Caleb J. Barnes

Analysis of streamwise-oriented vortex interactions for two wings in close proximity

This investigation addresses the impingement of the trailing vortex provided by a leader-wing upon a follower-wing operating in close proximity. Exploration of the relative spacing between the two wings reveals several distinct flow regimes occur within a small range of lateral positions of the incident vortex. These changes effectively alter the evolution of the follower-wing wake via mutual induction between the incident and trailing vortices. Several unsteady mechanisms impact the general flow field in each regime. The incident vortex for an inboard impingement rapidly decays over the wing due to transition to turbulence. A tip-aligned vortex results in a highly unsteady interaction and generates enhanced surface pressure fluctuations beneath the tip vortex. Placing the incident vortex outboard elicits mutual instability between the leader and follower-wing trailing vortices. While lift-enhancement was found to be dominated by an inviscid increase in effective angle of attack, viscous effects in the ne...

High-Fidelity LES Simulations of Self-Sustained Pitching Oscillations on a NACA0012 Airfoil at Transitional Reynolds Numbers

This work explores self-sustained pitching oscillations of a NACA0012 airfoil operating at low-to-moderate Reynolds numbers in which the aerodynamic flow is in a transitional regime. One-degree of freedom (DOF) pitching oscillations were explored over a range of Reynolds numbers (7.7 × 10 < Rec ≤ 2.0 × 10). Laminar separation flutter grows naturally at the lowest Reynolds numbers. At Rec = 1.5 × 10, which falls above the previously identified flutter regime, sustained oscillations emerged following a disturbance applied to the structural model. This finding extends the applicable range of flow speeds beyond those previously reported and identifies a bifurcation of solution states at the extended Reynolds numbers. In all cases, negative aerodynamic damping is largely provided by suction beneath a separation bubble located behind the elastic axis. This feature induces a moment conducive to the pitching motion. Open trailing edge separation on the opposite surface transitions and reattaches immediately preceding the maximum angles of incidence. This event imparts a spike in the moment opposed to the pitching direction briefly damping oscillations. Earlier transition and reattachment of the trailing edge separation for the Rec = 1.5 × 10 case signals an earlier entrance to the negative work regime compared to the Rec = 1.1 × 10 case and resulting in a decreased LCO amplitude.

High-Fidelity Simulations of a Hovering Wing

Simulation of normal-hovering mode kinematics was considered for an aspect-ratio 2 flat plate wing over the range of Reynolds numbers of 200 ≤ Rec ≤ 2×104. A high-order implicit large-eddy simulation technique was used which has been shown to be an effective tool for laminar/transitional/turbulent regimes present in moderate Reynolds number flows. This work focuses on investigating the three-dimensional flow structure on low-aspectratio wings including the effects of the aspect-ratio and Reynolds number. The complex flow structure was investigated and discussed in detail for Rec = 1, 000. Increasing the Reynolds number beyond Rec = 500 revealed that the leading edge vortex transforms into an arch-type structure which was not present for the lowest Reynolds number case. Strong low-pressure regions that occur at the arch legs were found to serve as significant liftenhancement mechanisms. Additionally, lift was shown to increase with Reynolds number until little change occurs beyond Rec > 1 × 10. Operating hovering cycles at the higher Reynolds numbers tested could be advantageous due to increasing ratios of cycle-averaged lift to average cycle power. Also, a low-aspect-ratio simulation was compared to a twodimensional infinite-span computation at Rec = 200. The strength of the downward jet for the low-aspect-ratio wing was found to diminish compared to the infinite-span case resulting in an effectively higher effective angle of attack and earlier separation at the symmetry plane.

Numerical Simulations of Streamwise-Oriented Vortex/Flexible Wing Interactions

In this work, both rigid and flexible wings are subjected to a numerically imposed streamwise-oriented vortex and the unsteady flow, aerodynamic loading, and structural dynamics are evaluated. Impingement of the streamwise vortex on the rigid wing produces a spiraling instability in the vortex just upstream of the leading-edge. This helical flow disruption, which alternates between the upper and lower surfaces is shown to provide a source of unsteady loading. In response, the flexible wings exhibit oscillations about a time-mean vertical deflection at sub-harmonics of the incident vortex instability. The spiraling undulations of the vortex are exacerbated with decreasing rigidity which is shown to be influenced by the time-mean deflection of the wing rather than feedback effects from the dynamic response. Evaluation of several vertical offsets of the incident vortex on rigid wings reveals a strong dependency between vertical positioning and unsteady behavior of the incident vortex. For instance, direct impingement or a negative vertical offset can produce strong adverse pressure gradients that form as a direct consequence of vortex-surface interaction. The resulting deceleration of the axial velocity contributes to the formation of helical instabilities and potentially invoke spiral breakdown in more severe conditions. Conversely, a positive vertical offset removes the helical instability by placing the streamwise vortex inline with a favorable pressure gradient produced by flow accelerating over the leading-edge. However, pressure gradients associated with separation and stall downstream have the potential to introduce suction-side instability. While the vertical offset is shown to be less important than the lateral positioning in terms of aerodynamic benefits, it can have a significant impact on unsteady loading.

Numerical exploration of the origin of aerodynamic enhancements in [low-Reynolds number] corrugated airfoils

This paper explores the flow structure of a corrugated airfoil using a high-fidelity implicit large eddy simulation approach. The first three-dimensional simulations for a corrugated wing section are presented considering a range of Reynolds numbers of Rec = 5 × 103 to 5.8 × 104 bridging the gap left by previous numerical and experimental studies. Several important effects are shown to result from the corrugations in the leading-edge region. First, interaction between the detached shear layer and the first corrugation peak promotes recirculation upstream and enhances transition to turbulence due to flow instabilities. Thus, early transitional flow develops on the corrugated wing which helps to delay stall even at Reynolds numbers as low as Rec = 1 × 104. Transition is shown to occur as early as Rec = 7.5 × 103 and quickly advances toward the leading-edge as Reynolds number is increased. Modification of the first corrugation peak height produces significantly reduced separation and improved aerodynamic for...

High-Fidelity Simulations of a Flexible Heaving Finite-Aspect-Ratio Wing

The current work seeks to explore the effect of structural flexibility for a finite-aspectratio wing under low Reynolds number conditions (Rec = 10, 000), undergoing plunging oscillations at a post-stall angle of attack. A high-order implicit LES approach is used to solve mixed laminar/transitional/turbulent flowfields present at low Reynolds numbers. The wing structure is modeled using a geometrically nonlinear p-version Reissner-Mindlin finite element plate model. Structural deflections and aerodynamic forces are implicitly coupled through a sub-iteration process. The effects of passive flexibility on flow structure and aerodynamic forces are explored for both static and a purely plunging motion. Wing dynamics produced for the flexible wing resulted in significantly enhanced lift due in part to a progressive root-to-tip leading-edge formation and a strengthened tip vortex. A highly flexible wing produced a structural response with an inflection point near 3/4 outboard along the span and an improved operating efficiency. The implications of flexibility were shown to include lift-enhancement and the ability of flexible structures to serve as energysaving mechanisms by reducing power requirements. Applications to mitigate the effects of unsteadiness, such as gust-response, were also apparent in the most flexible wings.

High-Fidelity Simulations of a Corrugated Airfoil

Bio-inspired corrugated wings are known to increase structural rigidity, improve aerodynamics at low Reynolds numbers, and delay ow separation. Previous numerical studies have been limited to two-dimensional simulations at very low Reynolds numbers (< 1 10) and few experimental studies exist to explain the detailed physics underlying the observed phenomenon. The current work explores the ow structure of a corrugated airfoil using a highdelity implicit large eddy simulation (ILES) approach. The e ects of transition were investigated at several angles of attack and a range of Reynolds numbers. Transitional ow was observed at Reynolds numbers as low as Rec = 7:5 10 for low angles of attack and became signi cant on the lower airfoil surface near Rec = 2 10. The ow behavior was found to be strongly a ected by the leading edge geometry due to interaction between the detached shear layer emanating from the leading edge and the rst corrugation peak. Additionally, ow structure and aerodynamic forces appeared to become less sensitive to Reynolds number at the higher values computed.