Leading-edge vortices due to low Reynolds number flow past a pitching delta wing

Abstract

Flow past a pitching delta wing is examined in a water channel for a range of mean angle of attack. The wing is perturbed sinusoidally over a tenfold range of reduced frequency, in order to determine the nature of the vortex development and breakdown. There occur two basic types of vortex development: at low frequencies, the vortex core develops in the upstream direction towards the apex; at high frequencies, there is ejection of the leading edge of the vortex core from the apex in the downstream direction. Correspondingly, the direction of the dynamic hysteresis loop of vortex breakdown location vs angle of attack is determined by the type of vortex development. During unsteady development of the vortex core, the axial velocity on the centerline of the vortex is essentially constant with distance along the core. At the onset of vortex breakdown, there is abrupt deceleration; the velocity variations in this region exhibit a similar form for a range of angle of attack and reduced frequency.Nomenclature C =chord f e -excitation frequency K = reduced frequency = irf e C/ UL x > -streamwise extent of deceleration along centerline of vortex core P = pitch of helical streamline Re = Reynolds number =U 00 C/v r = radius of helical streamline C/oo = freestream velocity u = axial velocity of leading-edge vortex u c -axial velocity on centerline of vortex ( w c)max = maximum value of axial velocity on centerline of vortex v e = swirl velocity of vortex x -distance from apex of wing along centerline of vortex core x b = distance of vortex breakdown from apex along centerline of core x' -distance along centerline of vortex core from onset of deceleration Xp = distance from apex along leading edge of wing to location of wire probe X R = reference location along leading edge of wing for evaluating parameters of vortex a = angle of attack a.= mean angle of attack \ e = effective wavelength = U w /f e <t > = swirl angle = tan ~l V e /û max = maximum value of swirl angle 0 = angular deflection of helical streamline pattern v = kinematic viscosity

Effects of Unsteady Trailing-Edge Blowing on Delta Wing Aerodynamics

“…This amplitude attenuation is similar for both the slender and nonslender wings. This observation is also similar to the findings of previous investigations for unsteady wings [21][22][23][24][25].…”

“…It can be observed that X bd =c and C N exhibit similar trends of increasing with increasing f . This is similar to the findings of previous investigations for unsteady wings [21][22][23][24][25]. The phase lag b of X bd =c for the slender delta wing is comparable to those of the nonslender delta wing.…”

“…The response of wing vortical flow is expected to be similar, at least qualitatively, to that of unsteady wings. Hysteresis and time-lag of vortical flows and vortex breakdown over pitching or plunging wings are well known [21][22][23][24][25]. In this article, to simulate the dynamic thrust vectoring for a maneuver, the jet velocity (hence, momentum coefficient) was varied as a function of time using a control valve.…”

Control of vortex breakdown by a transversely oriented wire

“…7 In the event that the delta wing undergoes unsteady motion, the nature of the vortex breakdown is altered. The most predominant feature is a phase shift between the motion of the wing and the onset of breakdown, as shown by Woffelt, 8 Gilliam et al, 9 Reynolds and Abtahi, 10 Hudson et al, 11 Thompson, 12 Magness et al, 13 Atta and Rockwell, 14 LeMay et al, 15 Jarrah, 16 Ashley et al, 17 and Rockwell;18 all of the foregoing investigations have been for pitching motion. Analogous types of phase shift of breakdown occur for rolling motion of the wing as shown by Hanff and Huang, 19 Ng et al, 20 and Cipolla et al 21 Conceptual features of the complex nature of vortex breakdown, interpreted in the context of experiments, theory, and numerical simulations are provided by the reviews and assessments of Sarpkaya, [22][23][24] Hall,25 Liebovich, 26,27 Escudier, 28 Brown and Lopez, 29 Lopez and Perry, 30 Delery, 31 and Wang and Rusak.…”

Laser-scanning particle image velocimetry applied to a delta wing in transient maneuver

“…Recent investigations have focussed on visualization of the vortex breakdown phenomenon during sinusoidal (Woffelt 1986, Atta andRockwell 1990) and ramp pitching Abtahi 1987, Magness et al 1989) motions. All of these studies have shown a lag in the location of vortex breakdown with respect to the motion of the wing.…”