Cycle-averaged Forces Research Articles

Flow Structures Around a Flapping-Wing Micro Air Vehicle Performing a Clap-and-Peel Motion

The vortical flow structures generated by the flapping wings of the DelFly II micro air vehicle in hovering flight configuration are investigated using particle image velocimetry. Synchronous force measurements are carried out to establish the relation between the unsteady forces and force generation mechanisms: particularly, the leading-edge vortex and the clap-and-peel motion. The formation of conical leading-edge vortices on both wings is revealed, which occurs rapidly at the start of the outstroke as a result of the wing–wing interaction. The leading-edge vortices of the outstroke interact with those of the instroke, which are shed and, by mutual induction, advect upstream as a vortex pair at the end of previous instroke. The leading-edge vortex pairs induce a strong inflow into the region formed between the upper and lower wings during the peeling phase, resulting in the formation of a low-pressure region. This, together with the leading-edge vortices and a momentum increase formed by the clap, accounts for the generation of relatively higher forces during the outstroke. The cycle-averaged forces are estimated with reasonable accuracy by means of a momentum-based approach using wake velocity information with an average error of 15%.

Control of a Minimally Actuated Biomimetic Vehicle Using Quarter-Cycle Wingbeat Modulation

This paper describes a technique, called quarter-cycle constant period frequency modulation, to control the motion of wings on a flapping wing micro-air vehicle. This technique allows control over the wingbeat period and three additional points (the two zero crossings and the reversal of wing direction) within a single wingbeat cycle, allowing modulation of the wing’s velocity to provide direct control over six degrees of freedom of overall vehicle motion. Using a blade element based aerodynamic model, both instantaneous and cycle-averaged forces and moments are analytically computed for a specific type of wingbeat motion that enables nearly decoupled, multi-degrees of freedom control of an aircraft. Wing motion is controlled using oscillators whose frequencies and three additional parameters change once per wingbeat cycle. A control oriented dynamic model of the vehicle is derived, which is based on a cycle-averaged representation of the forces and moments, and control derivatives are calculated. A cycle-averaged control law is designed to provide direct control over six degrees of freedom of the vehicle.

Force estimation from incompressible flow field data using a momentum balance approach

This study investigates how aerodynamic forces on a body can be evaluated using only instantaneous or averaged velocity field data through a control volume approach in an incompressible flow. The method allows for velocity field data to be missing inside the control volume, but requires that the product of the acceleration, the volume of the solid body, and the fluid density are negligible compared to the forces of interest. Validation of the method for accuracy has been conducted using three-dimensional data from a numerical simulation of unsteady flow around a static airfoil and has shown good agreement between actual and estimated force. Additionally, the method is tested using phase-averaged PIV data from flexible flapping membrane wings to calculate flapping cycle averaged forces that are compared with directly measured time-averaged forces. The numerical validation suggests that the method is accurate, while it is only able to give a rough estimate for the noisier experimental data. The lower accuracy of the forces estimated from the PIV data can be explained through experimental constraints, such as too large grid spacing in one of the three dimensions (in one of the cases), having to interpolate data on the control volume surface especially where the PIV laser light is shaded by the wing, and not covering the entire span of the wing.

Dynamics and Control of a Biomimetic Vehicle Using Biased Wingbeat Forcing Functions

A wingbeat forcing function and control method are presented that allow six-degree-of-freedom control of a flapping-wing micro air vehicle using only two actuators, each of which independently actuate a wing. Split-cycle constant-period frequency modulation with wing bias is used to produce nonzero cycle-averaged drag. The wing bias provides pitching-moment control and, when coupled with split-cycle constant-period frequency modulation, requires only independently actuated wings to enable six-degree-of-freedom flight. Wing bias shifts the cycle-averaged center-of-pressure locations of the wings, thus providing the ability to pitch the vehicle. Implementation of the wing bias is discussed, and modifications to the wingbeat forcing function are made to maintain wing position continuity. Instantaneous and cycle-averaged forces and moments are computed, cycle-averaged control derivatives are calculated, and a controller is developed. The controller is designed using a simplified aerodynamic model derived with blade-element theory and cycle averaging. The controller is tested using a simulation that includes blade-element-based estimates of the instantaneous aerodynamic forces and moments that are generated by the combined motion of the rigid-body fuselage and the flapping wings. Simulations using this higher-fidelity model indicate that the cycle-averaged blade-element-based controller is capable of achieving controlled flight.

Wingbeat Shape Modulation for Flapping-Wing Micro-Air-Vehicle Control During Hover

A new method of controlling a flapping-wing micro air vehicle by varying the velocity profiles of the wing strokes is presented in this manuscript. An exhaustive theoretical analysis along with simulation results show that this new method, called split-cycle constant-period frequency modulation, is capable of providing independent control over vertical and horizontal body forces as well as rolling and yawing moments using only two physical actuators, whose oscillatory motion is defined by four parameters. An actuated bob-weight is introduced to enable independent control of pitching moment. A general method for deriving sensitivities of cycle-averaged forces and moments to changes in wingbeat kinematic parameters is provided, followed by an analytical treatment for a case where the angle of attack of each wing is passively regulated and the motion of the wing spar in the stroke plane is driven by a split-cycle waveform. These sensitivities are used in the formulation of a cycle-averaged control law that successfully stabilizes and controls two different simulation models of the aircraft. One simulation model is driven by instantaneous aerodynamic forces derived from blade-element theory, while the other is driven by an empirical representation of an unsteady aerodynamic model that was derived from experiments.

Acceleration of neutral atoms in strong short-pulse laser fields

A charged particle exposed to an oscillating electric field experiences a force proportional to the cycle-averaged intensity gradient. This so-called ponderomotive force plays a major part in a variety of physical situations such as Paul traps for charged particles, electron diffraction in strong (standing) laser fields (the Kapitza-Dirac effect) and laser-based particle acceleration. Comparably weak forces on neutral atoms in inhomogeneous light fields may arise from the dynamical polarization of an atom; these are physically similar to the cycle-averaged forces. Here we observe previously unconsidered extremely strong kinematic forces on neutral atoms in short-pulse laser fields. We identify the ponderomotive force on electrons as the driving mechanism, leading to ultrastrong acceleration of neutral atoms with a magnitude as high as approximately 10(14) times the Earth's gravitational acceleration, g. To our knowledge, this is by far the highest observed acceleration on neutral atoms in external fields and may lead to new applications in both fundamental and applied physics.

A harmonic model of hydrodynamic forces produced by a flapping fin

The hydrodynamic control laws of unsteady fins inspired by swimming and flying animals are considered. A controller based on cycle-averaged forces requires a bandwidth lower than the flapping frequency, with correspondingly slow reactions to disturbances or commands in order to avoid undesirable feedback from the oscillating fins. A harmonic model of the periodic thruster forces was empirically found using a mechanical fin flapping in roll and pitch in hover, in uniform flow, and under various kinematic conditions. A multi-fin vehicle could use this model to account for the dominant non-linearities and minimize undesirable motions through coordinated control of individual fins.