Modelling vortex generator effects on turbulent boundary layers with integral boundary layer equations

Abstract. Vortex generators (VGs) are known to delay separation and stall, allowing the design of airfoils with larger stall margins, particularly for thick airfoil sections in the inboard and midboard regions of modern slender wind turbine blades. Including VG effects in blade design studies requires accurate VG models for fast lower-order techniques, like integral boundary layer (IBL) methods. Previous VG models for IBL methods have used engineering approaches tuned on airfoil aerodynamic data. The accuracy of these models depends on the availability of wind tunnel aerodynamic polar datasets for tuning, which are limited and time-consuming to expand for the relevant wind conditions, airfoil sections, and VG configurations being used in continuously growing wind turbine blades. This work proposes a VG model using IBL equations derived from flat-plate boundary layers under the influence of VGs. The new VG model empirically models the shape factor of the boundary layer and the viscous dissipation coefficient in the IBL framework to account for the additional momentum and dissipation in the boundary layer mean flow due to VGs. The model is developed from a wide range of flat-plate boundary layers and VGs to account for variations in VG vane size and placement on the turbulent boundary layer development influencing the airfoil aerodynamic characteristics. The new VG model, called RFOILVogue, is implemented in an in-house code RFOIL, an improvement over XFOIL, and validated with computational fluid dynamics (CFD) data and wind tunnel measurements of flat plates and airfoil sections equipped with VGs. Since it is derived from vortex dynamics in turbulent boundary layers, RFOILVogue better predicts both airfoil performance characteristics, such as positive stall angle, maximum lift, and drag, and boundary layer flow parameters, such as the separation location, compared to the existing tuned VG models. The VG model still suffers from some inherent drawbacks of reduced-order models like RFOIL, and future research directions for thick airfoils are proposed to overcome these drawbacks in VG modelling.