David E. Rival

Recovery of Energy from Leading- and Trailing-Edge Vortices in Tandem-Airfoil Configurations

CP = nondimensional power c = airfoil chord cl = sectional lift coefficient cd = sectional drag coefficient f = frequency h = plunge amplitude k = reduced frequency, fc=U1 p = pressure Re = Reynolds number, U1c= Ret = turbulent Reynolds number t = period u = streamwise velocity v = normal velocity x = streamwise direction y = normal direction = angle of attack o = mean angle of attack 1 = amplitude of angle of attack = low Reynolds number coefficient = angular frequency, 2 f ij = Kronecker delta = kinematic viscosity t = eddy viscosity = phase between pitch and plunge = airfoil phasing ! = vorticity Subscripts

Growth and separation of a start-up vortex from a two-dimensional shear layer

The evolution of an isolated line vortex generated by a starting two-dimensional jet is studied experimentally using time-resolved particle image velocimetry. The vortex growth in this current configuration is not linked to any externally imposed length scales or interactions with other vortical structures or walls that could potentially influence vortex growth. A model for the early-stage vortex growth, based on the transport of circulation from the shear layer into the vortex, is proposed and found to agree well with experimental data. The model provides a scaling scheme for vortex growth using shear-layer characteristic velocity and shear-layer thickness. The vortex growth is limited through a gradual separation of the vortex from the feeding shear layer, arising from decreased shear-layer curvature. This phenomenon is linked to a competition between the shear-layer tendency to remain in the streamwise direction and the induced velocity from the vortex on the shear layer. Finally, a dimensionless numbe...

Vortex interaction of tandem pitching and plunging plates: a two-dimensional model of hovering dragonfly-like flight.

The force evolution and associated vortex dynamics on a nominal two-dimensional tandem pitching and plunging configuration inspired by hovering dragonfly-like flight have been investigated experimentally using time-resolved particle image velocimetry. The aerodynamic forces acting on the flat plates have been determined using a classic control-volume approach, i.e. a momentum balance. It was found that only the tandem phasing of ψ = 90° was capable of generating similar levels of thrust when compared to the single-plate reference case. For this tandem configuration, however, a much more constant thrust generation was developed over the cycle. Further examination showed that the force and vortex development on the fore-plate was unaffected by the tandem configuration and that nearly all variations in performance could be attributed to the vortex interaction on the hind-plate. By calculating the trajectory and strength of the hind-plates trailing-edge vortex, the chain-like vortex interaction mechanism responsible for improved performance at ψ = 90° could be identified. The underlying result from this study suggests that the dominant vortex interaction in dragonfly flight is two dimensional and that the spanwise flow generated by root-flapping kinematics is not entirely necessary for efficient propulsion but potentially due to evolutionary restrictions in nature.

The Quantification of Hemodynamic Parameters Downstream of a Gianturco Zenith Stent Wire Using Newtonian and Non-Newtonian Analog Fluids in a Pulsatile Flow Environment

Although deployed in the vasculature to expand vessel diameter and improve blood flow, protruding stent struts can create complex flow environments associated with flow separation and oscillating shear gradients. Given the association between magnitude and direction of wall shear stress (WSS) and endothelial phenotype expression, accurate representation of stent-induced flow patterns is critical if we are to predict sites susceptible to intimal hyperplasia. Despite the number of stents approved for clinical use, quantification on the alteration of hemodynamic flow parameters associated with the Gianturco Z-stent is limited in the literature. In using experimental and computational models to quantify strut-induced flow, the majority of past work has assumed blood or representative analogs to behave as Newtonian fluids. However, recent studies have challenged the validity of this assumption. We present here the experimental quantification of flow through a Gianturco Z-stent wire in representative Newtonian and non-Newtonian blood analog environments using particle image velocimetry (PIV). Fluid analogs were circulated through a closed flow loop at physiologically appropriate flow rates whereupon PIV snapshots were acquired downstream of the wire housed in an acrylic tube with a diameter characteristic of the carotid artery. Hemodynamic parameters including WSS, oscillatory shear index (OSI), and Reynolds shear stresses (RSS) were measured. Our findings show that the introduction of the stent wire altered downstream hemodynamic parameters through a reduction in WSS and increases in OSI and RSS from nonstented flow. The Newtonian analog solution of glycerol and water underestimated WSS while increasing the spatial coverage of flow reversal and oscillatory shear compared to a non-Newtonian fluid of glycerol, water, and xanthan gum. Peak RSS were increased with the Newtonian fluid, although peak values were similar upon a doubling of flow rate. The introduction of the stent wire promoted the development of flow patterns that are susceptible to intimal hyperplasia using both Newtonian and non-Newtonian analogs, although the magnitude of sites affected downstream was appreciably related to the rheological behavior of the analog. While the assumption of linear viscous behavior is often appropriate in quantifying flow in the largest arteries of the vasculature, the results presented here suggest this assumption overestimates sites susceptible to hyperplasia and restenosis in flow characterized by low and oscillatory shear.

A criterion for vortex separation on unsteady aerodynamic profiles

Experiments on leading-edge vortex (LEV) growth and detachment in a free-surface water tunnel with ve plunging leading-edge pro les have been conducted, comprising direct-force and Particle Image Velocimetry measurements. The tests have been performed at a Reynolds number of Re = 10; 000, a reduced frequency of k = 0:25 and a Strouhal number of St = 0:16, the latter two being typical of ying and swimming in nature over a large range of Reynolds numbers. The leading-edge shape is shown to in uence the feeding shear layer; hence the development of the LEV. For a delayed onset of LEV growth, the vorticity-eruption process on the pro le surface can also be delayed, such that the crossannihilation of the feeding and eruption layers is postponed. This e ect in turn delays the arrival of the rear (LEV) stagnation point at the trailing edge, which, once breached, causes the half saddle to lift o and form a full saddle, in turn allowing the rapid feeding of trailing-edge vorticity forward to cut o the LEV. Therefore, the trailing edge (chord length) plays a critical role of limiting the LEV size (circulation) and as such is found to be the most characteristic length scale for the vortex-separation process at higher Reynolds numbers, where the eruption process will be less pronounced.

On vortex evolution in the wake of axisymmetric and non-axisymmetric low-aspect-ratio accelerating plates

Impulsively started, low-aspect-ratio elliptical and rectangular flat plates were investigated to determine the role of geometric asymmetries on vortex evolution. Dye visualizations, force measurements, and particle image velocimetry were used throughout to characterize the variation between shapes. For all the shapes studied, aspect ratio was observed to have the largest influence on force production and vortex evolution. Non-uniform curvature and edge discontinuities characteristic of ellipses (with aspect ratios other than one) and rectangles, respectively, play a secondary role. Furthermore, it was shown that stably attached vortex rings form behind the circular and square flat plates, which reduce the instantaneous drag force of each plate until the vortex rings break down. In contrast, all flat plates with aspect ratios other than one are subjected to fast-modulating elliptical vortex rings in the wake. These vortex rings increase the drag force of each plate until pinch-off occurs. Finally, pinch-off was identified with the streamwise pressure-gradient field and compared with formation numbers calculated using the circulation-based methodology, yielding good agreement for all plates with aspect ratios greater than one.

On the Simulation of Complex Gusts at Low Reynolds Numbers

Two specific gust forms were simulated using Computational Fluid Dynamics. Simultaneously a flat-plate model was manipulated in a water-tunnel facility to generate equivalent effective incidence and velocity variations at the leading edge. By comparing the two results, the potential of simulating a gust with equivalent model motions was thus undertaken. A first-order analysis using classical unsteady theory predicted that a gust was equivalent to a moving model experiencing the same velocities so long as the reduced frequency was low. However, direct force measurements were found to contradict this result from classical analysis showing large deviations in the total measured forces. Further measurements using Particle Image Velocimetry revealed that leading-edge vortex (LEV) growth on a moving model was equivalent to LEV growth from a gust for an equivalent effective leading-edge incidence and velocity. Despite this similarity in the LEV growth, both the added mass effects of an accelerating model, as well as the convective speed of the gust, were found to contribute large discrepancies between the gust simulation techniques.

Rapid area change in pitch-up manoeuvres of small perching birds.

Rapid pitch-up has been highlighted as a mechanism to generate large lift and drag during landing manoeuvres. However, pitching rates had not been measured previously in perching birds, and so the direct applicability of computations and experiments to observed behaviour was not known. We measure pitch rates in a small, wild bird (the black-capped chickadee; Poecile atricapillus), and show that these rates are within the parameter range used in experiments. Pitching rates were characterized by the shape change number, a metric comparing the rate of frontal area increase to acceleration. Black-capped chickadees increase the shape change number during perching in direct proportion to their total kinetic and potential energy at the start of the manoeuvre. The linear relationship between dissipated energy and shape change number is in accordance with a simple analytical model developed for two-dimensional pitching and decelerating airfoils. Black-capped chickadees use a wing pitch-up manoeuvre during perching to dissipate energy quickly while maintaining lift and drag through rapid area change. It is suggested that similar pitch-and-decelerate manoeuvres could be used to aid in the controlled, precise landings of small manoeuvrable air vehicles.

Characterizing the influence of upstream obstacles on very low head water-turbine performance

ABSTRACT The effect of an upstream obstacle – a backward-facing step (BFS) – on a very low head (VLH) water-turbine model has been investigated. The motivation of this study was to quantify the interaction between the VLH turbine and BFS, an abstraction of typical obstacles present in existing channels. Power measurements were obtained for three configurations; the turbine in the absence of the BFS was first examined as a baseline test, followed by configurations with the BFS placed at distances of half a turbine diameter and one turbine diameter upstream. It was found that turbine efficiency is comparable between the case with no step upstream and when the step is placed at one diameter. However, the configuration at half a diameter exhibited an efficiency deficit of approximately 7%. Particle image velocimetry measurements were then used to quantity the flowfield associated with loss in efficiency from the no step to the half a diameter step configuration. It was determined that the losses could be attributed to a highly non-uniform inlet velocity profile, which results in unsteady loading across the turbine blades.

On the separation mechanics of accelerating spheres

The instantaneous drag forces and wake mechanics of an accelerating sphere have been investigated experimentally. Drag forces are first compared to the circular flat plate, which is characterized by stable and Reynolds-number independent vortex-ring formation during accelerations from rest. For the sphere, vortex-ring formation is shown to be greatly suppressed by the time-dependent movement of the separation line during start-up towards the steady-state position, which induces strong vortex-body interactions. Next, inviscid theory is used to predict the state of the pressure-gradient field around a sphere during accelerations from a non-zero initial velocity. The azimuthal point of separation extracted from experimental data for the subcritical cases is found to be strongly correlated with the start of the adverse pressure gradient predicted by theory. For the supercritical cases, the point of separation is unaffected by the imposed accelerations and remains at the steady-state position. The results sugg...