W INGTIP vortex is an important subject in fluid mechanics, as it is involved inmany practical engineering problems that can be found, for example, in [1–4]. Thus, it has long been the subject of numerous experimental and/or numerical investigations. Chigier and Corsiglia [5] pioneered the experimental study of thewingtip vortex. Theymeasured, by using hot-wire anemometry, thewingtip vortex of a square-tipped rectangular wing up to a 12c downstream distance. The maximum axial velocity at the vortex core at x0=c 0:25 was 1:4U1. They showed that themaximum tangential velocity increases with the angle of attack, while the vortex core radius remains unchanged. Green [6] and Green and Acosta [7] used double-pulsed holography to measure the instantaneous velocity distribution in trailing vortices of a round-tipped rectangular wing. At a 10 deg angle of attack, the axial velocity at the vortex core was 1:6U1 at x0=c 2:0. Chow et al. [8] used hot-wire and seven-hole probes to measure the flow over and immediately downstream of a roundtipped rectangular wing with a NACA0012 section at Rec 4:6 10 and a 10 deg angle of attack. The measurement data of this study will be used as reference data in this work. Numerical studies began to appear in the late 1980s. Srinivasan et al. [9] used a thin-layer Navier–Stokes solver with the Baldwin– Lomax turbulence model [10] to examine the influence of the tip-cap shape and tip planform on the wingtip vortex. Their results showed good agreement with the experimental data of Spivey and Moorehouse [11] for the surface pressures, except for the surface pressure suction peak induced by the vortex in the vicinity of the wingtip. The computed vorticity contours of the tip vortex, however, were rather poor in the sense that theywere highly distorted andmore diffusive with the downstream distance. Dacles-Mariani and Zilliac [12] studied, both numerically and experimentally, the wingtip vortex in the nearfield in conjunctionwithChowet al.’s experimental study [8]. The Baldwin–Barth turbulence model [13] was used with the modified production term suggested by Spalart through private communication [12] to reduce the eddy viscosity at the vortex core. The predicted velocity profile was in good agreement with the measured data, but the core static pressure was underpredicted up to 25%at the downstreamboundary. Craft et al. [14] recently performed a numerical simulation of the experiment of Chow et al. [8]. Three turbulence models, the eddy viscosity model, the nonlinear eddy viscosity model of Suga [15], and the two-component-limit (TCL) second-moment closure model [16], were adopted in their simulation. The results obtained using linear and nonlinear eddy viscosity models showed a far too rapid decay of the vortex core. Only the TCL model successfully reproduced the principal features of the vortex flowfield. The TCL model is a Reynolds stress transport model, which is much more complicated for application to practical flows than the two-equation models in spite of its distinguished merits. It is well known that conventional two-equation models perform rather poorly for flows that are not in near-equilibrium flow. To remedy this situation, Yoshizawa et al. [17] suggested a nonequilibrium eddy viscosity model, which works well for swirling (or strong vorticity) flows. The motivation of the present work is to investigate whether this nonequilibrium model performs well for wingtip vortex flow in comparison with the TCL model, which is a first attempt to the authors’ knowledge. It is found that the model performs almost as good as the TCL model; hence, it is strongly recommended for practical flow computations of wingtip vortex flow.
Search from 250 M+ research papersSearch from 250 M+ research papers
Sep 15, 2015
Hongliang Sun + 1
Open Access