Lift and thrust generation by a butterfly-like flapping wing-body model: immersed boundary-lattice Boltzmann simulations

The flapping flight of tiny insects such as flies or larger insects such as butterflies is of fundamental interest not only in biology itself but also in its practical use for the development of micro air vehicles (MAVs). It is known that a butterfly flaps downward for generating the lift force and backward for generating the thrust force. In this study, we consider a simple butterfly-like flapping wing body model in which the body is a thin rod and the rectangular rigid wings flap in a simple motion. We investigate lift and thrust generation of the model by using the immersed boundary lattice Boltzmann method. First, we compute the lift and thrust forces when the body of the model is fixed for Reynolds numbers in the range of 50-1000. In addition, we estimate the supportable mass for each Reynolds number from the computed lift force. Second, we simulate free flights when the body can only move translationally. It is found that the expected supportable mass can be supported even in the free flight except when the mass of the body relative to the mass of the fluid is too small, and the wing body model with the mass of actual insects can go upward against the gravity. Finally, we simulate free flights when the body can move translationally and rotationally. It is found that the body has a large pitch motion and consequently gets off-balance. Then, we discuss a way to control the pitching angle by flexing the body of the wing body model.ArticleJOURNAL OF FLUID MECHANICS. 767:659-695 (2015)journal articl

Computational Fluid Dynamics Simulations of Oscillating Wings and Comparison to Lifting-Line Theory

Computational fluid dynamics (CFD) analysis was performed in order to compare the solutions of oscillating wings with Prandtl’s lifting-line theory. Quasi-steady and steady-periodic simulations were completed using the CFD software Star-CCM+. The simulations were performed for a number of frequencies in a pure plunging setup. Additional simulations were then completed using a setup of combined pitching and plunging at multiple frequencies. Results from the CFD simulations were compared to the quasi-steady lifting-line solution in the form of the axial-force, normal-force, power, and thrust coefficients, as well as the efficiency obtained for each simulation. The mean values were evaluated for each simulation and compared to the quasi-steady lifting-line solution. It was found that as the frequency of oscillation increased, the quasi-steady lifting-line solution was decreasingly accurate in predicting solutions

DESIGN AND CONTROL OF A HUMMINGBIRD-SIZE FLAPPING WING MICRO AERIAL VEHICLE

Flying animals with flapping wings may best exemplify the astonishing ability of natural selection on design optimization. They evince extraordinary prowess to control their flight, while demonstrating rich repertoire of agile maneuvers. They remain surprisingly stable during hover and can make sharp turns in a split second. Characterized by high-frequency flapping wing motion, unsteady aerodynamics, and the ability to hover and perform fast maneuvers, insect-like flapping flight presents an extraordinary aerial locomotion strategy perfected at small size scales. Flapping Wing Micro Aerial Vehicles (FWMAVs) hold great promise in bridging the performance gap between engineered flying vehicles and their natural counterparts. They are perfect candidates for potential applications such as fast response robots in search and rescue, environmental friendly agents in precision agriculture, surveillance and intelligence gathering MAVs, and miniature nodes in sensor networks

Modeling and System Identification of an Ornithopter Flight Dynamics Model

Ornithopters are robotic flight vehicles that employ flapping wings to generate lift and thrust forces in a manner that mimics avian flyers. At the small scales and Reynolds numbers currently under investigation for miniature aircraft, where viscous effects deteriorate the performance of conventional aircraft, ornithopters achieve efficient flight by exploiting unsteady aerodynamic flow fields, making them well-suited for a variety of unmanned vehicle applications. Parsimonous dynamic models of these systems are requisite to augment stability and design autopilots for autonomous operation; however, flapping flight is fundamentally different than other means of engineered flight and requires a new standard model for describing the flight dynamics. This dissertation presents an investigation into the flight mechanics of an ornithopter and develops a dynamical model suitable for autopilot design for this class of system. A 1.22 m wing span ornithopter test vehicle was used to experimentally investigate flapping wing flight. Flight data, recorded in trimmed straight and level mean flight using a custom avionics package, reported pitch rates and heave accelerations up to 5.62 rad/s and 46.1 m/s^2 in amplitude. Computer modeling of the vehicle geometry revealed a 0.03 m shift in the center of mass, up to a 53.6% change in the moments of inertia, and the generation of significant inertial forces. These findings justified a nonlinear multibody model of the vehicle dynamics, which was derived using the Boltzmann-Hamel equations. Models for the actuator dynamics, tail aerodynamics, and wing aerodynamics, difficult to obtain from first principles, were determined using system identification techniques with experimental data. A full nonlinear flight dynamics model was developed and coded in both MATLAB and FORTRAN programming languages. An optimization technique is introduced to find trim solutions, which are defined as limit cycle oscillations in the state space. Numerical linearization about straight and level mean flight resulted in both a canonical time-invariant model and a time-periodic model. The time-invariant model exhibited an unstable spiral mode, stable roll mode, stable dutch roll mode, a stable short period mode, and an unstable short period mode. Floquet analysis on the identified time-periodic model resulted in an equivalent time-invariant model having an unstable second order and two stable first order modes, in both the longitudinal and lateral dynamics

Design and Control of Flapping Wing Micro Air Vehicles

Flapping wing Micro Air Vehicles (MAVs) continues to be a growing field, with ongoing research into unsteady, low Re aerodynamics, micro-fabrication, and fluid-structure interaction. However, research into flapping wing control of such MAVs continues to lag. Existing research uniformly consists of proposed control laws that are validated by computer simulations of quasi-steady blade-element formulae. Such simulations use numerous assumptions and cannot be trusted to fully describe the flow physics. Instead, such control laws must be validated on hardware. Here, a novel control technique is proposed called Bi-harmonic Amplitude and Bias Modulation (BABM) which can generate forces and moments in 5 vehicle degrees of freedom with only two actuators. Several MAV prototypes were designed and manufactured with independently controllable wings capable of prescribing arbitrary wing trajectories. The forces and moments generated by a MAV utilizing the BABM control technique were measured on a 6-component balance. These experiments verified that a prototype can generate uncoupled forces and moments for motion in five degrees of freedom when using the BABM control technique, and that these forces can be approximated by quasi-steady blade-element formulae. Finally, the prototype performed preliminary controlled flight in constrained motion experiments, further demonstrating the feasibility of BABM

A Review of Biomimetic Air Vehicle Research: 1984-2014

Biomimetic air vehicles (BAV) are a class of unmanned aircraft that mimic the flapping wing kinematics of flying organisms (e.g. birds, bats, and insects). Research into BAV has rapidly expanded over the last 30 years. In this paper, we present a comprehensive bibliometric review of engineering and biology journal articles that were published on this subject between 1984 and 2014. These articles are organized into five topical categories: aerodynamics, guidance and control, mechanisms, structures and materials, and system design. All of the articles are compartmented into one of these categories based on their primary focus. Several aspects of these articles are examined: publication year, number of citations, journal, authoring organization and country, non-academic funding sources, and the flying organism focused upon for bio-mimicry. This review provides useful information on the state of the art of BAV research and insight on potential future directions. Our intention is that this will serve as a resource for those already engaged in BAV research and enable insight that promotes further research interest

Low Speed Flap-bounding in Ornithopters and its Inspiration on the Energy Efficient Flight of Quadrotors

Flap-bounding, a form of intermittent flight, is often exhibited by small birds over their entire range of flight speeds. The purpose of flap-bounding is unclear during low to medium speed (2 - 8 m/s) flight from a mechanical-power perspective: aerodynamic models suggest continuous flapping would require less power output and lower cost of transport. This thesis works towards the understanding of the advantages of flap-bounding and tries to employ the underlining principle to design quadrotor maneuver to improve power efficiency. To explore the functional significance of flap-bounding at low speeds, I measured body trajectory and kinematics of wings and tail of zebra finch (Taeniopygia guttata, N=2) during flights in a laboratory between two perches. The flights consist of three phases: initial, descending and ascending. Zebra finch first accelerated using continuous flapping, then descended, featuring intermittent bounds. The flight was completed by ascending using nearly-continuous flapping. When exiting bounds in descending phase, they achieved higher than pre-bound forward velocity by swinging body forward similar to pendulum motion with conserved mechanical energy. Takeoffs of black-capped chickadees (Poecile atricapillus, N=3) in the wild was recorded and I found similar kinematics. Our modeling of power output indicates finch achieves higher velocity (13%) with lower cost of transport (9%) when descending, compared with continuous flapping in previously-studied pigeons. To apply the findings to the design of quadrotor motion, a mimicking maneuver was developed that consisted of five phases: projectile drop, drop transition, pendulum swing, rise transition and projectile rise. The quadrotor outputs small amount (4 N) of thrust during projectile drop phase and ramps up the thrust while increasing body pitch angle during the drop transition phase until the thrust enables the quadrotor to advance in pendulum-like motion in the pendulum swing phase. As the quadrotor reaches the symmetric point with respect to the vertical axis of the pendulum motion, it engages in reducing the thrust and pitch angle during the rise transition phase until the thrust is lowered to the same level as the beginning of the maneuver and the body angle of attack minimized (0.2 deg) in the projectile rise phase. The trajectory of the maneuver was optimized to yield minimum cost of transport. The quadrotor moves forward by tracking the cycle of the optimized trajectory repeatedly. Due to the aggressive nature of the maneuver, we developed new algorithms using onboard sensors to determine the estimated position and attitude. By employing nonlinear controller, we showed that cost of transport of the flap-bounding inspired maneuver is lower (28%) than conventional constant forward flight, which makes it the preferable strategy in high speed flight (≥15 m/s)

An Analytical Investigation of Flapping Wing Structures for Micro Air Vehicles

An analytical model of flapping wing structures for bio-inspired micro air vehicles is presented in this dissertation. Bio-inspired micro air vehicles (MAVs) are based on insects and hummingbirds. These animals have lightweight, flexible wings that undergo large deformations while flapping. Engineering studies have confirmed that deformations can increase the lift of flapping wings. Wing flexibility has been studied through experimental construction-and-evaluation methods and through computational numerical models. Between experimental and numerical methods there is a need for a simple method to model and evaluate the structural dynamics of flexible flapping wings. This dissertation's analytical model addresses this need. A time-periodic assumed-modes beam analysis of a flapping, flexible wing undergoing linear deformations is developed from a beam analysis of a helicopter blade. The resultant structural model includes bending and torsion degrees of freedom. The model is non-dimensionalized. The ratio of the system's structural natural frequency to wingbeat frequency characterizes its constant stiffness, and the amplitude of flapping motion characterizes its time-periodic stiffness. Current flapping mechanisms and MAVs are compared to biological fliers on the basis of the characteristic parameters. The beam analysis is extended to develop an plate model of a flapping wing. The time-periodic stability of the flapping wing model is assessed with Floquet analysis. A flapping-wing stability diagram is developed as a function of the characteristic parameters. The analysis indicates that time-periodic instabilities are more likely for large-amplitude, high-frequency flapping motion. Instabilities associated with the first bending mode dominate the stability diagram. Due to current limitations of flapping mechanisms, instabilities are not likely in current experiments but become more likely at the operating conditions of biological fliers. The effect of structural design parameters, including wing planform and material stiffness, are assessed with an assumed-modes aeroelastic model. Wing planforms are developed from an empirical model of biological planforms. Non-linearities are described in the effect of membrane thickness on lift generation. Structural couplings due to time-periodic stiffness are identified that can decrease lift generation at certain wingbeat frequencies

Investigation of Aerodynamics of Flapping Wings for Miro Air Vehicle Applications

A coupled CFD-CSD solver was used to simulate the aerodynamics of a flexible flapping wing. The CFD solver is a compressible RANS (Reynolds Averaged Navier Stokes) solver. Multibody dynamics solver `MBDyn', was used as the structural solver to take into account non linear shell straining, making it possible to analyze low aspect ratio wings with large deformations. Validation of the two codes was carried out independently. The solvers were then coupled using python and validated against prior experiments and analysis on spanwise and chordwise flexible wings. As realistic MAV wings are extremely flexible and lightweight, under the effect of high inertial and aerodynamic forces, they undergo large non linear deformations over a flap cycle. However, there is a dearth of experimental data on well characterized flapping wings (with known structural and mass properties) at MAV-scale Reynolds numbers. Systematic experiments were carried out on rigid and flexible flapping wings in an open jet wind tunnel and forces were measured using a test bed. Pure flapping of rigid wings did not generate sufficient propulsive force and may not be a viable configuration. Passive pitching of rigid wing generated both, target vertical and propulsive forces. Dynamic wing twist was then incorporated using flexible wings. A flexible wing was fabricated using a combination of unidirectional carbon fiber strips (chordwise ribs), carbon rod (leading edge spar) and mylar film (membrane). Structural model of the wing (combination of beam and shell elements) was developed and then coupled to the CFD model. CFD-CSD analysis of flexible wing was carried out and good correlation was obtained for all the configurations. This comprehensive experimental data set can also be used to validate other aeroelastic analyses of the future. Further, the analysis was used to gain more insights into flow physics. It was observed that as a result of flexibility, by taking advantage of unsteady flow features, a lighter, simpler mechanism could be used to produce larger forces than a rigid wing. The validated, comprehensive analysis developed in this work may serve as a design tool for deciding configurations and wing kinematics of next generation MAVs

Experimental and computational analysis for insect inspired flapping wing micro air vehicles

Many creatures in nature have evolved the ability to fly and some seem to do so effortlessly with captivating movement. The flight characteristics of these natural fliers have greatly fascinated biologists and engineers for a long time that to this day researchers continue to actively work in this field of science with the aim of one day developing a Flapping Wing Micro Aerial Vehicle (FWMAV) which can replicate the flight of nature's creatures. These types of autonomous robotic vehicles can fulfil tasks which are not suitable for manned vehicles especially when risks to human safety are present. Flight techniques such as control, stability and manoeuvrability are flight characteristics which an FWMAV must possess if such a device is employed for various rescue missions. With this in mind symmetrical and asymmetrical wing motions are studied experimentally in the current research programme in such a way that the methodology employed for this type of flight can be implemented into future FWMAVs. In summary, the research performed during the course of this project produced innovative results in the form of the creation of two micro air vehicles with a thorough explanation of the development process and examination under experimental tests. Various parameters were analysed during the experimental tests such as force, moment, power and wing position measurements. The tests were performed on both models, one of which has the functionality to perform asymmetrical flapping and successfully generate moments about two different axes. A unique wing motion which favoured the upward vertical force production was investigated under various scenarios. The wings keep a fixed angle of attack during the downwards flapping motion and are allowed to passively rotate during the upstroke motion. Computational simulations were performed to investigate the hovering fluid dynamics, forces, moments and power required for various chordwise rotational positions and durations of wing rotation. This investigation aided in understanding the full effects of altering these parameters under hovering conditions for a rectangular wing. The valuable results found from this research program provide a better insight into various topics involving micro air vehicles in addition to developing future flight worthy insect inspired vehicles