In this work, direct numerical simulation (DNS) is used to
investigate how airfoil shape affects wake structure and
performance during a pitching-heaving motion. First, a classshape transformation (CST) method is used to generate airfoil
shapes. CST coefficients are then varied in a parametric study to
create geometries that are simulated in a pitching and heaving
motion via an immersed boundary method-based numerical
solver. The results show that most coefficients have little effect
on the propulsive efficiency, but the second coefficient does have
a very large effect. Looking at the CST basis functions shows that
the effect of this coefficient is concentrated near the 25% mark
of the foils chord length. By observing the thrust force and
hydrodynamic power through a period of motion it is shown that
the effect of the foil shape change is realized near the middle of
each flapping motion. Through further inspection of the wake
structures, we conclude that this is due to the leading-edge vortex
attaching better to the foil shapes with a larger thickness around
25% of the chord length. This is verified by the pressure
contours, which show a lower pressure along the leading edge of
the better performing foils. The more favorable pressure gradient
generated allows for higher efficiency motion.
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Can Flapping Propulsion Boost Airplane Technology? The Flapping-Tail Concept Airplane
Flapping propulsion has been deemed inefficient for practical use in thrusting actual
airplanes. In this paper, we revisit this claim in the light of several recent findings on the
unsteady aero/hydro dynamics of natural flyers/swimmers (e.g., birds, insects, cetaceans).
We propose a new airplane concept, called the Flapping-Tail Concept Airplane (FTCA), in
which the horizontal tail is driven by a power shaft into a pitching-plunging-flapping motion
through a flapping mechanism. For such a concept, we show that there is a significant
room for boosting flapping propulsive efficiency that may outperform the current turbofan
engine technologies. We use Garrick’s classical unsteady aerodynamic model for flapping
propulsion to show that allowing for a simultaneous flap deflection with pitching-plunging
may enhance the propulsive efficiency by 20%. Moreover, we propose other promising
interacting flow mechanisms that may enhance the propulsive efficiency even more and
provide a geometric control theoretic formulation to guide such an interaction. We also
show the favorable effect of operating in the stall regime with large amplitudes. Finally,
we study the effect of such an oscillating tail on the flight mechanics of the airplane and
provide recommendations for future investigations necessary to make the proposed vision
come closer to real applications.
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- Award ID(s):
- 1635673
- PAR ID:
- 10075264
- Date Published:
- Journal Name:
- AIAA Aerospace Sciences Meeting
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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null (Ed.)more » « less
Abstract Flapping insect wings experience appreciable deformation due to aerodynamic and inertial forces. This deformation is believed to benefit the insect’s aerodynamic force production as well as energetic efficiency. However, the fluid-structure interaction (FSI) models used to estimate wing deformations are often computationally demanding and are therefore challenged by parametric studies. Here, we develop a simple FSI model of a flapping wing idealized as a two-dimensional pitching-plunging airfoil. Using the Lagrangian formulation, we derive the reduced-order structural framework governing wing’s elastic deformation. We consider two fluid models: quasi-steady Deformable Blade Element Theory (DBET) and Unsteady Vortex Lattice Method (UVLM). DBET is computationally economical but does not provide insight into the flow structure surrounding the wing, whereas UVLM approximates flows but requires more time to solve. For simple flapping kinematics, DBET and UVLM produce similar estimates of the aerodynamic force normal to the surface of a rigid wing. More importantly, when the wing is permitted to deform, DBET and UVLM agree well in predicting wingtip deflection and aerodynamic normal force. The most notable difference between the model predictions is a roughly 20° phase difference in normal force. DBET estimates wing deformation and force production approximately 15 times faster than UVLM for the parameters considered, and both models solve in under a minute when considering 15 flapping periods. Moving forward, we will benchmark both low-order models with respect to high fidelity computational fluid dynamics coupled to finite element analysis, and assess the agreement between DBET and UVLM over a broader range of flapping kinematics.
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Flapping-Wing Micro-Air-Vehicles (FWMAVs) are bio-inspired air vehicles that mimic insect and bird flight. The dynamic behavior of these systems is typically described by a multi-body, multi-time-scale, nonlinear, time-varying dynamical system. Interestingly, this rich dynamics lead to unconventional stabilization mechanisms whose study essentially necessitates a mathematically rigorous analysis. In this paper, we use higherorder averaging, which is based on chronological calculus, to show that insects and their man-made counterparts (FWMAVs) exploit vibrational control to stabilize their body pitching angle. Such an unconventional stabilization cannot be captured by direct averaging. We also experimentally demonstrate such a phenomenon by constructing an experimental setup that allows for two degrees of freedom for the body; forward motion and pitching motion. We measure the response of the body pitching angle using a digital camera and an image processing algorithm at different flapping frequencies. It is found that there is a flapping frequency threshold beyond which the body pitching response is naturally (without feedback) stabilized, which conforms with the vibrational control concept. Moreover, we also construct a replica of the experimental setup with the FWMAV being replaced by a propeller revolving at constant speed, which results in a constant aerodynamic force, leaving no room for vibrational control. The response of the propellersetup is unstable at all frequencies, which also corroborates the fact that the observed stabilization of the FWMAV-setup at high frequencies is a vibrational stabilization phenomenon.more » « less
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Abstract Insect wings are heterogeneous structures, with flexural rigidity varying one to two orders of magnitude over the wing surface. This heterogeneity influences the deformation the flapping wing experiences during flight. However, it is not well understood how this flexural rigidity gradient affects wing performance. Here, we develop a simplified 2D model of a flapping wing as a pitching, plunging airfoil using the assumed mode method and unsteady vortex lattice method to model the structural and fluid dynamics, respectively. We conduct parameter studies to explore how variable flexural rigidity affects mean lift production, power consumption and the forces required to flap the wing. We find that there is an optimal flexural rigidity distribution that maximizes lift production; this distribution generally corresponds to a 3:1 ratio between the wing’s flapping and natural frequencies, though the ratio is sensitive to flapping kinematics. For hovering flight, the optimized flexible wing produces 20% more lift and requires 15% less power compared to a rigid wing but needs 20% higher forces to flap. Even when flapping kinematics deviate from those observed during hover, the flexible wing outperforms the rigid wing in terms of aerodynamic force generation and power across a wide range of flexural rigidity gradients. Peak force requirements and power consumption are inversely proportional with respect to flexural rigidity gradient, which may present a trade-off between insect muscle size and energy storage requirements. The model developed in this work can be used to efficiently investigate other spatially variant morphological or material wing features moving forward.more » « less
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Migratory birds have the ability to save energy during flight by arranging themselves in a V-formation. This arrangement enables an increase in the overall efficiency of the group because the wake vortices shed by each of the birds provide additional lift and thrust to every member. Therefore, the aerodynamic advantages of such a flight arrangement can be exploited in the design process of micro air vehicles. One significant difference when comparing the anatomy of birds to the design of most micro air vehicles is that bird wings are not completely rigid. Birds have the ability to actively morph their wings during the flapping cycle. Given these aspects of avian flight, the objective of this work is to incorporate active bending and torsion into multiple pairs of flapping wings arranged in a V-formation and to investigate their aerodynamic behavior using the unsteady vortex lattice method. To do so, the first two bending and torsional mode shapes of a cantilever beam are considered and the aerodynamic characteristics of morphed wings for a range of V-formation angles, while changing the group size in order to determine the optimal configuration that results in maximum propulsive efficiency, are examined. The aerodynamic simulator incorporating the prescribed morphing is qualitatively verified using experimental data taken from trained kestrel flights. The simulation results demonstrate that coupled bending and twisting of the first mode shape yields the highest propulsive efficiency over a range of formation angles. Furthermore, the optimal configuration in terms of propulsive efficiency is found to be a five-body V-formation incorporating coupled bending and twisting of the first mode at a formation angle of 140 degrees. These results indicate the potential improvement in the aerodynamic performance of the formation flight when introducing active morphing and bioinspiration.more » « less
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