Session X04: Aerodynamics: Pitching Wings

Investigating the Influence of Pitch Rate and Pivot Location on Aerodynamic Performance and Leading-Edge Vortex Dynamics of Rotating and Pitching Flat Plates

Unsteady flow separation and leading-edge vortices (LEV) greatly affect the aerodynamic performance of insect wings, helicopter rotor blades, among others. Such unsteady aerodynamic phenomenon is strongly influenced by pitch rate and pivot location of the wing. The present investigation employs direct force measurement and particle image velocimetry to study a rotating and pitching flat plate. An aspect ratio 6 flat plate, rotating at a tip velocity-based Reynolds number of 5000 and pitching from 0-90^o is used. The effects of varying reduced pitch rate K and pitch pivot locations x_p/c on the aerodynamic lift C_L and drag C_D coefficients, as well as the LEV system is investigated. The results show a generalization in scaling of C_L and C_D with K and x_p/c and relate such scaling to the formation and growth of LEVs. Higher K results in peak values of C_L and C_D coefficients occurring at higher pitch angles but have higher peak values than at lower K. On the other hand, moving x_p/c from leading edge towards the trailing edge delays separation but this results in decreasing LEV strength and subsequently lower C_L and C_D peak values. Furthermore, for different x_p/c, a convective time shift is successful for collapse of C_L and C_D peaks at same non-dimensional convective time t^*.   

Transient Dynamics of the Flow Over a Pitching Wing at Low Reynolds Number

At aerodynamically low Reynolds numbers, lifting surfaces often experience an abrupt stall due to the bursting of a laminar separation bubble. This study examines laminar separation bubble formation and bursting on a NACA 0018 semi-span finite wing model with a semi-aspect ratio of 2.5 at a Reynolds number of 1×10⁵. Bubble formation and bursting are induced by pitch-up and pitch-down motions between angles of attack of 10° and 13°. The effect of pitch rate is examined by varying the duration of the motion from 4 to 80 convective timescales. A second model approximating a two-dimensional airfoil is employed as a baseline for the evaluation of three-dimensional end effects on the transient flow over the finite wing model during the pitching motion. Simultaneous time-resolved force and two-component particle image velocimetry measurements are performed to characterise the transient aerodynamic loads resulting from the pitching motion and relate these loads to the flow-field development. For a constant pitch rate, substantial variations in the durations of the flow-field transient occur. The dynamics of separation bubble formation and bursting during the transient change of angle of attack is also compared to the dynamics observed during a change in Reynolds number investigated previously.   

Characterizing Dynamic Stall at High Reynolds number using a Variable Pressure Wind Tunnel

The objective of this work is to elucidate the effect of chord Reynolds number, Re_c , and airfoil kinematics on the salient fluid structures generated by a NACA0021 airfoil undergoing dynamic stall at 2 × 10⁵ ≤ Re_c ≤ 8 × 10⁶. This is accomplished by pitching the airfoil in the High Reynolds number Test Facility (HRTF) at Princeton University. The HRTF has a working pressure of up to 24 MPa (238 bar), achieving high Re_c through low freestream velocities, U_∞ ≤ 10 m/s. By scaling pressure instead of velocity, the experiments bypass compressibility and time-scale challenges faced by studies of dynamic stall in traditional wind tunnels operating at high Re_c and atmospheric pressure. The results reveal unique relations between Re_c and the non-equilibrium response of the boundary layer - namely, the stall angle as well as the temporal signatures of the transition region, boundary layer separation point, and dynamic stall vortex, all of which indicate the type of dynamic stall being observed. These findings are pertinent to large and small-scale aeronautics, wind energy, and biological flows.    

The Vortical Field Downstream of an Airfoil Oscillated from Rest for One Cycle

The flow fields generated from airfoils undergoing small amplitude, high frequency cyclic motions (e.g. pitching, heaving, combined pitching/heaving) continue to be a topic of interest for thrust generation at low Reynolds numbers. Past studies have typically investigated these flow fields once the transient start-up has died out and the downstream flow field forms into an unsteady, but cyclic, semi-infinite vortical wake (i.e. the “steady state” condition). In the current work the flow field downstream of a NACA0012 airfoil that experiences a single oscillation about the ¼-chord location is examined using PIV to investigate the starting dynamics. The prescribed motion starts impulsively from α=0° and varies between ±α_max following a sinusoidal motion trajectory ending back at α=0°. The resulting flow fields show that multiple vortices of both signs were formed due to the impulsive start, two changes in direction and the impulsive stop of the motion. The size and strength of the vortices were found to depend on both the maximum angle and frequency of motion. The dynamics of the vortices were also found to depend on both the maximum angle and the frequency of the motion. For low frequency conditions isolated vortices formed and convected with little interaction. As the frequency was increased vortices began to form in proximity to each other resulting in complex interaction dynamics including pairing, merging, and combining. Progressively weaker vortices continued to form after the motion was completed, with the flow field taking on order of two convective times to return to the starting α=0° wake condition.   

Finite-time Lyapunov exponent and force partitioning method in the wake of a pitching airfoil

Unsteady flow around a pitching airfoil at Re= 1000 is investigated using both finite-time Lyapunov exponent (FTLE) and the force and moment partitioning method (FMPM). FTLE is used to analyze the kinematics of the flow by defining a scalar field based on the amount of Lagrangian stretching experienced by the fluid within the field. The FMPM quantifies the dynamical impact of flow kinematics by partitioning the loads induced on the airfoil by different physical mechanisms, including distinct vortex structures. The study uses simulation data around a sinusoidally pitching NACA0015 airfoil which exhibits dynamic stall vortex shedding. Maximizing ridges of the positive and negative-time FTLE fields have been shown to outline distinct regions of unsteady and vortex dominated flow fields, and their evolution correlates with important dynamic phenomena, such as flow separation, vortex shedding, and reattachment. Here, the FTLE ridges, saddles and scalar fields are compared with the FMPM influence field and the force/moment contributions from distinct vortex structures. Combining these kinematic and dynamic approaches further expands our understanding of the nonlinear relationship between flow field features and mechanical performance of immersed bodies is unsteady flows.   

2D/3D Topological data analysis of vortex dominated flows

Persistent homology (PH) is a topological data analysis (TDA) technique used to decipher complex data by detecting and tracking topological features. We apply methods of PH to the vortex wakes generated by pitching and heaving flat plates as models of bio-inspired propulsion. Velocity fields from stereoscopic particle image velocimetry are analyzed using Cubical PH with an effort to determine if there exists a relationship between the topological connectivity of the field and its physical interaction. Results show that using TDA to analyze these flow field interactions identifies vortex cores and boundaries as persistent features within their respective H0 and H1 homology groups. Furthermore, metrics such as a bottleneck or Wasserstein distance provide a path for quantifying the significance of vortex shedding and its corresponding change in topology. Current work focuses on applying this method to 3D vortex flow data of rigid, bio-inspired trapezoidal pitching panels. Future work focuses on implementing other PH techniques, specifically zigzag persistence and multiparameter persistence to track persisting features through multidimensional analysis.   

Rapidly pitching plates in decelerating motion near the ground.

Birds utilize rapid pitch-up motions for various purposes: perching birds employ this motion to slow down and come to a complete stop while hunting birds, like bald eagles, employ it to catch prey and swiftly fly away. Inspired by these observations, our research investigates how natural flyers achieve diverse flying objectives by rapidly pitching their wings during deceleration. To explore the impact of ground proximity on unsteady dynamics, we conducted experimental and analytical investigations, focusing on rapidly pitching plates during deceleration in close proximity to the ground. Initially, we executed simultaneous deceleration and pitch-up motion close to the ground. Experimental results demonstrate that the instantaneous lift increases as the pitching wing approaches the ground while the initial peak drag force remains relatively unchanged. Our analytical model conforms to this trend, predicting an increase in lift force as the wing approaches the ground, indicating enhanced added mass and circulatory lift force due to the ground effect. Next, we analyzed asynchronous motion cases, where rapid pitching motions were initiated at different stages of deceleration. The results reveal that when the wing pitch is synchronized with the start of deceleration, larger counter-rotating vortices form early in the maneuver. These vortices generate stronger dipole jets that orient backward in the later stages of the maneuver after impinging with the ground surface, facilitating hunting birds to accelerate after catching prey. Conversely, when the wing pitch is delayed, smaller vortices form, but their formation is postponed until late in the maneuver. This delayed vortex formation generates beneficial unsteady forces late in the maneuver that facilitate a smooth landing or perching. Thus, by strategically coordinating rapid pitch-up motion with deceleration, natural flyers achieve wide range of flying objectives   

Wake dynamics of actively pitching and passively heaving tandem flappers

The study investigates the wake dynamics of two actively pitching and passively heaving elliptic foils in a tandem configuration in the low Reynolds number regime. The numerical simulations are carried out using an inhouse fluid-structure interaction solver based on the Cut-Finite Element Method (CutFEM) on hierarchical b-spline grids. In this study, both the foils are free to heave in the cross-flow direction as they are elastically mounted along the plunge degree-of-freedom and undergo a prescribed sinusoidal pitch oscillation about the foil centre. A bifurcation study for the passive heaving response is carried out with the increasing oncoming flow velocity, keeping solid-to-fluid mass ratio, natural frequency of the elastic support, structural damping, pitching amplitude and frequency constant. The flow-induced vibration characteristics are compared between two significantly different foil geometries with aspect ratios of 1.5 and 6. The effect of the gap flow on manifesting different wake patterns is studied for three different intermediate gaps between the two foils. Furthermore, the influence of the intermediate gap flow on the dynamical wake transition is analysed, and the synchronisation behaviour in the collective dynamics of these two foils is revealed. The underlying flow physics is unravelled by identifying various wake modes and underlying vortex-structure interactions.   

Adding heterogeneous inputs to transition networks to improve unsteady airfoil lift prediction.

The prediction of lift during in-flight conditions poses significant challenges, and the development of effective tools for predicting aerodynamic loads is of great importance. In the current investigation, a data-driven approach is used to predict the lift generated by a NACA0015 airfoil under highly separated flow conditions at a Reynolds number of 5.5x10⁵ using a discrete set of surface and flow field sensors as input. The airfoil was pitched around its static stall angle,  α_ss = 20°, with a pitching amplitude of 8°. The experimental data included six cases with reduced frequencies k from 0.025 to 0.15. A weighted-average based transition network was applied to measurements from 36 surface pressure taps, with 20 installed on the suction side and 16 on the pressure side of the airfoil. Predictive results were compared against those also incorporating planar flow field data, such as vorticity levels in specific zones near the airfoil, to improve the accuracy of lift predictions. The degree and nature of improvement gained by expanding the inputs to the transition network will be discussed in terms of phase-averaged performance of the prediction, and performance in capturing cycle-to-cycle variations in the experimental data.