Validation of a model for estimating the strength of the vortex created by a Vortex Generator from its Bound Circulation

Abstract

A hypothesis is tested and validated for predicting the vortex strength induced by a vortex generator in wall-bounded flow by combining the knowledge of the Vortex Generator (VG) geometry and the approaching boundary layer velocity distribution. In this paper, the spanwise distribution of bound circulation on the vortex generator is computed from integrating the pressure force along the VG height calculated using CFD. It is then assumed that all this bound circulation is shed into the wake to fulfill Helmholtz's theorem and then curl up into one primary tip vortex. To validate this, the trailed circulation estimated from the distribution of the bound circulation is compared to the one in the wake behind the vortex generator determined directly from the wake velocities at some downstream distance. In practical situations, the pressure distribution on the vane is unknown and consequently other estimates of the spanwise force distribution on the VG must instead be applied, such as using 2D airfoil data corresponding to the VG geometry at each wall-normal distance. Such models have previously been proposed and used as an engineering tool to aid preliminary VG design and it is not the purpose of this paper to refine such engineering models, but to validate their assumptions such as applying a lifting line model on a VG that has a very low aspect ratio and placed in wall boundary layer. Herein, high Reynolds number boundary layer measurements of VG induced flow were used to validate the Reynolds Averaged Navier-Stokes (RANS) modeled circulation results and are used for further illustration and validation of the hypothesis.