Kenneth Granlund

Investigations of Lift-Based Pitch-Plunge Equivalence for Airfoils at Low Reynolds Numbers

The limits of linear superposition in two-dimensional high-rate low-Reynolds-number aerodynamics are examined by comparing the lift-coefficient history and flowfield evolution for airfoils undergoing harmonic motions in pure pitch, pure plunge, and pitch―plunge combinations. Using quasi-steady airfoil theory and Theodorsens formula as predictive tools, pitching motions are sought that produce lift histories identical to those of prescribed plunging motions. It follows that a suitable phasing of pitch and plunge in a combined motion should identically produce zero lift, canceling either the circulatory contribution (with quasi-steady theory) or the combination of circulatory and noncirculatory contributions (with Theodorsens formula). Lift history is measured experimentally in a water tunnel using a force balance and is compared with two-dimensional Reynolds-averaged Navier―Stokes computations and Theodorsens theory; computed vorticity contours are compared with dye injection in the water tunnel. Theodorsens method evinces considerable, and perhaps surprising, resilience in finding pitch-to-plunge equivalence of lift-coefficient―time history, despite its present application to cases in which its mathematical assumptions are demonstrably violated. A combination of pitch and plunge motions can be found such that net lift coefficient is nearly identically zero for arbitrarily high reduced frequency, provided that amplitude is small. Conversely, cancellation is possible at large motion amplitude, provided that reduced frequency is moderate. The product of Strouhal number and nondimensional amplitude is therefore suggested as the upper bound for when superposition and linear predictions remain valid in massively unsteady two-dimensional problems.

Experiments and Computations on Abstractions of Perching

The flight maneuver of perching is abstracted as a linear pitch ramp, with and without a deceleration in the free-stream direction. We consider, first, experimental-computational comparison for flowfield and aerodynamic force coefficients for an SD7003 airfoil pitching from α = 0o to 45o; and second, an experimental survey of reduced frequency and pivot point for a range of flat plate pitching cases from 0o to 90o. The computational approach is 3D Large Eddy Simulation, and the experimental approach is by three degree of freedom electric motion-rig in a water tunnel. Accurate flowfield resolution in deep-stall is seen to require a large spanwise extent of computational domain. Meanwhile, experiment can be plagued with blockage, and dynamic blockage was seen to behave differently than static blockage. Even very low reduced frequencies of motion give lift overshoot beyond static stall, but comparatively large frequencies are necessary before the lift curve slope changes, either due to rate effects or acceleration effects. Moving the pitch pivot point further aft tends to attenuate both lift and drag production, and pitching about the three-quarter chord point cancels the rate-effect, in agreement with quasi-steady linear airfoil theory. Surprisingly, the aerodynamic coefficient history differs little between cases with and without streamwise deceleration, except towards the very end of the motion. The implication is that perching-type of ground tests or computations can be adequately conducted in a steady free-stream.

Airfoil Longitudinal Gust Response in Separated vs. Attached Flows

Airfoil aerodynamic loads are expected to have quasi-steady, linear dependence on the history of input disturbances, provided that small-amplitude bounds are observed. We explore this assertion for the problem of periodic sinusoidal streamwise gusts, by comparing experiments on nominally 2D airfoils in temporally sinusoidal modulation of freestream speed in a wind tunnel vs. sinusoidal displacement of the airfoil in constant freestream in a water tunnel. In the wind tunnel, there is a streamwise unsteady pressure gradient causing a buoyancy force, while in the water tunnel one must subtract the inertial load of the test article. Both experiments have an added-mass contribution to aerodynamic force. Within measurement resolution, lift and drag, fluctuating and mean, were in good agreement between the two facilities. For incidence angle below static stall, small-disturbance theory was found to be in good agreement with measured lift history, regardless of oscillation frequency. The circulatory component of ...

Augmentation of Inviscid Airfoil Theory to Predict and Model 2D Unsteady Vortex Dominated Flows

A criterion for predicting flow separation and reattachment at the leading-edge using a Leading-Edge Suction Parameter (LESP) is presented. Stemming from inviscid theory, the LESP serves to predict the onset of separation or reattachment at the leading-edge for any unsteady motion using a critical value which is defined by the airfoil shape and Reynolds number of operation. This criterion is applied to a flat plate and an SD7003 airfoil undergoing various pitch and plunge motions and the critical LESP values for these airfoils are seen to predict the onset of separation or reattachment at the leading-edge, on both upper and lower surfaces. Separation at the leading-edge and subsequent formation of a leading-edge vortex (LEV) is accompanied by a loss in the leading-edge suction force resulting in increased drag. However, formation of LEV also serves to prevent separation at the trailing-edge and keeps the bound circulation intact, thus yielding high lift even at large angles of attack where the flow would have been fully separated otherwise. Using the criterion presented in this paper, it is possible to design kinematics which promote or suppress LEV formation by moving the LESP above or below its critical value.

Vortex dynamics around pitching plates

Vortex dynamics of wakes generated by rectangular aspect-ratio 2 and 4 and two-dimensional pitching flat plates in free stream are examined with direct numerical simulation and water tunnel experiments. Evolution of wake vortices comprised of tip, leading-edge, and trailing-edge vortices is compared with force history for a range of pitch rates. The plate pivots about its leading edge with reduced frequency from π/8 to π/48, which corresponds to pitching over 1 to 6 chord lengths of travel. Computations have reasonable agreement with experiments, despite large differences in Reynolds number. Computations show that the tip effects are confined initially near the wing tips, but begin to strongly affect the leading-edge vortex as the motion of the plate proceeds, with concomitant effects on lift and drag history. Scaling relations based on reduced frequency are shown to collapse aerodynamic force history for the various pitch rates.

Theoretical, Computational and Experimental Studies of a Flat Plate Undergoing High-Amplitude Pitching Motion

A pitch-up, hold, pitch-down motion for a flat plate is studied using theoretical, computational (immersed boundary method), and experimental (water-tunnel) methods. This motion is one of several canonical pitch motions introduced by the AIAA Fluid Dynamics Technical Committee’s Low Reynolds Number Discussion Group. An inviscid theoretical method that is applicable to non-periodic motions and that accounts for large amplitudes and nonplanar wakes is employed. Results from theory are compared against those from computation and experiment which are also compared with each other. The variation of circulatory and apparent-mass loads as a function of pivot location for this motion is examined. The flow phenomena leading up to leading edge vortex shedding and the limit of validity of the inviscid theory in the face of vortex dominated flows is investigated. Also, the effect on pitch amplitude on leading edge vortex shedding is examined and two distinctly different vortex dominated flows are studied using dye flow visualizations from and experiment and vorticity plots from computation.

Effect of Root Cutout on Force Coefficients of Rotating Wings

b = wingspan, m c = wing chord, m Re = Reynolds number, Vref; maxc∕v rr = wing root radius or root cutout rt = wing tip radius, m r75 = radius to reference plane, axis-relative method, m r75 = radius to reference plane, root-relative method, m s = distance travelled at wing reference plane, m s∕c = stroke-to-chord ratio S = wing area, m Vref; max = maximum local velocity at reference plane, m · s −1 Vroot = local velocity at wing root, m · s −1 V tip = local velocity at wing tip, m · s −1

Experiments on Free-to-Pivot Hover Motions of Flat Plates

Using force measurements and flow visualization in a water tunnel, we consider motions of a flat plate with square edges, free to pivot about its leading edge, between incidence angle limits of ±45°. The plate’s leading edge undergoes a prescribed sinusoidal motion, either of rectilinear translation, or of pivoting or waving about a fixed point 0.5 chords away from one of the plate’s wingtips. During most of the translation semi-stroke in either direction, the plate rests against its incidence limiter to produce a positive angle of attack; this reverses on the opposite semi-stroke, producing a motion akin to normal-hover with delayed rotation. Two geometries are considered: a nominally 2D or wall-to-wall plate, and a plate of aspect ratio 3.4. Reynolds number effects in the range of 5000-20,000 were not found to be significant, but the ratio of stroke amplitude to plate chord determines Depending on stroke to chord amplitude, lag between plate rotation and translation will differ, and the resulting vortex production history and aerodynamic load production history will differ. Large stroke to chord ratios produces higher thrust coefficients and simpler vortex wakes. Thrust coefficient histories are very similar between the translating 2D and AR=3.4 plates, and resistive force coefficients are very similar amongst all three cases – suggesting that whatever distinctions between the three cases may be present in the flowfield due to putative spanwise pressure gradient, these effects do not systematically alter the integrated aerodynamic forces.

Unsteady aerodynamic characteristics of a translating rigid wing at low Reynolds number

Rectilinearly surging wings are investigated under several different velocity profiles and incidence angles. The primary wing studied here was an aspect ratio 4 rectangular flat plate. Studies on acceleration distance, ranging from 0.125c to 6c, and incidence angles 5°–45° were performed to obtain a better understanding of the force and moment histories during an extended surge motion over several chord-lengths of travel. Flow visualization and particle image velocimetry were performed to show the flow structures responsible for variations in force and moment coefficients. It was determined that the formation and subsequent shedding of a leading edge vortex correspond to oscillations in force coefficients for wings at high angle of attack. Comparing unsteady lift results to static force measurements, it was determined that for cases with large flow separation, even after 14 chords traveled at a constant velocity, the unsteady forces do not converge to the fully developed values. Forces were then broken up...

Low Reynolds number acceleration of flat plate wings at high incidence (Invited)

© 2016, (publisher Name). All rights reserved. This paper discusses the force history and flow topology of accelerating flat plate wings. The work is a collaborative effort to study fundamental, unsteady low Reynolds number flows under the umbrella of the NATO AVT-202 task group. The motion kinematics are designed to be relevant to the Micro-Air Vehicle (MAV) flight regime. A combination of empirical and computational techniques are used to obtain data for comparison. There is a striking correlation of lift history data and flow topology from both experimental and computational datasets. In an effort to source inputs for a low-order model, a Leading Edge Vortex (LEV)/Trailing Edge Vortex (TEV) relative advection velocity of 0:5.U∞ has been estimated based on the data.