An improved formulation of drag estimation for thick airfoils is presented. Drag underprediction in XFOIL like viscous-inviscid interaction methods can be quite significant for thick airfoils used in wind turbine applications (up to 30% as seen in the present study). The improved drag formulation predicts the drag accurately for airfoils with reasonably small trailing edge thickness. The derivation of drag correction is based on the difference between the actual momentum loss thickness based on free stream velocity and the one based on the velocity at the edge of the boundary layer. The improved formulation is implemented in the most recent version of XFOIL and RFOIL (an aerodynamic design and analysis method based on XFOIL, developed by a consortium of ECN, NLR and TU Delft after ECN acquired the XFOIL code. After 1996, ECN maintained and improved the tool.) and the results are compared with experimental data, results from commercial CFD methods like ANSYS CFX and other methods like DTU-AED EllipSys2D and CENER WMB. The improved version of RFOIL shows good agreement with experimental data. Nomenclature α Angle of attack ∆θ Error in θ δ Boundary layer thickness δ * Boundary layer displacement thickness ∞ Subscript for incident free stream condition ρ Density of fluid θ Boundary layer momentum thickness ξ, η Streamline space coordinates A, B G − β equilibrium locus coefficients airf oil Subscript for airfoil parameters c Airfoil chord length C τ EQ Equilibrium maximum shear stress coefficient c d Sectional drag coefficient c l Sectional lift coefficient D Drag e Subscript for boundary layer edge condition
An improved formulation for lift estimation for integral boundary layer (IBL) methods (i.e. RFOIL, XFOIL) for thick airfoils is presented. Lift over-prediction (5 − 10% around (l/d)max) in RFOIL (similarly in XFOIL) is observed for thick airfoils for a wide range of angles of attack. The lift slope is over-predicted resulting in the increasing error in lift with increasing angle of attack. The wake geometry in RFOIL and XFOIL is determined from the inviscid calculations which seems to give rise to the above problem. A scheme has been developed for IBL methods and implemented in RFOIL, to include the effects of viscous flow on the wake geometry which lead to improved lift prediction for thick airfoils. New insights were obtained regarding the discrepancy in predicting the maximum lift. It is observed that lift over-prediction persists in case of thick trailing edge (TTE) airfoils even with the improved method. The cause for this behavior is identified and discussed in order to evaluate the possibilities of improvement. High Reynolds number and increased free-stream turbulence intensity have been observed to inhibit the onset of flow separation and delay stall. These effects are not yet captured accurately in RFOIL indicating a need for further investigation. Nomenclature α Angle of attack c Airfoil chord length c d Sectional drag coefficient c l Sectional lift coefficient h T E Airfoil trailing edge thickness M ∞ Free stream Mach number N crit Critical amplification factor Re Chord length based Reynolds number X, Y Cartesian space coordinates
An improved formulation of drag estimation for thick airfoils is presented. Drag underprediction in XFOIL like viscous-inviscid interaction methods can be quite significant for thick airfoils used in wind turbine applications (up to 30% as seen in the present study). The improved drag formulation predicts the drag accurately for airfoils with reasonably small trailing edge thickness. The derivation of drag correction is based on the difference between the actual momentum loss thickness based on free stream velocity and the one based on the velocity at the edge of the boundary layer. The improved formulation is implemented in the most recent version of XFOIL and RFOIL (an aerodynamic design and analysis method based on XFOIL, developed by a consortium of ECN, NLR and TU Delft after ECN acquired the XFOIL code. After 1996, ECN maintained and improved the tool.) and the results are compared with experimental data, results from commercial CFD methods like ANSYS CFX and other methods like DTU-AED EllipSys2D and CENER WMB. The improved version of RFOIL shows good agreement with experimental data. Nomenclature α Angle of attack ∆θ Error in θ δ Boundary layer thickness δ * Boundary layer displacement thickness ∞ Subscript for incident free stream condition ρ Density of fluid θ Boundary layer momentum thickness ξ, η Streamline space coordinates A, B G − β equilibrium locus coefficients airf oil Subscript for airfoil parameters c Airfoil chord length C τ EQ Equilibrium maximum shear stress coefficient c d Sectional drag coefficient c l Sectional lift coefficient D Drag e Subscript for boundary layer edge condition
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