Three-dimensional flows around low-aspect-ratio flat-plate wings at low Reynolds numbers

Abstract

Three-dimensional flows over impulsively translated low-aspect-ratio flat plates are investigated for Reynolds numbers of 300 and 500, with a focus on the unsteady vortex dynamics at post-stall angles of attack. Numerical simulations, validated by an oil tow-tank experiment, are performed to study the influence of aspect ratio, angle of attack and planform geometry on the wake vortices and the resulting forces on the plate. Immediately following the impulsive start, the separated flows create wake vortices that share the same topology for all aspect ratios. At large time, the tip vortices significantly influence the vortex dynamics and the corresponding forces on the wings. Depending on the aspect ratio, angle of attack and Reynolds number, the flow at large time reaches a stable steady state, a periodic cycle or aperiodic shedding. For cases of high angles of attack, an asymmetric wake develops in the spanwise direction at large time. The present results are compared to higher Reynolds number flows. Some non-rectangular planforms are also considered to examine the difference in the wakes and forces. After the impulsive start, the time at which maximum lift occurs is fairly constant for a wide range of flow conditions during the initial transient. Due to the influence of the tip vortices, the three-dimensional dynamics of the wake vortices are found to be quite different from the two-dimensional von Kármán vortex street in terms of stability and shedding frequency.

The leading-edge vortex and quasisteady vortex shedding on an accelerating plate

“…Comparisons with low Reynolds number towing tank experiments ͑for 3D foils͒ confirms the efficacy of this approach. 4 The computational domain extends overall to a distance of 64 and 32 chord lengths in the streamwise and normal directions. Our IB method uses a series of overlapping, consecutively larger and coarser domains.…”

“…The early transient results of PW matched somewhat closely with Wagner's theory of unsteady airfoils. 7 However, the peak in lift coefficient found by Taira and Colonius, 4 Dickinson and Götz, 5 and others was not emphasized in the results of PW when a power of m = 1 was applied.…”

“…Existing literature, including Birch et al 1 and Taira and Colonius, 4 credit the attachment of 3D startup LEVs primarily to spanwise flow. Such flow toward the wingtip tends to move momentum and vorticity out of the LEV, giving it stability.…”

“…The fact that flapping wings tend to displace only two to four chord lengths during each half-stroke implies that flapping-wing animals can benefit from the large lift augmentation of initial LEV growth. Taira and Colonius 4 computed impulsively started threedimensional ͑3D͒ flows at Re= 300 and 500. In this study, the aspect ratio, angle of attack, and geometry of a flat plate were varied.…”

Control of vortex shedding on two- and three-dimensional aerofoils

“…For low AR, three-dimensional flat plates at low Re, vortex shedding still occurs, but data are very limited. Taira & Colonius [14] investigated low-AR flat plates for Re = 300 and 500 over a range of a and for rectangular, elliptical, semicircular and deltashaped planforms. The onset of vortex shedding is delayed to higher Re and a as the AR is decreased, owing to a stabilizing influence of the tip vortices.…”