Modelling vortex generators 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 in-board and mid-board 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 use 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 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 is implemented in an in-house code RFOIL, an improvement over XFOIL, validated with CFD data and wind tunnel measurements of flat plates and airfoil sections equipped with VGs. The new VG model RFOILVogue better captures the positive stall characteristics than the existing VG models for IBL equations. Cases with severe adverse pressure gradients are identified as areas of improvement for the developed VG model, and a methodology is proposed for future work.