Unsteady airfoil aerodynamics in attached flow: From unsteady thin airfoil theory to wind turbine application
Attached-flow unsteady aerodynamics underpin the dynamic stall models used in wind turbine aerodynamic and aeroelastic codes, particularly over the outboard blade region that dominates power production and loading. Here, angle of attack and relative velocity vary while the flow remains predominantly attached. A complete engineering model combines airfoil polar lookup, shed-wake memory, non-circulatory loads, consistent force definitions, and separated-flow dynamics. Although the underlying theory is classical, existing descriptions do not provide a complete and internally consistent implementation route for these attached-flow contributions in wind turbine solvers. This work formulates the attached-flow contributions as lift, drag, and moment coefficients for blade-element momentum (BEM), lifting-line (LL), and actuator-line (AL) methods, for use with 2-D airfoil polars from measurements or CFD. Starting from classical unsteady thin-airfoil theory, circulatory and non-circulatory loads are derived in coefficient form and key modeling choices are clarified. Shed-wake memory is formulated using downwash velocity rather than angle of attack as the aerodynamic state variable. Rotor-level implementation is verified using two cases. A coned straight-blade case provides a cross-method benchmark and quantifies thrust and power errors caused by omitting three required contributions. Lift-direction projection has the largest influence on power, while omitting the mid-chord heaving-acceleration term removes the non-circulatory normal-force cancellation and produces a thrust error. A zero-onset-flow vertical-axis wind turbine (VAWT) case verifies that, in the ideal thin-airfoil limit, all circulatory and non-circulatory contributions cancel, yielding zero total rotor torque.