The passage toward stall of nonslender delta wings at low Reynolds number

Abstract

Separated flow over the leeside of relatively nonslender delta wings was studied experimentally. Such flowfields are more complex than those of the slender delta wing of very low aspect ratio. A version of Stereo Digital Particle Image Velocimetry was applied to measurements in a low speed water tunnel, at Reynolds numbers below 20,000, for delta wing models of 50° and 65° leading edge sweep angles and 30° windward-side leading edge bevels. Since the objective was to draw comparisons to the stall of classical high aspect ratio wings, low angles of attack were emphasized, with most data points taken in the 5°-20° angle of attack range. Measurements were taken over the starboard portion of the wing planform in crossflow planar slices near the apex region, yielding all three components of the velocity field, albeit restricted to planar cuts. Vorticity and circulation were calculated from these measurements. All three components of vorticity were obtained in select cases, by central-differencing velocity data across triplets of adjacent interrogation planes. In addition, flow visualization by dye injection into the windward apex stagnation region was used to confirm the presence of primary and secondary leading edge vortices, to qualitatively verify the locations of vortex breakdown, and to verify the stereo digital particle image velocimetry results. Both delta wings exhibit stable, coherent leading edge vortices at very low angles of attack, down to 2.5°. Results for the 65° wing were in accordance with the literature. The 50° wing, however, exhibited flow characteristics akin to both slender delta wings, and wings of high aspect ratio, and generally exhibited stronger and more robust leading edge vortices than usually observed. For the 50° wing, the primary leading edge vortices were stable below 10° angle of attack, with gradual and steady upstream progression of the vortex breakdown region with increasing angles of attack, from aft of the trailing edge to approximately the midchord. Secondary leading edge vortices were found to decay more abruptly, and at lower angle of attack than the primaries, all but disappearing by 10° angle of attack. This fact has the potential of serving as the basis for a predictive criterion for breakdown of the primary vortices. The entire vortex system undergoes large-scale instabilities in the 12°-20° angle of attack range. While the flow visualization was inconclusive, particle image velocimetry confirmed that breakdown sweeps over the entire forward third of the wing planform in going from 12.5° to 15° angle of attack. This change is characterized by a sharp drop in axial velocity in the primary leading edge vortex core region, along with a loss of coherent vortical structure normally associated with this region. The leading edge shear layer, however, remains in an organized rolled-up state. By 20°, the flow over the leeward side of the wing is at the threshold of complete separation, with flow along the wing centerline stalling as the left and right separated regions grow and merge. Both wings exhibited a largely stagnant region outboard of the primary LEV and inboard of the leading edge shear layer, especially at angles of attack beyond 10°. This phenomenon is consistent with some prior observations at Reynolds numbers on the order of 20,000 and below, and differs sharply from that at higher Reynolds numbers. Further experiments are necessary to elucidate the cause and extent of Reynolds number influence on separation near the leeward surface. Also, the 50° wing is probably of too high sweep to be a true limiting case for the existence of coherent leading edge vortices, for the conditions of the present experiment. But the abruptness of its stall and the close relationship between the leading edge vortex flow and the leeward surface boundary layer are qualitatively indicative of such a transitional case from slender delta wing separation to classical airfoil stall.