Michael V. Ol

Leading-Edge Vortex Structure of Nonslender Delta Wings at Low Reynolds Number

The velocity field near the apex region of moderately swept delta wings was measured in a water tunnel, using a version of stereoscopic digital particle imaging velocimetry. Flow visualization was also used to verify these results. In contrast to most recent studies, low angles of attack were emphasized, with most data in the range of 5–20 deg. Delta wings of 50- and 65-deg leading-edge sweep and 30-deg windward-side bevels were tested at Reynolds numbers of 6x10^3 –1.5x10^4. At these low Reynolds numbers, secondary leading-edge vortices were weak, giving way to essentially stagnant flow outboard of the primary leading-edge vortices at the higher angles of attack. Otherwise, velocity data for the 65-deg wing were consistent with well-known observations for slender delta wings. The 50-deg wing exhibited unexpectedly strong primary leading-edge vortices at low angles of attack, with a generally conical velocity field. Upstream progression of vortex breakdown with increasing angle of attack exhibited extensive regions of streamwise undulation. Leading-edge shear-layer rollup was observed in crossflow planes well downstream of the breakdown region, but with an increased occurrence of paired vortical structures of opposite sign inside the shear layer itself.

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.

Résumé of the AIAA FDTC Low Reynolds Number Discussion Group's Canonical Cases

The AIAA Fluid Dynamics Technical Committee’s Low Reynolds Number Discussion Group has introduced several “canonical” pitch motions, with objectives of (1) experimental-numerical comparison, (2) assessment of closed-form models for aerodynamic force coefficient time history, and (3) exploration of the vast and rather amorphous parameter space of the possible kinematics. The baseline geometry is a flat plate of nominally 2.5% thickness and round edges, wall-to-wall in ground test facilities and spanwise-periodic or 2D in computations. Motions are various smoothings of a linear pitch ramp, hold and return, of 40 and 45 amplitude. In an attempt to discern acceleration effects, sinusoidal and linear-ramp motions are compared, where the latter have short runs of high acceleration and thus high noncirculatory lift and pitch. Parameter variations include comparison of the flat plate with an airfoil and ellipse, variation of reduced frequency, pitch pivot point location and comparison of pitch to quasi-steady equivalent plunge. All motions involve strong leading edge vortices, whose growth history depends on pitch pivot point location and reduced frequency, and which can persist over the model suction-side for well after motion completion. Noncirculatory loads were indeed found to be localized to phases of motion where acceleration was large. To the extent discernable so far, closed-form models of lift coefficient on the pitch upstroke are relatively straightforward, but not so on the downstroke, where motion history effects complicate the return from stall. Broad Reynolds number independency, in flowfield evolution and lift coefficient, was found in the 10 to 10 range.

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 ...

Wake Vorticity Measurements for Low Aspect Ratio Wings at Low Reynolds Number

Trailing vortex structure of low aspect ratio wings was studied in a water tunnel at Reynolds numbers of 8000 and 24,000 using dye injection and digital particle image velocimetry in cross-flow planes in the near wake, for rectangular, semi-elliptical, and delta-wing planforms. The velocity data were used to calculate lift via circulation and effective span, and the results were compared with force balance measurements and classical inviscid theory. The objectives of the study were to assess how low-Reynolds number effects might affect the measurement of lift coefficient from tip-vortex circulation, how well the measurements fit the various theoretical models of lift curve slope for low aspect ratio wings, and the extent to which planform shape affects lift coefficient while aspect ratio and planform area are kept constant. All models were thin flat plates with square edges

High-Amplitude Pitch of a Flat Plate: an Abstraction of Perching and Flapping

We compare water tunnel experiment and 2D vortex-particle computation for a generalization of the classical problem of flat-plate constant-rate pitch and related motions, at frequencies and Reynolds numbers relevant to Micro Air Vehicle applications. The motivation is problems of maneuvering, perching and gust response. All of the examined flows evince a strong leading edge vortex. Increasing pitch rate tends to tighten the leading edge vortex and to produce a trailing-edge vortex system dominated by a counter-rotating pair. Pitch pivot point location is crucial to the leading edge vortex size and formation history, and to its subsequent behavior in convecting over the airfoil suction-side. Despite the respective limitations of the experiment and computations, agreement in vorticity fields between the two at an overlapping case at Re = 10,000 is good, whence it is possible to use the computation to obtain integrated force data unavailable in the experiment. These were studied for Re= 100 and 1000. Lift prediction from the computation shows a direct proportionality of lift to the pitch rate on the pitch upstroke. Finally, we compare pitch vs. plunge, and find that quasi-steady prediction is reasonably successful in predicting a combined pitch-plunge that effectively cancels the leading edge vortex, but not in canceling the trailing vortex system.

Computation vs. Experiment for High-Frequency Low-Reynolds Number Airfoil Pitch and Plunge

For a set of pure-pitch and pure-plunge sinusoidal oscillations of the SD7003 airfoil, phase-averaged measurements using particle image velocimetry in a water tunnel are compared with computations using an Immersed Boundary Method and an unsteady Reynolds-Averaged Navier Stokes solver. Re = 40,000 and Re = 10,000, based on free stream velocity and airfoil chord, were chosen as representative values for, respectively, a case where transition in attached boundary layers would be of some importance, and a case where transition would not be expected to occur in attached boundary layers. The two computational approaches were compared for capacity to resolve shed vortical structures near the airfoil and in the wake, and for capacity to resolve the mean streamwise momentum balance in the wake. The plunge and pitch were each at reduced frequency k = 3.93 and with kinematically equivalent amplitudes of effective angle of attack, with the pivot point at the quarter chord. For the plunge cases, agreement between computation and experiment was qualitatively excellent and quantitatively acceptable, but for the pitch cases, the wake structure in the experiment was markedly different from that predicted by both computations, which were however similar among one another. This result was not appreciably altered by whether or not the test section walls were modeled in the computation. In all cases, Reynolds number effects were found to be negligible. Experimental-computational agreement for plunge, but lack of agreement for pitch, is presently left unresolved.

Experimental Investigation of Pitching and Plunging Airfoils at Reynolds Number between 1x10^4 and 6x10^4

An experimental investigation was performed on a nominally two-dimensional pitching and plunging SD7003 and flat plate at Reynolds number 1 × 10, 3 × 10, and 6 × 10. The experiment was conducted at the University of Michigan water channel facility using phaseaveraged particle image velocimetry (PIV) technique to quantify the flow field. Two sets of airfoil kinematics were used in this study; a combined pitching and plunging motion, and a pure plunging motion. The flow topology and wall velocity profiles from the PIV measurements showed a Re dependence on a pitching and plunging SD7003 where the extent of flow separation is reduced at a relatively high Re. On the contrary, flat plate displayed a large leading edge separation flow characteristic that was independent of Re. For both airfoil cross-sections used in the experiment, turbulence statistics indicated laminar to turbulent transition phenomena at low Re. The study shows the leading edge shape effect on the flow transition and separation characteristics. A pure plunging motion of SD7003 and flat plate at Re = 60,000 showed the formation of the leading and trailing edge vortices. In addition, a quantitative analysis showed an apparent phase lag present on SD7003 relative to the flat plate. In order to validate the experimental data, a flow comparison between the University of Michigan and AFRL was performed.

Flexible- and rigid-wing micro air vehicle : Lift and drag comparison

Introduction M INIATURIZATION of unmanned air vehicles in military applications leading toward the so-called micro air vehicles (MAV) has introduced considerable challenges in aerodynamic efficiency, handling and control. The U.S. Air Force Research Laboratory, Munitions Directorate, Flight Vehicles Integration Branch developed a MAV with a flexible wing for U.S. Air Force Special Tactics Teams. The flexible wings can be folded, allowing storage of the MAV in a compact tube.

Fluid Dynamics of Pitching and Plunging Airfoils of Reynolds Number between 1×10 4 and 6×10 4

We consider a combined experimental (two-dimensional particle image velocimetry in a water tunnel) and computational (two-dimensional Reynoldsaveraged Navier-Stokes) investigation to examine the effects of chord Reynolds number on the dynamics of rigid SD7003 airfoil undergoing pitching and plunging motion in nominally two-dimensional conditions. Appreciable qualitative distinction in a moderately dynamically-stalled case in going from Re = 1×10 4 to Re = 6×10 4 was observed, suggesting nontrivial impact of viscosity even in conditions of strong forcing by motion kinematics. Additionally, computed lift coefficient time history is compared with Theodorsen’s unsteady linear airfoil theory. The velocity and vorticity fields were in excellent agreement between experiment and computation for those phases of motion where the flow was attached; moderate agreement was achieved when the flow was separated. The small disagreements were consistent with the expected inaccuracies due to the turbulence model used. Similarly, Theodorsen’s theory was able to predict the computed lift coefficient quite well when the flow was attached, and moderately acceptable otherwise.