The Influence of Unsteady Wind on the Performance and Aerodynamics of Vertical Axis Wind Turbines A Dissertation Submitted for the Degree of Doctor of Philosophy by Louis Angelo M. Danao The University of Sheffield Department of Mechanical Engineering September 2012 Abstract Interest in small–scale wind turbines as energy sources in the built environment has increased due to the desire of consumers in urban areas to reduce their carbon footprint. Vertical axis wind turbines (VAWTs) have shown to be potentially well suited within the urban landscape. However, there is a large gap in the fundamental understanding of VAWT operation in turbulent, unsteady wind that is typical of the built environment. This dissertation investigates the aerodynamics and performance of VAWTs in fluctuating wind through experiments and numerical simulations. All experimental investigations utilise a low–speed open section wind tunnel. The use of a shutter mechanism that generates unsteady wind in the wind tunnel is detailed. Performance measurements for turbine power use a validated method previously developed in the same laboratory with slight modification for unsteady wind performance. Both steady and unsteady power performance tests results are presented. Near–blade flow physics during steady wind operation is scrutinised using Particle Image Velocimetry (PIV). Complementing the findings in experiments, numerical simulations using Unsteady Reynolds Averaged Navier–Stokes Computational Fluid Dynamics (URANS CFD) are employed. The numerical model is validated using experimental data. Blade force measurements that are not available from experiments are extracted from the numerical models to provide additional insight for performance analysis. A survey of varying unsteady wind parameters is conducted to examine the effects of various unsteady wind conditions on the performance of the VAWT. The aerodynamics is inspected through vorticity visualisations alongside blade force metrics to link performance to blade stall. Results show marginal improvement on VAWT performance (CP) with small wind speed fluctuations versus steady wind CP. Operating the VAWT at tip speed ratios (λ) higher than steady wind peak CP λ also improve performance. Conditions other than the stated above reduce VAWT CP. 2 Declaration Described in this dissertation is work performed in the Department of Mechanical Engineering, the University of Sheffield between December 2009 and August 2012. I hereby declare that no part of this work has been submitted as an exercise for a degree at this or any other university. This dissertation is entirely the result of my own work and includes nothing which is the outcome of collaboration, except when stated otherwise. This dissertation contains 122 figures and approximately 45,000 words. Signed: Louis Angelo M. Danao Dated: ____ /____ /________ 3 Dedicated to my wife Nina, for believing in me. 4 Acknowledgements First and foremost, I would like to thank my supervisor, Dr Robert Howell, for his advice and encouragement all throughout the last three years. His invaluable insight and consistent mentoring have made my work more enjoyable and interesting. Furthermore, I would like to thank Professor Ning Qin for his very useful comments in my early days of CFD modelling. I would also like to thank several persons in my research group. Jonny’s well explained demonstrations regarding the ins and outs of wind tunnel work and VAWT performance testing using his spin down technique have brought my experience in experimental aerodynamics work from virtually nothing to acceptable levels. His assistance in the PIV measurements was extremely helpful. Furthermore, I would like to thank Jon, Oke, Joe and Dorit for extra hands and constructive comments in my experiments and CFD work. Additional thanks are extended to the technicians in the workshop for all fabrication work they have done for my experiment setup. On a personal note, I am particularly grateful to my family especially my wife Nina and daughter Toni for keeping me grounded and sane as I ventured into this journey. Their love and support have kept me positive and helped me stay in the right path. Finally, I would like to thank the Almighty God for the strength and patience He has given me, without which I would have certainly failed. The Engineering Research and Development for Technology program of the Department of Science and Technology through the University of the Philippines – College of Engineering is gratefully acknowledged for the financial assistance that allowed me to pursue this endeavour. 5 Nomenclature Symbols A rotor frontal swept area, 2RL, (in hotwire anemometry, constant 1) AR blade aspect ratio, L/c B in hotwire anemometry, constant 2 c blade chord C drag coefficient d C lift coefficient l C moment coefficient m CP power coefficient d characteristic dimension of obstacle c d diameter of tracer particle d D gust length g d pressure outlet boundary distance from VAWT axis o d side wall boundary distance from VAWT axis s f characteristic frequency of unsteady wind c F drag force d F lift force l gr inflation growth rate of mesh I rotor rotational mass moment of inertia rig k reduced gust frequency g k–ε turbulence model based on turbulent kinetic energy and turbulent dissipation k–ε RNG variant of k–ε using Re-Normalisation Group methods k–ω turbulence model based on turbulent kinetic energy and specific dissipation k–ω SST variant of k–ω by Menter (1993) L blade length N number of blades, (in statistics, number of sample points) n in hotwire anemometry, constant 3 p ambient pressure (Pascals) P ambient pressure (mmHg) P blade power (three blades) B P wind power w q dynamic pressure R rotor radius, (in ideal gas law, specific gas constant) Re blade Reynolds number R number of revolutions per wind cycle g 6 Nomenclature Symbols continued . . . S–A Spalart–Allmaras turbulence model S Stoke’s number k s standard error y t time T temperature T applied brake torque app T blade torque (single blade) b T blade torque (three blades) B T resistive torque res Tu turbulence intensity U instantaneous wind speed, (invorticity, velocity along x–axis) U free stream wind speed ∞ U amplitude of fluctuation of unsteady wind amp U mean speed of unsteady wind mean V hotwire voltage, (invorticity, velocity along y–axis) V blade velocity, Rω b W relative velocity of wind with respect to blade, (invorticity, velocity along z–axis) y+ dimensionless wall distance y sample value i yˆ fit value Greek symbols α angle of attack α amplitude of angle of attack A α mean angle of attack o ΔCP change in CP Δt in CFD, time step size θ azimuth position κ pitching aerofoil reduced frequency λ tip speed ratio, Rω/U ∞ λ* tip speed ratio at peak CP λ tip speed ratio corresponding to ω mean mean μ laminar viscosity μ dynamic viscosity of fluid f μ turbulent viscosity t ξ rotor angular acceleration ρ air density ρ density of tracer particle d σ rotor solidity, Nc/R  3D vorticity  vorticity along z–axis z τ tracer particle response time ω rotor angular speed ω in unsteady wind, mean of ω mean 7 Nomenclature Abbreviations CFD Computational Fluid Dynamics DES detached eddy simulation FOV field of view HAWT horizontal axis wind turbine LES large eddy simulation LEV leading edge vortex NACA National Advisory Committee for Aeronautics OES organised eddy simulation PIV Particle Image Velocimetry RANS Reynolds Averaged Navier–Stokes TEV trailing edge vortex URANS Unsteady RANS VAWT vertical axis wind turbine VTM vorticity transport model 8 Contents Abstract............................................................................................................................................ 2 Declaration ..................................................................................................................................... 3 Acknowledgements .................................................................................................................... 5 Nomenclature ............................................................................................................................... 6 Contents ........................................................................................................................................... 9 List of Figures ............................................................................................................................. 13 List of Tables ................................................................................................................................ 18 Introduction ................................................................................................................................ 19 1.1 Research Objectives ..................................................................................................... 25 1.2 Synopsis ........................................................................................................................... 26 1.3 Publications ................................................................................................................... 28 Literature Review .................................................................................................................... 30 2.1 Introduction ...................................................................................................................30 2.2 Numerical Modelling of the VAWT ........................................................................ 31 2.2.1 Momentum Theory .............................................................................................. 32 2.2.2 Vortex models ........................................................................................................ 34 2.2.3 Other models .......................................................................................................... 37 2.2.4 Summary ................................................................................................................. 38 2.3 Computational Fluid Dynamics ............................................................................. 40 9 Contents 2.3.1 URANS and LES ................................................................................................... 40 2.3.2 Turbulence Modelling and Dynamic Stall .................................................... 45 2.3.3 Summary ................................................................................................................. 59 2.4 Performance Basics ..................................................................................................... 61 2.4.1 Aerofoil Profile ...................................................................................................... 61 2.4.2 Solidity .....................................................................................................................64 2.4.2 Blade Sweep ............................................................................................................ 66 2.4.3 Unsteady Incoming Wind .................................................................................. 68 2.5 Summary ......................................................................................................................... 74 Experimental Methods ........................................................................................................... 76 3.1 Introduction ................................................................................................................... 76 3.2 Wind Tunnel Facility .................................................................................................. 77 3.3 Wind Turbine Model ................................................................................................... 78 3.4 Start–up Mechanism .................................................................................................. 80 3.5 Shutter Mechanism...................................................................................................... 81 3.6 Measurement Instrumentation ............................................................................... 82 3.6.1 Rotational Velocity .............................................................................................. 82 3.6.2 Torque ...................................................................................................................... 83 3.6.3 Wind Velocity ........................................................................................................84 3.7 Steady Wind Performance ......................................................................................... 86 3.8 Unsteady Wind Performance ...................................................................................89 3.9 Particle Image Velocimetry ....................................................................................... 91 3.9.1 PIV Equipment ...................................................................................................... 92 3.10 Experimental Error Analysis ................................................................................... 97 3.10.1 Air Temperature and Pressure ......................................................................... 97 3.10.2 Flow Velocity .........................................................................................................98 3.10.3 RPM Measurements ...........................................................................................100 3.10.4 Torque Measurements ...................................................................................... 101 3.10.5 Cumulative Error in CP .................................................................................... 101 10