William C. Sandberg

Simulation of Flow About Flapping Airfoils Using Finite Element Incompressible Flow Solver

Ae niteelemente owsolverbasedonunstructuredgridsisemployedforstudyingtheunsteadye owpastoscillating airfoils. The viscous e ow past a NACA0012 airfoil at various pitching frequencies is simulated. The variation of the force coefe cient with reduced frequency is compared to experimental and other numerical studies. The effect of variation of the amplitude of the pitching motion on the force coefe cient shows that the critical parameter for thrust generation is not the reduced frequency but the Strouhal number based on the maximum excursion of the trailing edge. The e ow about theairfoil in a combined pitching and heaving motion, a modefound in many insects, is also simulated. The effects of varying the phase angle between the pitch and the heave motions is studied. The thrust coefe cient was compared with experimental studies and good agreement is obtained. It is found that the maximumthrustcoefe cient isobtained forwhen thepitchmotionleads theheavemotion by 120 deg andmaximum propulsive efe ciency occurs at a phase angle of 90 deg.

A computational investigation of the three-dimensional unsteady aerodynamics of Drosophila hovering and maneuvering.

SUMMARY Three-dimensional unsteady computations of the flow past a fruit fly Drosophila under hovering and free flight conditions are computed. The kinematics of the wings and the body of the fruit fly are prescribed from experimental observations. The computed unsteady lift and thrust forces are validated with experimental results and are in excellent agreement. The unsteady aerodynamic origin of the time-varying yaw moment is identified. The differences in the kinematics between the right and the left wings show that subtle change in the stroke angle and deviation angle can result in the yaw moment for the turning maneuver. The computed yaw moment reaches a peak value at the beginning of the maneuver and remains positive throughout the remainder of the maneuver. The origin of the yaw moment is investigated by computing the center of pressures on each wing and the individual moment arms. This investigation leads to the conclusion that it is the forward force and a component of the lift force that combine to produce the turning moment while the side force alone produces the restoring torque during the maneuver. The vorticity shed from the wings leading edge and the tips show a loop like structure that during stroke reversals pinches off into Λ-like structures that have not been previously observed in the wakes of flapping fliers.

Computational Fluid Dynamics Study for Optimization of a Fin Design

Abstract : The three-dimensional, unsteady computations of an Unmanned Underwater vehicle with flapping fins were carried out. Several parametric studies were performed varying the amplitude and frequency of oscillation of the fin and the angle of attack of the fin at the root. The objective of these computations was to investigate the importance of these parameters on the fluid dynamics of force production in order to propel the vehicle at a constant speed of 3 kt. An unstructured grid-based unsteady Navier-Stokes solver with automatic adaptive remeshing was used to compute the flow about the vehicle through several complete cycles of fin oscillation for each of the cases studied. The computations show that the angle of attack of 20 of the root section of the fin is near optimum. The vehicle is capable of sustaining a 3 kt current and maintaining position with the fins flapping at a frequency of 2 Hz and an amplitude of 11 4%. As the frequency of oscillation is increased, the net thrust produced increases, but the vehicle will be subjected to large excursions in the normal force. As the fin is made rigid, there is a substantial penalty in lift during the upstroke.

THE INFLUENCE OF FIN RIGIDITY AND GUSTS ON THE FORCE PRODUCTION IN FISHES AND INSECTS : A COMPUTATIONAL STUDY

The three-dimensional unsteady computations of fish swimming with oscillating and deforming fins of varying rigidity were carried out. The objective of these variable rigidity computations was to investigate the importance of fin deformation on the fluid dynamics of force production. An unstructured grid-based unsteady Navier-Stokes solver with automatic adaptive remeshing was used to compute the flow about the wrasse through several complete cycles of pectoral fin oscillation for each of the fins studied. The computations show that when the fin is made rigid by specifying the motion with just the leading edge of the fin tip, the thrust produced during the upstroke is less than half of the peak thrust produced by the flexible cases. During the downstroke, the rigid fin and the fin with the motion prescribed with only the leading and trailing edges produced no positive thrust, while all the flexible cases considered reproduced the thrust production of the fully deformable fin. In the case of the rigid fin, there is a substantial penalty in lift during the upstroke. We have also computed the unsteady flow computations over the Drosophila wing with the flight conditions ranging from hovering to a downward gust velocity nearly equal to the mean wing tip velocity. We showed that the wake capture mechanism which is responsible for a peak in thrust production just after stroke reversal diminished with increasing downward velocity and is entirely absent when this velocity reaches the mean wing tip velocity.

Computations of Flapping Flow Propulsion for Unmanned Underwater Vehicle Design

Three-dimensional unsteady computations of the flow past a flapping and deforming fin are performed. The computed unsteady lift and thrust force-time histories are validated with experimental data and are in good agreement. Several fin parametric studies are performed for a notional unmanned underwater vehicle. The parametric studies investigated the force production of the fin as a function of varying the flexibility, the bulk amplitude of fin rotation, the vehicle speed, and the fin stroke bias angle. The results of these simulations are used to evaluate the hydrodynamic performance of the vehicle and to support controller development. Computations are also performed to map out the hydrodynamic characteristics of a new test vehicle, designed and built at Naval Research Laboratory to demonstrate the hovering and low-speed maneuvering performance of a set of actively controlled curvature fins.

Computations of Insect and Fish Locomotion with Applications to Unconventional Unmanned Vehicles

Living creatures such as insects, birds, and fish generate lift and thrust most often by executing large-amplitude wing flapping, possibly with substantial shape deformation from root to tip. The flow for these motions is unsteady, and conventional steady-state aerodynamics is unable to correctly compute the time history of their flapping-force generation. Three-dimensional unsteady computations of flapping about the deforming wing or fin surface are necessary to correctly predict the lift and thrust throughout the flapping cycle. It is only by executing such computations for creatures or vehicles with moving and deforming surfaces that we can gain insights into the time-varying pressure distribution on all surfaces and how that results in flapping-force generation. This can be coupled with visualization of the origination and evolution of body, wing, and wake vorticity. Three-dimensional unsteady flow computations of the flapping flights of the fruit fly, a pectoral-fin swimmer (the bird wrasse), and a variety of unmanned air vehicles were carried out in pursuit of this information. The performance of these flapping wings under gust conditions was also investigated. The effect of fin deformation on the force production was studied. Novel biomimetic vehicles, incorporating information gained from these computations, were designed and built and their performance is described.

DEVELOPMENT AND TESTING OF UNCONVENTIONAL MICRO AIR VEHICLE CONFIGURATIONS

The Naval Research Laboratory (NRL) is developing a group of micro air vehicle (MAV) concepts intended for operation in urban or other confined environments. Primary flight requirements for these MAVs are low speed maneuverability, vertical or near vertical takeoff and landing, the potential for hovering, and compatibility with ground operation as a “perched” sensor platform. The additional requirement for such MAVs to be small enough (wingspans of less than 150 mm) to operate unobtrusively has focused attention on flapping foil propulsion and other unconventional configurations. In the low Reynolds number (2,000 ≤ Re ≤ 30,000) and low speed (2-5 m/s) regimes applicable to such tiny aircraft, airfoil performance degradation significantly reduces propeller efficiency as size decreases. Flapping wings can be dynamically advantageous for propulsion under these conditions. While many flapping wing vehicles such as ornithopters attempt to mimic the flight of birds or insects, it is possible to use flapping foil propulsion in ways that are inspired by biological flight but do not copy it directly. “Aerial swimming” vehicles use a flapping wing that resembles a boat’s sail with the mast running horizontally, driven by a central oscillating beam. The wing’s camber reverses on each half cycle. Three configurations have flown successfully: a vehicle with a fixed forward wing and a rear flapping wing; a tandem fixed-wing design with a third flapping wing that claps down atop the rear fixed surface on each stroke; and a vehicle with tandem pairs of biplane configured flapping wings, in which each pair moves in opposition so as to alternately clap together and separate. This latter vehicle, which does not employ fixed lifting surfaces, has the advantage of being dynamically balanced in flight so that its center of mass

Modeling and Control Design for a Flapping-Wing Nano Air Vehicle

A full six-degree-of-freedom vehicle model is constructed for a flapping-wing nano air vehicle (NAV) which includes components for the body, wings, sensors, and unique shape memory alloy (SMA) driven actuator mechanisms. The design of these actuator mechanisms and the link between the SMAs and wing kinematics is described. Algorithms for sensory feedback control of the vehicle dynamics are designed and implemented in simulation. The outputs of four control modules command changes in the wing stroke amplitude, mean position, and plane angle. An extended Kalman filter is developed to improve attitude estimation and stabilize the NAV. Vehicle responses to hover, forward flight and turning commands are assessed and desirable performance is achieved.

Simulation of a Torpedo Launch Using A 3-D Incompressible Finite Element Solver and Adaptive Remeshing.

Abstract : An implicit finite element solver for three dimensional incompressible flows with adaptive remeshing has been developed. This flow solver is employed for the simulation of an unsteady torpedo launch from a submarine. Several mesh movement algorithms have been developed and implemented. The use of gliding points on surfaces in the vicinity of a moving body has proven valuable in reducing the number of remeshings and thus reducing the total CPU time required for the simulation. The adaptive flow solver has been parallelized and is written in a manner that allows portability among various supercomputer architectures. (AN)

Bioinspired Design Process for an Underwater Flying and Hovering Vehicle

l We review here the results obtained during the past several years in a series of computational and experimental investigations aimed at understanding the origin of high-force production in the flapping wings of insects and the flapping and deforming fins of fish and the incorporation of that information into bioinspired vehicle designs. We summarize the results obtained on pectoral fin force production, flapping and deforming fin design, and the emulation of fish pectoral fin swimming in unmanned vehicles. In particular, we discuss the main results from the computational investigations of pectoral fin force production for a particular coral reef fish, the bird wrasse (Gomphosus varius), whose impressive underwater flight and hovering performance matches our vehicle mission requirements. We describe the tradeoffs made between performance and produceability during the bio-inspired design of an actively controlled curvature pectoral fin and the incorporation of it into two underwater flight vehicles: a two-fin swimming version and four-fin swimming version. We describe the unique computational approach taken throughout the fin and vehicle design process for relating fin deformation time-histories to specified desired vehicle dynamic behaviors. We describe the development of the vehicle controller, including hardware implementation, using actuation of the multiple deforming flapping fins as the only means of propulsion and control. Finally, we review the comparisons made to date between four-fin vehicle experimental trajectory measurements and controller simulation predictions and discuss the incorporation of those comparisons into the controller design.