Numerical Simulations of a Wingtip Vortex in the Near Field

Abstract

We investigate the accuracy of current state-of-the-art turbulence models and a compressible Reynolds-averaged Navier-Stokes solver in computing the formation of a wingtip vortex in the near field. The Reynolds-averaged Navier-Stokes solvers used in this investigation are the NPARC WIND 5.0 and Wind-US 1.0 codes. The turbulence models explored are the standard Spalart-Allmaras model, the Spalart-Allmaras model with correction for system rotation and streamline curvature, the Menter shear stress transport model, and the Rumsey-Gatski explicit algebraic stress model. Additionally, we study how solution accuracy is affected by using higher-order numerical schemes as opposed to more grid points. Accuracy is assessed by comparing the results of the wingtip-vortex computations with the data of a reliable, thorough experiment. The solutions obtained using a fifth-order-accurate numerical scheme show that the Spalart-Allmaras turbulence model with corrections for rotation and streamline curvature predicts the mean flow most accurately. However, we find that within the vortex, none of the turbulence models explored accurately captures the magnitudes of the turbulence quantities or the lag of the Reynolds stress components behind the corresponding strain-rate components.