Towards a vortex generator model for integral boundary layer methods

In this study a new approach to model the effect of vortex generators in integral boundary layer equations is described. Vortex generators (VGs) are commonly used on wind turbine blades to avoid early separation of flow which helps not only to increase the lift but also delays the stall. Delaying the stall angle of wind turbine blades will allow for operation over larger range of angle of attacks and thus increase power production from wind turbines. Typically, VGs are submerged in the boundary layer and generate vortices that mix high-energy fluid from outer flow with the slow-moving boundary layer. Within this study the effect of the VGs on the 2-D boundary layers are modeled as additional mixing. The presence of a new shear layer will lead to additional viscous dissipation and affect the wall shear stress. To model these effects new terms are introduced into the integral boundary layer equations to account for the extra mass and momentum flux and turbulence production. The additional unknowns introduced into the system of equations are derived using CFD simulations. Initial CFD simulations on a flat plate with body fitted meshes around VGs are used to obtain an algebraic model. The new model is implemented in an aerodynamic analysis and design tool and preliminary results are presented. The theory developed here will be extended for flows over airfoils.