David M. Birch

Structure and Induced Drag of a Tip Vortex

The three-dimensional flow structure of a tip vortex in the near wake of both a rectangular, square-tipped NACA 0015 airfoil and a high-lift cambered airfoil was investigated by using a seven-hole pressure probe at Re = 2.01 x 10 5 . Lift-induced drag was computed based on vorticity and was compared with force-balance data. For both the airfoils tested, the vortex strength reached a maximum immediately behind the trailing edge and remained nearly constant up to two chord lengths downstream. As the airfoil incidence increased, the increase in the lift force resulted in a basically linear increase in the vortex strength and the peak values of the tangential velocity and vorticity, whereas the vortex radius did not appear to have a clear dependence on the vortex strength. Depending on the airfoil incidence, the core axial velocity could be wake-like or jet-like. The normalized circulation within the inner region of the nearly axisymmetric tip vortex exhibited a universal, or self-similar, structure. The NACA 0015 airfoil, however, possessed smaller tangential velocities but similar vortex core diameters compared to those of a cambered airfoil

Investigation of the near-field tip vortex behind an oscillating wing

The near-field tip-vortex flow structure behind an oscillating NACA 0015 wing was investigated at

Similarity of the streamwise velocity component in very-rough-wall channel flow

{\hbox {{\it Re}}}\,{=}\,1.86 \times 10^{5}

IUTAM Symposium on Flow Control and MEMS

. For attached-flow and light-stall oscillations, a small hysteretic property existed between the pitch-up and pitch-down motion, and many of the vortex flow features were found to be qualitatively similar to those of a static wing. For deep-stall oscillations, the wing oscillations imposed a strong discrepancy in contour shapes and magnitudes between the pitch-up and pitch-down phases of the oscillation cycle. The vortex was less organized during pitch-down (as a result of leading-edge-vortex-induced massive flow separation) than during pitch-up. The tangential velocity, circulation and lift-induced drag increased progressively with the airfoil incidence, and had higher magnitudes during pitch-up than during pitch-down, while varying slightly with the downstream distance. The vortex size, however, was larger during pitch-down than during pitch-up. The axial flow was always wake-like during the deep-stall oscillation cycle. The normalized circulation within the inner region of the tip vortex also exhibited a self-similar structure, similar to that of a static wing, and was insensitive to the reduced frequency.

Self-similarity of trailing vortices

The streamwise velocity component is studied in fully developed turbulent channel flow for two very rough surfaces and a smooth surface at comparable Reynolds numbers. One rough surface comprises sparse and isotropic grit with a highly nonGaussian distribution. The other is a uniform mesh consisting of twisted rectangular elements which form a diamond pattern. The mean roughness heights (± the standard deviation) are, respectively, about 76(±42) and 145(±150) wall units. The flow is shown to be two-dimensional and fully developed up to the fourth-order moment of velocity. The mean velocity profile over the grit surface exhibits self-similarity (in the form of a logarithmic law) within the limited range of 0.04 y/h 0.06, but the profile over the mesh surface does not, even though the mean velocity deficit and higher moments (up to the fourth order) all exhibit outer scaling over both surfaces. The distinction between self-similarity and outer similarity is clarified and the importance of the former is explained. The wake strength is shown to increase slightly over the grit surface but decrease over the mesh surface. The latter result is contrary to recent measurements in rough-wall boundary layers. Single- and twopoint velocity correlations reveal the presence of large-scale streamwise structures with circulation in the plane orthogonal to the mean velocity. Spanwise correlation length scales are significantly larger than corresponding ones for both internal and external smooth-wall flows.

Tip vortex behind a wing undergoing deep-stall oscillation

Proceedings of the IUTAM Symposium held at the Royal Geographical Society, 19-22 September 2006, hosted by Imperial College, London, England.

Vortex Shedding and Spacing of a Rotationally Oscillating Cylinder

Trailing vortices have been repeatedly shown to exhibit a remarkably robust self-similarity independent of the Reynolds number and upstream boundary conditions. The collapse of the inner-scaled circulation profiles of a trailing vortex has even been previously demonstrated for the cases of highly unsteady and turbulent vortex systems, as well as for vortices which were incompletely developed. A number of factors which contribute to and may artificially promote this self-similarity are discussed. It is shown that the amplitude of vortex “wandering” (or the random modulations in the vortex trajectory) observed in some experimental measurements are of sufficient amplitude to cause any arbitrary finite and axisymmetric flow structure to collapse with an idealized trailing vortex when scaled on inner parameters. It is further shown that, for the case of an incompletely developed wing-tip vortex, similarity in the outer core region may be an artefact of the rate of roll-up of the vortex sheet. Great care must, ...

Effect of Trailing-Edge Flap on a Tip Vortex

The flow structure of a tip vortex in the near field of a NACA 0015 wing with an effective aspect ratio of 5.04 undergoing a deep-stall oscillation with a(t) = 18 deg + 6 deg sin ωt at Re = 1.86 × 10 5 was investigated. The wing oscillation imposed a strong discrepancy in contour shapes and magnitudes between the pitch-up and pitch-down phases of the oscillation cycle. The vortex was more organized and nearly axisymmetric for x/c > 0.5 during pitch-up than during pitch-down. The peak tangential velocity and vorticity and the strength and size of the vortex increased with a(t), except in the vicinity of α max , and had higher values during pitch-up than during pitch-down. The axial flow was always wake like and the velocity deficit decreased with α(t), while exhibiting a sharp increase and decrease on the upstroke and downstroke in the vicinity of α max , respectively. The tangential velocity decreased slightly with the downstream distance. The vortex size increased rather significantly with x/c during pitch-down while remaining virtually unchanged during pitch-up. The inner region of the vortex exhibited a self-similar structure, similar to that of a stationary wing. The induced drag increased with a(t) and had a local maximum at 20 deg during pitch-up.

Tip Vortex Behind a Wing Oscillated with Small Amplitude

Introduction T HE possibility of the suppression or elimination of vortex shedding is of considerable practical interest from the standpoint of wake modification and reduction of drag, as well as of flowinduced vibration. Various passive and active control schemes have been attempted to affect the vortex wake formation process. Recently, it has been shown that a considerable amount of control of the cylinder vortex wake can be achieved through rotational oscillation and that when the flow takes place in a fluid relative to a rotationally oscillating cylinder, a new series of flow phenomena could arise.1−4 Tenada1 studied the effects of rotational oscillation for Re(= du∞/ν, where ν is the fluid viscosity) ranging between 30 and 300, and indicated that, at very high oscillation frequency f0 and amplitude, the dead-fluid region behind a cylinder and the vortex-shedding process could be nearly eliminated. The amplitude is given by 1 = π θ f0d/2u∞ > 7–27, where θ is the peak-to-peak amplitude in degrees, d is the cylinder diameter, and u∞ is the freestream velocity. Recently, Filler et al.2 studied experimentally the frequency response of the shear layers separating from a circular cylinder subjected to small-amplitude oscillations, that is, 1 ≤ 0.03, for Re = 250–1200, and observed a coupling of the cylinder oscillations with both modes of vortex shedding, that is, shear-layer vortices and primary Karman vortex shedding. Filler et al. also reported that by rotationally oscillating the cylinder at or near the natural Karman frequency, the shear-layer instability was promoted and the Karman mode of vortex shedding was also affected. On the other hand, Tokumaru and Dimotakis3 have shown that large-amplitude ( 1 ≤ 16) and highfrequency ( f0/ fk = 1–20, where fk is the natural Karman shedding frequency) rotational oscillations, together with the spinning of the cylinder, can suppress the vortex shedding and produce significant reduction in the profile drag acting on the cylinder at Re = 1.5 × 104. The objective of this study was to investigate the variation of the lateral and longitudinal spacings of the shed vortices and the vortex formation with the cylinder oscillation at Re = 1.75 × 103 by the use of hydrogen-bubble and particle streakline flow visualization methods. Special attention was given to the study of the type of wake synchronization that might occur throughout an intermediate oscillation range ( f0/ fk < 4 and 1 ≤ 1.0), between those of Filler et al. and Tokumaru and Dimotakis.

Calibration and use of n-hole velocity probes

The near-wake tip vortex flow structure behind a NACA 0015 airfoil with a trailing-edge flap was investigated. Lift-induced drag was computed based on vorticity and was compared with force-balance data. The vortex strength reached a maximum immediately behind the trailing edge and remained nearly constant up to two chord lengths downstream (x/c = 3). The displaced flap produced a more concentrated vortex of similar diameter and a higher induced drag compared to that of a baseline airfoil and had a larger radial gradient in circulation strength for flap angle δ < 15 deg; the vortex radius increased significantly for δ =2 0deg. For δ < ‐ 15 deg, the axial flow velocity was jetlike with the peak values increased with the flap angle. The nearly symmetric vortex was observed at x/c =2 .25 fo ra displaced flap while at x/c =1 . 5f or a baseline airfoil. The stength and interaction of the secondary and main vortices along the tip were also found to increase with the flap angle, and the vortex flow (immediately downstream of the deflected flap) was dominated by the presence of multiple vortices. The normalized circulation in the inner part of the symmetric vortex exhibited a self-similar structure, insensitive to the flap angle.