Computational fluid dynamics (CFD) mesh independency techniques for a straight blade vertical axis wind turbine

This paper numerically investigates four methods, namely mesh refinement, General Richardson Extrapolation (GRE), Grid Convergence Index (GCI), and the fitting method, in order to obtain a mesh independent solution for a straight blade vertical axis wind turbine (SB-VAWT) power curve using computational fluid dynamics (CFD). The solution is produced by employing the 2D Unsteady Navier–Stokes equations (URANS) with two turbulence models (Shear Stress Transport (SST) Transitional and ReNormalized Groups (RNG) κ−ɛ models). The commonly applied mesh refinement is found to be computationally expensive and not often practical even for a full 2D model of the turbine. The mesh independent power coefficient produced using the General Richardson Extrapolation method is found to be encouraging. However, the Grid Convergence Index may not be applicable in mesh independency tests due to the oscillatory behaviour of the convergence for the turbine power coefficient. As an alternative, the fitting method shows a good potential for the predicting of the mesh independent power coefficient without the necessity to consider a massive number of meshes.

[1]  Derek B. Ingham,et al.  CFD Sensitivity Analysis of a Straight-Blade Vertical Axis Wind Turbine , 2012 .

[2]  Cheng-Hsiung Kuo,et al.  Effects of pitch angle and blade camber on flow characteristics and performance of small-size Darrieus VAWT , 2013, J. Vis..

[3]  Jiang Luo,et al.  Conjugate heat transfer analysis of a cooled turbine vane using the V2F turbulence model , 2007 .

[4]  P. Roache Conservatism of the Grid Convergence Index in Finite Volume Computations on Steady-State Fluid Flow and Heat Transfer , 2003 .

[5]  F. Menter,et al.  A Correlation-Based Transition Model Using Local Variables—Part II: Test Cases and Industrial Applications , 2006 .

[6]  G H Yu,et al.  Numerical simulation of a wind turbine airfoil: Dynamic stall and comparison with experiments , 2010 .

[7]  S. Tullis,et al.  Response of a Vertical Axis Wind Turbine to Time Varying Wind Conditions Found within the Urban Environment , 2010 .

[8]  P. Roache QUANTIFICATION OF UNCERTAINTY IN COMPUTATIONAL FLUID DYNAMICS , 1997 .

[9]  J. C. Tyler,et al.  Analysis of Pitch and Plunge Effects on Unsteady Airfoil Behavior , 1992 .

[10]  F. Carta A comparison of the pitching and plunging response of an oscillating airfoil , 1979 .

[11]  S. Orszag,et al.  Development of turbulence models for shear flows by a double expansion technique , 1992 .

[12]  Hui Hu,et al.  An Experimental Investigation on Aerodynamic Hysteresis of a Low-Reynolds Number Airfoil , 2008 .

[13]  Ernesto Benini,et al.  The Darrieus wind turbine: Proposal for a new performance prediction model based on CFD , 2011 .

[14]  Nobuyuki Fujisawa,et al.  Observations of dynamic stall on Darrieus wind turbine blades , 2001 .

[15]  Rajat Gupta,et al.  Computational fluid dynamics analysis of a twisted three-bladed H-Darrieus rotor , 2010 .

[16]  Lewis F. Richardson,et al.  Weather Prediction by Numerical Process , 1922 .

[17]  I. E. Barton,et al.  Comparison of SIMPLE‐ and PISO‐type algorithms for transient flows , 1998 .

[18]  Shengyi Wang,et al.  Numerical investigations on dynamic stall of low Reynolds number flow around oscillating airfoils , 2010 .

[19]  J. Leishman Dynamic stall experiments on the NACA 23012 aerofoil , 1990 .

[20]  L. Carr Progress in analysis and prediction of dynamic stall , 1988 .

[21]  Thierry Maître,et al.  Modeling of the flow in a Darrieus water turbine: Wall grid refinement analysis and comparison with experiments , 2013 .

[22]  Ernesto Benini,et al.  Numerical evaluation of aerodynamic and inertial contributions to Darrieus wind turbine blade deformation , 2013 .

[23]  Ivette Rodriguez,et al.  On the validity of the Oberbeck-Boussinesq approximation in a tall differentially heated cavity with water , 2012 .

[24]  Mazharul Islam,et al.  Desirable Airfoil Features for Smaller-Capacity Straight-Bladed VAWT , 2007 .

[25]  F. Menter,et al.  A Correlation-Based Transition Model Using Local Variables—Part I: Model Formulation , 2006 .

[26]  Zhi Tao,et al.  Turbulence Modelling of Deep Dynamic Stall at Low Reynolds Number , 2010 .

[27]  Grant Ingram,et al.  A low-Reynolds-number, high-angle-of-attack investigation of wind turbine aerofoils , 2011 .

[28]  Florian R. Menter,et al.  Review of the shear-stress transport turbulence model experience from an industrial perspective , 2009 .

[29]  F. Scarano,et al.  Visualization by PIV of dynamic stall on a vertical axis wind turbine , 2009 .

[30]  Hyeonsoo Yeo,et al.  Investigation of Rotor Performance and Loads of a UH-60A Individual Blade Control System , 2010 .

[31]  K. Mulleners,et al.  The onset of dynamic stall revisited , 2012 .

[32]  Ning Qin,et al.  Wind tunnel and numerical study of a small vertical axis wind turbine , 2008 .

[33]  Giorgio Pavesi,et al.  Comparison of different numerical approaches to the study of the H-Darrieus turbines start-up , 2013 .

[34]  David A. Johnson,et al.  Numerical modeling of an S809 airfoil under dynamic stall, erosion and high reduced frequencies , 2012 .

[35]  L. Richardson The Approximate Arithmetical Solution by Finite Differences of Physical Problems Involving Differential Equations, with an Application to the Stresses in a Masonry Dam , 1911 .

[36]  A. Sakout,et al.  Simulations of the Fluid Flow around a Rotating Vertical Axis Wind Turbine , 2007 .

[37]  Jiyuan Tu,et al.  Computational Fluid Dynamics: A Practical Approach , 2007 .

[38]  Wei-Haur Lam,et al.  Numerical study of straight-bladed Darrieus-type tidal turbine , 2009 .

[39]  Wael Mokhtar,et al.  A CFD Study of Wind Turbine Aerodynamics , 2012 .

[40]  Ulrich Rist,et al.  Investigations of time-growing instabilities in laminar separation bubbles , 2002 .

[41]  M. H. Mohamed,et al.  Performance investigation of H-rotor Darrieus turbine with new airfoil shapes , 2012 .

[42]  Christopher J. Roy,et al.  Review of Discretization Error Estimators in Scientific Computing , 2010 .

[43]  Tim Lee,et al.  Investigation of flow over an oscillating airfoil , 2004, Journal of Fluid Mechanics.

[44]  Zhi Tao,et al.  Turbulence modeling of deep dynamic stall at relatively low Reynolds number , 2012 .

[45]  Samir Ziada,et al.  Computational fluid dynamics simulation of the aerodynamics of a high solidity, small‐scale vertical axis wind turbine , 2012 .

[46]  Paul E. Allaire,et al.  Investigation of Self-Starting Capability of Vertical Axis Wind Turbines Using a Computational Fluid Dynamics Approach , 2011 .

[47]  Ernesto Benini,et al.  Numerical Investigation of Laminar to Turbulent Boundary Layer Transition on a Naca 0012 Airfoil for Vertical-Axis Wind Turbine Applications , 2011 .

[48]  U. Mehta,et al.  Starting vortex, separation bubbles and stall: a numerical study of laminar unsteady flow around an airfoil , 1975, Journal of Fluid Mechanics.

[49]  Weeratunge Malalasekera,et al.  An introduction to computational fluid dynamics - the finite volume method , 2007 .

[50]  Kai Richter,et al.  Improved Two-Dimensional Dynamic Stall Prediction with Structured and Hybrid Numerical Methods , 2011 .

[51]  W. Mccroskey,et al.  Dynamic Stall Experiments on Oscillating Airfoils , 1975 .

[52]  I. Tani Low-speed flows involving bubble separations , 1964 .

[53]  W. J. Mccroskey,et al.  An Experimental Study of Dynamic Stall on Advanced Airfoil Sections. Volume 1. Summary of the Experiment. , 1982 .

[54]  Mohsen Karimi,et al.  Effects of different mesh schemes and turbulence models in cfd modelling of stirred tanks , 2012 .

[55]  Kevin W. McLaren,et al.  A NUMERICAL AND EXPERIMENTAL STUDY OF UNSTEADY LOADING OF HIGH SOLIDITY VERTICAL AXIS WIND TURBINES , 2011 .

[56]  Jörg Franke,et al.  Application of generalized Richardson extrapolation to the computation of the flow across an asymmetric street intersection , 2008 .

[57]  C. P. van Dam,et al.  Bubble-Induced Unsteadiness on A Wind Turbine Airfoil , 2002 .

[58]  L. Richardson,et al.  The Deferred Approach to the Limit. Part I. Single Lattice. Part II. Interpenetrating Lattices , 1927 .

[59]  Chao Li,et al.  2.5D large eddy simulation of vertical axis wind turbine in consideration of high angle of attack flow , 2013 .

[60]  P. Roache Perspective: A Method for Uniform Reporting of Grid Refinement Studies , 1994 .

[61]  D. Favier,et al.  COMBINED TRANSLATION/PITCH MOTION: A NEW AIRFOIL DYNAMIC STALL SIMULATION , 1988 .

[62]  P. Durbin Near-wall turbulence closure modeling without “damping functions” , 1991, Theoretical and Computational Fluid Dynamics.

[63]  Ken Badcock,et al.  CFD Investigation of 2D and 3D Dynamic Stall , 2004 .