An official website of the United States government
The rising global trend to reduce dependence on fossil fuels has provided significant motivation toward the development of alternative energy conversion methods and new technologies to improve their efficiency. Recently, oscillating energy harvesters have shown promise as highly efficient and scalable turbines, which can be implemented in areas where traditional energy extraction and conversion are either unfeasible or cost prohibitive. Although such devices are quickly gaining popularity, there remain a number of hurdles in the understanding of their underlying fluid dynamics phenomena. The ability to achieve high efficiency power output from oscillating airfoil energy harvesters requires exploitation of the complexities of the event of dynamic stall. During dynamic stall, the oncoming flow separates at the leading edge of the airfoil to form leading ledge vortex (LEV) structures. While it is well known that LEVs play a significant role in aerodynamic force generation in unsteady animal flight (e.g. insects and birds), there is still a need to further understand their spatiotemporal evolution in order to design more effective energy harvesting enhancement mechanisms. In this work, we conduct extensive experimental investigations to shed-light on the flow physics of a heaving and pitching airfoil energy harvester operating at reduced frequencies of k = fc=U1 = 0.06-0.18, pitching amplitude of 0 = 75 and heaving amplitude of h0 = 0:6c. The experimental work involves the use of two-component particle image velocimetry (PIV) measurements conducted in a wind tunnel facility at Oregon State University. Velocity fields obtained from the PIV measurements are analyzed qualitatively and quantitatively to provide a description of the dynamics of LEVs and other flow structures that may be present during dynamic stall. Due to the difficulties of accurately measuring aerodynamic forces in highly unsteady flows in wind tunnels, a reduced-order model based on the vortex-impulse theory is proposed for estimating the aerodynamic loadings and power output using flow field data. The reduced-order model is shown to be dominated by two terms that have a clear physical interpretation: (i) the time rate of change of the impulse of vortical structures and (ii) the Kutta-Joukowski force which indirectly represents the history effect of vortex shedding in the far wake. Furthermore, the effects of a bio-inspired flow control mechanism based on deforming airfoil surfaces on the flow dynamics and energy harvesting performance are investigated. The results show that the aerodynamic loadings, and hence power output, are highly dependent on the formation, growth rate, trajectory and detachment of the LEV. It is shown that the energy harvesting efficiency increases with increasing reduced frequency, peaking at 25% when k = 0.14, agreeing very well with published numerical results. At this optimal reduced frequency, the time scales of the LEV evolution and airfoil kinematics are matched, resulting in highly correlated aerodynamic load generation and airfoil motion. When operating at k > 0:14, it is shown that the aerodynamic moment and airfoil pitching motion become negatively correlated and as a result, the energy harvesting performance is deteriorated. Furthermore, by using a deforming airfoil surface at the leading and trailing edges, the peak energy harvesting efficiency is shown to increase by approximately 17% and 25% relative to the rigid airfoil, respectively. The performance enhancement is associated with enhanced aerodynamic forces for both the deforming leading and trailing edges. In addition, The deforming trailing edge airfoil is shown to enhance the correlation between the aerodynamic moment and pitching motion at higher reduced frequencies, resulting in a peak efficiency at k = 0:18 as opposed to k = 0:14 for the rigid airfoil.
more »
« less
State Variable Form of Unsteady Airfoil Aerodynamics with Vortex Shedding
This paper presents a state-variable formulation to model and simulate the 2D unsteady aerodynamics of an airfoil undergoing arbitrary motion kinematics. The model builds upon a large-angle unsteady aerodynamic formulation in which the airfoil is represented using a lumped vortex element (LVE) model. The airfoil is divided into several panels, with a bound vortex placed on each panel. At any time instant, the bound-vortex strengths are determined by employing zero-normal-flow conditions at the control points located on each panel. The vorticity shed from the trailing edge of the airfoil is modeled using discrete vortices that move freely in the flow field. The required state variables are first identified, and all the time derivative terms of the state variables are then derived to form the final state-variable representation. Trailing-edge vortex shedding is incorporated using the Kelvin condition. The final state variable equation can be solved as an ordinary differential equation using any standard ODE-solving algorithm. Three case studies are presented here to evaluate the predictions of the model. In the cases considered here, the airfoil undergoes various unsteady plunge motions. The aerodynamic load history and the wake patterns are compared against the results from the low-order model developed by Narsipur et al. [1] in previous research. The comparison shows that the current state-variable formulation captures the unsteady flow characteristics and the aerodynamic load in good agreement with the reference results.
more »
« less
- Award ID(s):
- 2015983
- PAR ID:
- 10333330
- Date Published:
- Journal Name:
- AIAA SCITECH 2022 Forum
- Page Range / eLocation ID:
- AIAA 2022-1667
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
More Like this
-
-
The coupled interaction between an unsteady vortical flow and dynamics of an aerodynamic structure is a canonical problem for which analytical studies have been typically restricted to either static or prescribed structural motions. The present effort extends beyond these restrictions to include a Joukowski airfoil on elastic supports and its aeroelastic influence on the incident vortex, where it is assumed that all vorticity in the flow field can be represented by a collection of line vortices. An analytical model for the vortex motion and the unsteady fluid forces on the airfoil is derived from inviscid potential flow, and the evolution of the unsteady airfoil wake is governed by the Brown and Michael equation. The aerodynamic sound generated by the aeroelastic interaction of an incident vortex, shed Brown-Michael vortices, and the moving airfoil is estimated for low-Mach-number flows using the Powell-Howe acoustic analogy.more » « less
-
In this paper, we present an approach to obtain a desired leading-edge vortex (LEV) shedding pattern from unsteady airfoils through the execution of suitable motion kinematics. Previous research revealed that LEV shedding is associated with the leading-edge suction parameter (LESP) exceeding a maximum threshold. A low-order method called LESP-modulated discrete vortex method (LDVM) was also developed to predict the onset and termination of LEV shedding from an airfoil undergoing prescribed motion kinematics. In the current work, we present an inverse-aerodynamic formulation based on the LDVM to generate the appropriate motion kinematics to achieve a prescribed LESP variation, and thus, the desired LEV shedding characteristics from the airfoil. The algorithm identifies the kinematic state of the airfoil required to attain the target LESP value through an iterative procedure performed inside the LDVM simulation at each time step. Several case studies are presented to demonstrate design scenarios such as tailoring the duration and intensity of LEV shedding, inducing LEV shedding from the chosen surface of the airfoil, promoting or suppressing LEV shedding during an unsteady motion on demand, and achieving similar LEV shedding patterns using different maneuvers. The kinematic profiles generated by the low-order formulation are also simulated using a high-fidelity unsteady Reynolds-averaged Navier–Stokes method to confirm the accuracy of the low-order model.more » « less
-
The dynamic interactions between an incident line vortex and a symmetric Joukowski airfoil on elastic translational support are formulated analytically and evaluated numerically, where the unsteady shedding of vorticity from the airfoil trailing edge is modeled by the emended Brown and Michael equation. This mathematical framework explores the effects of initial vortex placement, vortex strength, and the system aeroelastic parameters on the selection of the vortex trajectory to pass either above or below the airfoil, where special attention is paid to the conditions where direct impingement occurs.more » « less
-
An analytical model is developed for the lift force produced by unsteady rotating wings; this configuration is a simple representation of a flapping wing. Modelling this is important for the aerodynamic and control-system design for bio-inspired drones. Such efforts have often been limited to being two-dimensional, semi-empirical, sometimes computationally expensive, or quasi-steady. The current model is unsteady and three-dimensional, yet simple to implement, requiring knowledge of only the wing kinematics and geometry. Rotating wings produce a vortex loop consisting of the root vortex, leading-edge vortex, tip vortex and trailing-edge vortex, which grows with time. This is modelled as a tilted planar loop, geometrically specified by the wing size, orientation and motion. By equating the angular impulse of the vortex loop to that of the fluid volume driven by the wing, the circulatory lift force is derived. Potential flow theory gives the fluid-inertial lift. Adding these two contributions yields the total lift formula. The model shows good agreement with a range of experimental and computational cases. Also, a steady-state lift model is developed that compares well with previous work for various angles of attack.more » « less
- Free Publicly Accessible Full Text
-
Accepted Manuscript1.0
- Conference Paper:
- https://doi.org/10.2514/6.2022-1667
