Session G18: Aerodynamics: Unsteady I

Effect of controlled spanwise bending on the stability of the leading-edge vortex

When an airfoil is accelerated from rest at a high angle of attack, a leading-edge vortex (LEV) forms, which soon gets destabilized and convects downstream. In this work, we control the spanwise bending of a flat plate wing to actively influence the vorticity transfer from the LEV. Our aim is to investigate the effect of spanwise curvature variation on the geometry, growth, and stability of the LEV during the acceleration phase. A 3D printed flat-plate with a chord of 5 cm and span of 15 cm is towed in a small fish tank at different angles of attack greater than 15$^\circ$. The plate starts from rest and reaches a Reynolds number of 5000 after travelling different multiples and submultiples of chord-length. We carry out dye-flow visualization and measure the circulation build up and the convection velocity of the LEV with the help of particle image velocimetry (PIV). The unsteady loads coming on to the wing is measured with a force sensor. An analytical scheme for computing the load from the measured displacement of the plate is presented and compared with the force sensor data. Preliminary results indicate that controlled curvature variation can influence the formation and stability of an LEV.   

Vorticity dynamics of revolving wings: The role of planetary vortex tilting on the stability of leading-edge vortex

This work investigates the radial vorticity dynamics and the stability of leading-edge vortices (LEVs) in revolving wings. Previous studies have shown that Coriolis acceleration plays a key role in stabilizing the LEV; however, the exact mechanism remains unclear. This study tests a new hypothesis based on the curl of the Coriolis acceleration in the vorticity equation, which corresponds to the radial tilting of the planetary vortex (PVTr). The PVTr could reorient planetary vorticity into radial vorticity that reduces the strength of the LEV, preventing the LEV from growing and becoming unstable. To test this, an in-house immersed-boundary-method-based flow solver was used to generate velocity and vorticity fields of revolving wings of different aspect ratio (AR $=$ 3, 5, 7) and Reynolds number (Re $=$ 110, 1400). It is found that the PVTr consistently negates the LEV vorticity for all the AR and Re investigated, although its effect is outweighed by other 3D effects at Re $=$1400. It is also found that the strength of the PVTr increases along the wing span until approximately a chord length from the wing tip. The averaged magnitude of PVTr within the LEV and the dependency of its relative strength on the aspect ratio and Reynolds number are also investigated.   

Leading edge vortex formation and detachment of a flapping foil energy harvester

An experimental investigation is conducted to study the leading edge vortex (LEV) formation and detachment of a flapping foil operating in energy harvesting regime. Two dimensional particle image velocimetry measurements are conducted in the wind tunnel at reduced frequencies of $k \quad =$ \textit{fc/U} $=$ 0.05 - 0.20. The LEV characteristics such as the growth rate, size, strength, and trajectory are reported. It is shown that during the evolution process, the LEV characteristics are strongly dependent on the feeding shear layer velocity, where as the detachment process is dictated by the reduced frequency. Flow topology is used to discuss the detachment mechanism, and it is found that the transition from bluff body detachment to boundary layer eruption occurs at $k \quad =$ 0.11. In addition, vortex formation analysis is conducted to investigate the relationship between optimal energy harvesting efficiency and optimal LEV formation. We demonstrate that the optimal LEV formation number ($T \quad =$ 4) is achieved within the range of optimal reduced frequencies for energy harvesting applications ($k \quad =$ 0.1- 0.15).   

Numerical Investigation of an Oscillating Flat Plate Airfoil.

This research investigates the vortex dynamics of a plunging flat plate airfoil by analyzing the vorticity transport in 2D simulations. A horizontal airfoil is subject to a freestream flow at Re$=$10000. A prescribed vertical sinusoidal motion is applied to the airfoil. Smoothed Profile Method (SPM) models the fluid-structure interaction. SPM as a diffuse interface model considers a thickness for the interface and applies a smooth transition from solid to fluid. As the forces on the airfoil are highly affected by the interaction of the generated vortices from the surface, it is very important to find out whether a diffuse interface solver can model a flow dominated by vorticities. The results show that variation of lift coefficient with time agrees well with the experiment. Study of vortex evolution shows that similar to experiments, when the plate starts moving downward from top, the boundary layer is attached to the surface and the leading-edge vortex (LEV) is very small. By time, LEV grows and rolls up and a secondary vortex emerges. Meanwhile, the boundary layer starts to separate and finally LEV detaches from the surface. In overall, SPM as a diffuse interface model can predict the lift force and vortex pattern accurately.   

Unsteady fluid dynamics around a hovering wing

The unsteady flow around a hovering flat plate wing has been investigated experimentally using particle image velocimetry and direct force measurements. The measurements are conducted on a wing that rotates symmetrically about the stroke reversal at a reduced frequency of $k=0.32$ and Reynolds number of $Re=220$. The Lagrangian finite-time Lyapunov exponent method is used to analyse the unsteady flow fields by identifying dynamically relevant flow features such as the primary leading edge vortex (LEV), secondary vortices, and topological saddles, and their evolution within a flapping cycle. The flow evolution is divided into four stages that are characterised by the LEV (a)emergence, (b)growth, (c)lift-off, and (d)breakdown and decay. Tracking saddle points is shown to be helpful in defining the LEV lift-off which occurs at the maximum stroke velocity. The flow fields are correlated with the aerodynamic forces revealing that the maximum lift and drag are observed just before LEV lift-off. The end of wing rotation in the beginning of the stroke stimulates a change in the direction of the LEV growth and the start of rotation at the end of the stroke triggers the breakdown of the LEV.   

Transport Mechanisms Governing initial Leading-Edge Vortex Development on a Pitching Wing

The formation and evolution of Leading Edge Vortices (LEVs) are ubiquitous in natural fliers and maneuvering wings, and have a profound impact on aerodynamic loads. The formation of an LEV is experimentally investigated on a pitching flat-plate wing of aspect-ratio 2, and dimensionless pitch rates of $k=\Omega c/2U$ of 0.1, 0.2, and 0.5, at a Reynolds number of $10^4$. The sources and sinks of vorticity that contribute to the growth and evolution of the LEV are investigated at spanwise regions of interest, and their relative balance is compared to other wing kinematics, and the case of a two-dimensional pitching wing.   

Parametric Dependence of Initial LEV Behavior on Maneuvering Wings

A maneuvering rectangular wing of aspect ratio 2 is examined experimentally using dye visualization and PIV to characterize the initial development of the leading-edge vortex (LEV) during a rolling maneuver in a uniform free stream. Understanding the underlying physics during the early evolution of the vortex is important for developing strategies to manipulate vortex evolution. Varying the dimensionless radius of gyration of the wing ($R_g$/c, where Rg is the radius of gyration and c is the chord) and the advance ratio (J=U/$\Omega$$R_g$, where U is the free-stream velocity and $\Omega$ is the roll rate) affects the structure of the vortex and its propensity to remain attached. The influence of these parameters will be discussed, toward identification of similarity parameters governing vortex development.   

Reduced-order aeroelastic model for limit-cycle oscillations in vortex-dominated unsteady airfoil flows

In previous research, Ramesh et al (JFM,2014) developed a low-order discrete vortex method for modeling unsteady airfoil flows with intermittent leading edge vortex (LEV) shedding using a leading edge suction parameter (LESP). LEV shedding is initiated using discrete vortices (DVs) whenever the Leading Edge Suction Parameter (LESP) exceeds a critical value. In subsequent research, the method was successfully employed by Ramesh et al (JFS, 2015) to predict aeroelastic limit-cycle oscillations in airfoil flows dominated by intermittent LEV shedding. When applied to flows that require large number of time steps, the computational cost increases due to the increasing vortex count. In this research, we apply an amalgamation strategy to actively control the DV count, and thereby reduce simulation time. A pair each of LEVs and TEVs are amalgamated at every time step. The ideal pairs for amalgamation are identified based on the requirement that the flowfield in the vicinity of the airfoil is least affected (Spalart, 1988). Instead of placing the amalgamated vortex at the centroid, we place it at an optimal location to ensure that the leading-edge suction and the airfoil bound circulation are conserved. Results of the initial study are promising.   

Unsteady lift and thrust of a 2D flapping thin airfoil in the presence of additional leading edge vortices

The effect of leading-edge vortices (LEVs) on the lift, thrust and moment of a two-dimensional heaving and pitching foil is analyzed from the unsteady, linear potential theory. General expressions taking into account the effect of unsteady point vortices interacting with the oscillatory trailing wake are first derived. Then, simplified expressions for the initial stages of the growing LEV on each half-stroke are used to obtain analytical closed expressions for the main contribution of these vortices to the lift, thrust and moment. It is found that, within the linear potential framework and the Brown-Michael model, the LEV contributes to the aerodynamic forces and moment only for combined pitching and heaving motions of the foil, being a relevant contribution for sufficiently large values of the product of the reduced frequency and the amplitude of the heaving and/or pitching motions. The results are compared with available experimental data and numerical simulations.   

The leading-edge vortex of yacht sails

We experimentally show, for the first time, that a stable Leading-Edge Vortex (LEV) can be formed on an asymmetric spinnaker, which is a high-lift sail used by yachts to sail downwind. We tested a 3D printed rigid sail in a water flume at a chord-based Reynolds number of ca. $10^4$. We found that on the leeward side of the sail (the suction side), the flow separates at the leading edge reattaching further downstream and forming a stable LEV. The LEV grows in diameter from the root to the tip of the sail, where it merges with the tip vortex. We detected the LEV using the $\gamma$ criterion, and we verified its stability over time. The lift contribution provided by the LEV was computed solving a complex potential model of each sail section. This analysis indicated that the LEV provides a substantial contribution to the total sail's lift. These findings suggest that the maximum lift of low-aspect-ratio wings with a sharp leading edge, such as spinnakers, can be enhanced by promoting a stable LEV.