Wing-tip vortex dynamics at moderate Reynolds numbers

Abstract

The flow over a flat-tipped wing at three Reynolds numbers: Re=1×104, Re=4×104, and Re=1×105 is investigated using direct numerical simulation. A set of grid independent results are obtained which allow for the dynamics of the tip flow, trailing vortices, and their interplay with the boundary layer dynamics to be examined in detail. The results show significant changes across the Reynolds number range. At the lowest Reynolds number, a single trailing vortex forms downstream of the trailing edge, whereas multiple vortices form over the tip at higher Reynolds numbers. The tip geometry is shown to be important with regard to the development of different structures and in the transition of the flow from laminar to turbulent. This is due to unstable shear layers, with turbulent flow becoming entrained in the vortex cores at higher Reynolds numbers. These changing vortex dynamics mean that the value of the minimum vortex core pressure and its location change with Reynolds number. This has important consequences for cavitation inception and scaling for hydrodynamic applications. The influence of the tip flow on the boundary layer is further considered by comparing the flow with that of an infinite-span wing. Analysis of the two cases shows that the tip flow reduces the effective angle of attack, which prevents the flow separation at the leading edge that is responsible for the boundary layer transition for the infinite-span case. This, in turn, changes the character of the trailing edge flow which would have significant consequences on the trailing edge noise.