Fluids 29(1):13–22
Jardin T, David L, Farcy A (2009) Characterization of vortical structures and loads based on time-resolved PIV for asymmetric hovering flapping flight. Exp Fluids 46(5):847–857
Kurtulus DF, Scarano F, David L (2006) Unsteady aerodynamic forces estimation on a square cylinder by TR-PIV. Exp Fluids 42(2):185–196
Lee T, Su YY (2012) Low Reynolds number airfoil aerodynamic loads determination via line integral of velocity obtained with particle image velocimetry. Exp Fluids 53(5):1177–1190
Liu X, Katz J (2006) Instantaneous pressure and material acceleration measurements using a four-exposure PIV system. Exp Fluids 41(2):227–240
Mohebbian A, Rival DE (2012) Assessment of the derivative-moment transformation method for unsteady-load estimation. Exp Fluids 53(2):319–330
Noca F, Shiels D, Jeon D (1999) A comparison of methods for evaluating time-dependent fluid dynamic forces on bodies, using only velocity fields and their derivatives. J Fluids Struct 13(5):551–578
Oudheusden BW et al (2007) Evaluation of integral forces and pressure fields from planar velocimetry data for incompressible and compressible flows. Exp Fluids 43(2–3):153–162
Ragni D et al (2009) Surface pressure and aerodynamic loads determination of a transonic airfoil based on particle image velocimetry. Meas Sci Technol 20:074005
Ragni D, Oudheusden BW, Scarano F (2011) 3D pressure imaging of an aircraft propeller blade-tip flow by phase-locked stereoscopic PIV. Exp Fluids 52(2):463–477
Sezer-Uzol N, Long LN (2006) 3-D time-accurate CFD simulations of wind turbine rotor flow fields. AIAA paper, vol 394, p 2006
Shen WZ et al (2005) Tip loss corrections for wind turbine computations. Wind Energy 8(4):457–475
Simms DA et al (2001) NREL unsteady aerodynamics experiment in the NASA-Ames wind tunnel: a comparison of predictions to measurements. National Renewable Energy Laboratory, Golden
Sotiropoulos F, Abdallah S (1991) The discrete continuity equation in primitive variable solutions of incompressible flow. J Comput Phys 95(1):212–227
Suzuki T, Ji H, Yamamoto F (2009) Unsteady PTV velocity field past an airfoil solved with DNS: part 1. Algorithm of hybrid simulation and hybrid velocity field at Re ≈ 103. Exp Fluids 47(6):957–976
Tangler JL (2002) The nebulous art of using wind-tunnel airfoil data for predicting rotor performance. ASME 2002 wind energy symposium. American Society of Mechanical Engineers, pp 190–196
Villegas A, Diez FJ (2014) On the quasi-instantaneous aerodynamic load and pressure field measurements on turbines by non-intrusive PIV. Renew Energy 63:181–193
Westerweel J (1997) Fundamentals of digital particle image velocimetry. Meas Sci Technol 8:1379
Yarusevych S, Sullivan PE, Kawall JG (2006) Coherent structures in an airfoil boundary layer and wake at low Reynolds numbers. Phys Fluids 18(4):044101
Yarusevych S, Sullivan PE, Kawall JG (2009) On vortex shedding from an airfoil in low-Reynolds-number flows. J Fluid Mech 632:245
Author information
Authors and Affiliations
Corresponding author
Electronic supplementary material
Below is the link to the electronic supplementary material.
Rights and permissions
About this article
Cite this article
Villegas, A., Diez, F.J. Evaluation of unsteady pressure fields and forces in rotating airfoils from time-resolved PIV. Exp Fluids 55, 1697 (2014). https://doi.org/10.1007/s00348-014-1697-5
Received:
Revised:
Accepted:
Published:
DOI: https://doi.org/10.1007/s00348-014-1697-5