Vorticity Confinement Applied to Turbulent Wing Tip Vortices for Wake-integral Drag Prediction

Abstract

The vorticity confinement (VC) method was used with total variation diminishing (TVD) schemes to reduce possible over-confinement and applied to tip vortices shed by edges of wings in order to predict induced drag using far-field integration. The optimal VC parameter was determined first by application to 2-D vortices and then to tip vortices shed by a 3-D wing. The 3-D inviscid simulations were post-processed using the wake-integral technique to determine lift-induced drag force. Dependence of the VC parameter on the flight Mach number and the angle of attack was evaluated. Grid convergence studies were conducted for 2-D vortices and for induced drag generated by 3-D wing. VC was used with TVD minmod and differentiable flux limiters to evaluate their effect on the VC method. Finally, the VC approach was combined with the Reynolds stress equation turbulence model, and the results were compared to experimental data of tip vortex evolution.

On application of high-order compact finite-difference schemes to compressible vorticity confinement method

“…This method eliminates the need for any empirical constant however it has less capability to conserve the vorticity than the other methods considering the constant confinement coefficient. Pierson and Povitsky [13,14] used the second-order upwind scheme and they combined the VC method with the TVD schemes in order to increase the stability of the upwind scheme and this technique can prevent from the over-confinement of vortical structures.…”