NUMERICAL/EXPERIMENTAL INVESTIGATION INTO MULTIPLE VORTEX STRUCTURES FORMED OVER WINGS WITH FLAT END-CAPS

The development of a wingtip vortex in the region adjacent the wing end-cap to approximately two chordlengths downstream from the trailing edge is strongly influenced by the end-cap treatment. The flat end-cap geometry produces multiple, relatively strong vortices in the near-field as opposed to the single vortex generated using the rounded end-cap, configuration. However, difficulties in gridding the sharp edges of the wingtip have resulted in relatively few numerical studies of the near-field development of the wingtip vortex from a flat end-cap configuration. In the present work the formation and merging process of multiple vortex structures formed over flat end-caps is investigated numerically through solutions of the RANS equations using both one equation and differential Reynolds stress turbulence models, and experimentally through flow visualization and hot wire anemometry. Introduction Tip vortices shed from finite-span wings are of considerable technological importance, with applications to airplane and submarine wings, helicopter rotor blades, and marine and aviation propellers to name but a few. In nearly all instances, these vortices have undesirable effects, such as aerodynamic inefficiency, mechanical fatigue, and noise (c.f. Green [1]). Of primary interest in this investigation is the formation and very-near-field development of a tip vortex generated from a rectangular wing with a flat end-cap. This geometry is representative of that encountered in the deployment of flaps for high-lift configurations, where, for instance, tip vortex formation and near-field evolution is an important issue in noise control. Previous experimental studies have shown that the vortex development process for flat end-caps is very different from that for rounded end-caps in that multiple shear-layer vortices exist in the vicinity of the wingtip [2-5]. Using hot wire anemometry, Francis and Kennedy [2] observed, at a Reynolds number of 247,000 and an angle-of-attack of 4°, a single secondary vortex over the flat end-cap, which eventually merged with the primary suction-side vortex near the trailing edge. However, flow visualization studies by Shekarriz et al. [3,4] and Katz and Galdo [5] at lower Reynolds numbers (37,000<#e<220,000) and higher angles of attack (oc<12°) showed multiple secondary vortices. These shear-layer vortices are not observed over rounded end caps, since there is no tendency for the flow to separate as the fluid passes from the pressure side, across the cap, and to the suction side. In addition to experimental work, Reynolds-Averaged Navier-Stokes (RANS) calculations have also been performed previously to investigate the near field structure of a wing-tip vortex. The vast majority of these studies have investigated wings with rounded or beveled end-cap geometries [6-10], and have shown that CFD can accurately predict the initial roll-up stage. None of these studies, however, specifically investigated the development and merging process of multiple vortices that form over wings with flat endcaps. In a more recent work [11], RANS calculations were performed for a generic high-lift configuration at flap deflections of 29° and 39°. Numerical Method and Turbulence Model In the current study, the steady, incompressible, RANS equations were integrated using an unstructured, segregated, pressure-based finite-volume procedure as implemented within the Fluent version 5.0 code (Fluent, Inc., Lebanon, NH). The RANS equations are well known, and hence for purposes of brevity are not shown (c.f. Hinze [12]). In terms of the solution/discretization procedure, pressure-velocity coupling was achieved using the SIMPLEC [13] algorithm. Differencing of the convective terms was implemented using a third-order, bounded QUICK [14] interpolation scheme for the momentum equations and a second-order, bounded upwind scheme for all turbulence equations. The viscous terms were discretized using second-order central differencing. Pressures were interpolated to the cell faces using a second-order interpolation scheme [15]. Two different turbulence models were used: a one-equation Spalart-Allmaras (S-A) model [16] and a differential Reynolds stress model (RSM) [17,18]. * Copyright © 2001 by the American Institute of Aeronautics and Astronautics, Inc. All rights reserved. * Assistant Professor, Department of Mechanical and Aerospace Engineering, Senior Member AIAA f Graduate Student, Department of Mechanical and Aerospace Engineering, Student Member AIAA * Professor, Department of Mechanical and Aerospace Engineering, Senior Member AIAA