Estimation of Unsteady Aerodynamics in the Wake of a Freely Flying European Starling (Sturnus vulgaris)

Wing flapping is one of the most widespread propulsion methods found in nature; however, the current understanding of the aerodynamics in bird wakes is incomplete. The role of the unsteady motion in the flow and its contribution to the aerodynamics is still an open question. In the current study, the wake of a freely flying European starling has been investigated using long-duration high-speed Particle Image Velocimetry (PIV) in the near wake. Kinematic analysis of the wings and body of the bird has been performed using additional high-speed cameras that recorded the bird movement simultaneously with the PIV measurements. The wake evolution of four complete wingbeats has been characterized through reconstruction of the time-resolved data, and the aerodynamics in the wake have been analyzed in terms of the streamwise forces acting on the bird. The profile drag from classical aerodynamics was found to be positive during most of the wingbeat cycle, yet kinematic images show that the bird does not decelerate. It is shown that unsteady aerodynamics are necessary to satisfy the drag/thrust balance by approximating the unsteady drag term. These findings may shed light on the flight efficiency of birds by providing a partial answer to how they minimize drag during flapping flight.     

Numerical models for the simulation of flexible artificial heart valves: part I--computational methods

A numerical model of the coupled motion of a flexing surface in a high Reynolds number flow is presented for the simulation of flexible polyurethane heart valves in the aortic position. This is achieved by matching a Lagrangian dynamic leaflet model with a panel method based flow solver. The two models are coupled via the time-dependent pressure field using the unsteady Bernoulli equation. Incorporation of sub-cycling in the dynamic model equations and fast pre conditioning techniques in the panel method solver yields efficient convergence and near real-time simulations of valve motion. The generality of dynamic model allows different material properties and/or geometries to be studied easily and interactively. This interactivity is realized by embedding the models within a design environment created using the software IRIS Explorer. Two flow domains are developed, an infinite domain and an internal domain using conformal mapping theory. In addition bending stress on the valve is computed using a simple stress model based on spline and circle equation techniques.     

On the Estimation of Time Dependent Lift of a European Starling (Sturnus vulgaris) during Flapping Flight

We study the role of unsteady lift in the context of flapping wing bird flight. Both aerodynamicists and biologists have attempted to address this subject, yet it seems that the contribution of unsteady lift still holds many open questions. The current study deals with the estimation of unsteady aerodynamic forces on a freely flying bird through analysis of wingbeat kinematics and near wake flow measurements using time resolved particle image velocimetry. The aerodynamic forces are obtained through two approaches, the unsteady thin airfoil theory and using the momentum equation for viscous flows. The unsteady lift is comprised of circulatory and non-circulatory components. Both approaches are presented over the duration of wingbeat cycles. Using long-time sampling data, several wingbeat cycles have been analyzed in order to cover both the downstroke and upstroke phases. It appears that the unsteady lift varies over the wingbeat cycle emphasizing its contribution to the total lift and its role in power estimations. It is suggested that the circulatory lift component cannot assumed to be negligible and should be considered when estimating lift or power of birds in flapping motion.     

Numerical Models for the Simulation of Flexible Artificial Heart Valves: Part I - Computational Methods

Abstract

A numerical model of the coupled motion of a flexing surface in a high Reynolds number flow is presented for the simulation of flexible polyurethane heart valves in the aortic position. This is achieved by matching a Lagrangian dynamic leaflet model with a panel method based flow solver. The two models are coupled via the time-dependent pressure field using the unsteady Bernoulli equation.

Incorporation of sub-cycling in the dynamic model equations and fast pre conditioning techniques in the panel method solver yields efficient convergence and near real-time simulations of valve motion. The generality of dynamic model allows different material properties and/or geometries to be studied easily and interactively. This interactivity is realized by embedding the models within a design environment created using the software IRIS Explorer ^TM.

Two flow domains are developed, an infinite domain and an internal domain using conformal mapping theory. In addition bending stress on the valve is computed using a simple stress model based on spline and circle equation techniques.     

Control for small-speed lateral flight in a model insect

Controls required for small-speed lateral flight of a model insect were studied using techniques based on the linear theories of stability and control (the stability and control derivatives were computed by the method of computational fluid dynamics). The main results are as follows. (1) Two steady-state lateral motions can exist: one is a horizontal side translation with the body rolling to the same side of the translation by a small angle, and the other is a constant-rate yaw rotation (rotation about the vertical axis). (2) The side translation requires an anti-symmetrical change in the stroke amplitudes of the contralateral wings, and/or an anti-symmetrical change in the angles of attack of the contralateral wings, with the down- and upstroke angles of attack of a wing having equal change. The constant-rate yaw rotation requires an anti-symmetrical change in the angles of attack of the contralateral wings, with the down- and upstroke angles of attack of a wing having differential change. (3) For the control of the horizontal side translation, control input required for the steady-state motion has an opposite sign to that needed for initiating the motion. For example, to have a steady-state left side-translation, the insect needs to increase the stroke amplitude of the left wing and decrease that of the right wing to maintain the steady-state flight, but it needs an opposite change in stroke amplitude (decreasing the stroke amplitude of the left wing and increasing that of the right wing) to enter the flight.     

Numerical Models for the Simulation of Flexible Artificial Heart Valves: Part II - Valve Studies

Abstract

Using a coupled Lagrangian dynamic leaflet model and an unsteady potential flow solver the motion of a polyurethane type heart valve is simulated in the aortic position. The simulations incorporate two flow domains; the first comprises only the leaflets which are embedded within an unsteady flow of infinite expanse, and the second incorporates the influence of the aortic geometry via a conformal mapping. Simulations are performed for a cardiac output of 51itres/min and a beat period of 72 b.p.m. corresponding to a typical aortic pulse. Resulting valve motions are computed for various leaflet bending stiffnesses in both flow domains. In addition both the bending stress and strain and their time rate of change are evaluated. Valve motion displays the characteristic rapid opening, stable opening and slow closing phases as detailed in the literature. The computed stress values along the leaflet surface are of the order of those found experimentally.     

Tail effects on yaw stability in birds

Bird tails, which are an aerodynamic surface in the horizontal plane, are treated with regard to their effects on yaw stability. Reference is made to wings of very small aspect ratio similar to the values of bird tails in order to identify features which are significant for the aerodynamic yawing moment characteristics due to sideslip. It is shown that there are yawing moments of considerable magnitude for this aspect ratio region. Furthermore, the lift coefficient, which also exerts an influence, is included in the treatment of yaw stability. To show more concretely the addressed effects for birds, the yawing moment characteristics of the wing-tail combination of a pigeon, which is considered as a representative example, are treated in detail. For this purpose, a sophisticated aerodynamic method capable to deal with the mutual flow interactions between the tail and the wing is used to compute results of high precision. The yawing moment characteristics of the pigeon wing-tail combination with respect to the sideslip angle and the lift coefficient are determined, with emphasis placed on the contribution of the tail. It is shown that there is a significant contribution of the tail to yaw stability. The findings of this paper on the contribution of the tail to the yawing moment characteristics are supported by an evaluation of existing experimental data. Furthermore, the physical mechanisms are considered which are the reasons for the stabilizing role of the tail. These effects concern the contribution of the drag acting at the tail to the yawing moment. In addition, it is shown that extended legs and feet, when exposed to the airflow, can contribute to yaw stability.     

Yaw stability in gliding birds

A new concept for describing the yaw stability in gliding birds is presented. This concept introduces dynamic stiffness in yaw as an appropriate indication of stability. Other than the conventional metric of static yaw stability given by the gradient of the aerodynamic yawing moment with respect to the sideslip angle, the dynamic stiffness does not only provide a qualitative indication of stability but also a precise quantitative measure of the restoring action in the yaw axis. With the use of scaling relations, it is shown that the dynamic stiffness of birds is sufficiently high though their static yaw stability may be very small. The underlying mechanism is that the yaw moment of inertia is more reduced with a decrease in size than the restoring aerodynamic moment. Reference is made to the yaw stability in aircraft and related flying qualities requirements. Thus, numerical values are derived which can be used as a standard of comparison providing a rating basis for the dynamic yaw stiffness in small flying objects, like birds. Furthermore, it is shown that the wings of birds produce yawing moments due to sideslip so large that a sufficiently high level of dynamic yaw stiffness can be achieved. From the results derived in this paper, it may be concluded that birds—unlike aircraft—need no vertical tail for yaw stability.     

Dynamic Flight Stability of a Model Hoverfly in Inclined-Stroke-Plane Hovering

Most hovering insects flap their wings in a horizontal plane,called ‘normal hovering'.But some of the best hoverers,e.g.true hoverflies,hover with an inclined stroke plane.In the present paper,the longitudinal dynamic flight stability of a model hoverfly in inclined-stroke-plane hovering was studied.Computational fluid dynamics was used to compute the aerodynamic derivatives and the eigenvalue and eigenvector analysis was used to solve the equations of motion.The primary findings are as follows.(1) For inclined-stroke-plane hovering,the same three natural modes of motion as those for normal hovering were identified:one unstable oscillatory mode,one stable fast subsidence mode,and one stable slow subsidence mode.The unstable oscillatory mode and the fast subsidence mode mainly have horizontal translation and pitch rotation,and the slow subsidence mode mainly has vertical translation.(2) Because of the existence of the unstable oscillatory mode,inclined-stroke-plane hovering flight is not stable.(3) Although there are large differences in stroke plane and body orientations between the inclined-stroke-plane hovering and normal hovering,the relative position between the mean center of pressure and center of mass for these two cases is not very different,resulting in similar stability derivatives,hence similar dynamic stability properties for these two types of hovering.     

Speed stability in birds

Solutions for the speed stability problem in bird flight at low speed are developed. Speed stability is usually considered not to exist in flapping flight at speeds below the speed of the minimum power required, and in gliding flight below the speed for maximum range. Approaches thus far for solving the speed stability problem are relating to a 1-degree-of-freedom model of the bird where the speed is regarded as the only motion variable involved. However, a speed deviation is inherently associated with a deviation in the height. In this paper, an expanded treatment with an appropriate mathematical model is presented. The expanded treatment is based on a 2-degree-of-freedom model of the bird. Thus, it is possible to account for the speed and the height changes. With this expanded treatment, it can be shown that there is speed stability in the gliding flight of birds, whether the speed is below the speed for maximum range or above. This also holds for flapping flight with regard to speeds below the speed of the minimum power required. Further, it is shown that there can be speed instability if the bird acts as a controller to suppress height deviations. For this purpose, a model of the bird acting as a controller is presented.     

Combined effects of pulsatile flow and dynamic curvature on wall shear stress in a coronary artery bifurcation model

A three-dimensional model with simplified geometry for the branched coronary artery is presented. The bifurcation is defined by an analytical intersection of two cylindrical tubes lying on a sphere that represents an idealized heart surface. The model takes into account the repetitive variation of curvature and motion to which the vessel is subject during each cardiac cycle, and also includes the phase difference between arterial motion and blood flowrate, which may be nonzero for patients with pathologies such as aortic regurgitation. An arbitrary Lagrangian Eulerian (ALE) formulation of the unsteady, incompressible, three-dimensional Navier-Stokes equations is employed to solve for the flow field, and numerical simulations are performed using the spectral/hp element method. The results indicate that the combined effect of pulsatile inflow and dynamic geometry depends strongly on the aforementioned phase difference. Specifically, the main findings of this work show that the time-variation of flowrate ratio between the two branches is minimal (less than 5%) for the simulation with phase difference angle equal to 90 degrees, and maximal (51%) for 270 degrees. In two flow pulsatile simulation cases for fixed geometry and dynamic geometry with phase angle 270 degrees, there is a local minimum of the normalized wall shear rate amplitude in the vicinity of the bifurcation, while in other simulations a local maximum is observed.     

Optic flow-based collision-free strategies: From insects to robots

Flying insects are able to fly smartly in an unpredictable environment. It has been found that flying insects have smart neurons inside their tiny brains that are sensitive to visual motion also called optic flow. Consequently, flying insects rely mainly on visual motion during their flight maneuvers such as: takeoff or landing, terrain following, tunnel crossing, lateral and frontal obstacle avoidance, and adjusting flight speed in a cluttered environment. Optic flow can be defined as the vector field of the apparent motion of objects, surfaces, and edges in a visual scene generated by the relative motion between an observer (an eye or a camera) and the scene. Translational optic flow is particularly interesting for short-range navigation because it depends on the ratio between (i) the relative linear speed of the visual scene with respect to the observer and (ii) the distance of the observer from obstacles in the surrounding environment without any direct measurement of either speed or distance. In flying insects, roll stabilization reflex and yaw saccades attenuate any rotation at the eye level in roll and yaw respectively (i.e. to cancel any rotational optic flow) in order to ensure pure translational optic flow between two successive saccades. Our survey focuses on feedback-loops which use the translational optic flow that insects employ for collision-free navigation. Optic flow is likely, over the next decade to be one of the most important visual cues that can explain flying insects' behaviors for short-range navigation maneuvers in complex tunnels. Conversely, the biorobotic approach can therefore help to develop innovative flight control systems for flying robots with the aim of mimicking flying insects’ abilities and better understanding their flight.     

Mechanical stability of trees under dynamic loads

Tree stability in windstorms and tree failure are important issues in urban areas where there can be risks of damage to people and property and in forests where wind damage causes economic loss. Current methods of managing trees, including pruning and assessment of mechanical strength, are mainly based on visual assessment or the experience of people such as trained arborists. Only limited data are available to assess tree strength and stability in winds, and most recent methods have used a static approach to estimate loads. Recent research on the measurement of dynamic wind loads and the effect on tree stability is giving a better understanding of how different trees cope with winds. Dynamic loads have been measured on trees with different canopy shapes and branch structures including a palm (Washingtonia robusta), a slender Italian cypress (Cupressus sempervirens) and trees with many branches and broad canopies including hoop pine (Araucaria cunninghamii) and two species of eucalypt (Eucalyptus grandis, E. teretecornus). Results indicate that sway is not a harmonic, but is very complex due to the dynamic interaction of branches. A new dynamic model of a tree is described, incorporating the dynamic structural properties of the trunk and branches. The branch mass contributes a dynamic damping, termed mass damping, which acts to reduce dangerous harmonic sway motion of the trunk and so minimizes loads and increases the mechanical stability of the tree. The results from 12 months of monitoring sway motion and wind loading forces are presented and discussed.     

Simple pulsatile flow in an artery with a constriction

A smooth isolated, axisymmetric occlusion in a straight vascular tube is a tractable problem for pulsatile flow calculations via finite-difference approximations to the Navier-Stokes equation. Steady flow depends on the Reynolds number and two geometric parameters which describe the stenosis. The mere addition of a simple harmonic to the mean flow adds two more parameters. One is the reduced frequency, or Strokes number, and the other epsilon, the ratio of unsteady to steady flux. After describing steady stenosis flow examples, the dynamic patterns of pulsatile flow are illustrated indicating the inadequacy of basing hypotheses of atherosclerosis on mean (steady) flow.     

Numerical simulation of flow fields and particle trajectories in ciliary suspension feeding

A model describing the ciliary driven flow and motion of suspended particles in downstream suspension feeders is developed. The quasi-steady Stokes equations for creeping flow are solved numerically in an unbounded fluid domain around cylindrical bodies using a boundary integral formulation. The time-dependent flow is approximated with a continuous sequence of steady state creeping flow fields, where metachronously beating ciliary bands are modelled by linear combinations of singularity solutions to the Stokes equations. Generally, the computed flow fields can be divided into an unsteady region close to the driving ciliary bands and a steady region covering the remaining fluid domain. The size of the unsteady region appears to be comparable to the metachronal wavelength of the ciliary band. A systematic investigation is performed of trajectories of infinitely small (fluid) particles in the simulated unsteady ciliary driven flow. A fraction of particles appear to follow trajectories, that resemble experimentally observed particle capture events in the downstream feeding system of the polycheate Sabella penicillus, indicating that particles can be captured by ciliary systems without mechanical contact between particle and cilia. A local capture efficiency is defined and its value computed for various values of beat frequencies and other parameters. The results indicate that the simulated particle capture process is most effective when the flow field oscillates within timescales comparable to transit timescales of suspended particles passing the unsteady region near the ciliary bands. However, the computed retention efficiencies are found to be much lower than those obtained experimentally.     

Investigation of saccadic eye movement effects on the fluid dynamic in the anterior chamber

The aqueous humor (AH) flow in the anterior chamber (AC) due to saccadic movements is investigated in this research. The continuity, Navier-Stokes and energy equations in 3D and unsteady forms are solved numerically and the saccadic motion was modeled by the dynamic mesh technique. Firstly, the numerical model was validated for the saccadic movement of a spherical cavity with analytic solutions and experimental data where excellent agreement was observed. Then, two types of periodic and realistic saccadic motions of the AC are simulated, whereby the flow field is computed for various saccade amplitudes and the results are reported for different times. The results show that the acting shear stress on the corneal endothelial cells from AH due to saccadic movements is much higher than that due to normal AH flow by buoyancy induced due to temperature gradient. This shear stress is higher on the central region of the cornea. The results also depict that eye saccade imposes a 3D complicated flow field in the AC consist of various vortex structures. Finally, the enchantment of heat transfer in the AC by AH mixing as a result of saccadic motion is investigated.     

New modeling approach for bounding flight in birds

A new modeling approach is presented which accounts for the unsteady motion features and dynamics characteristics of bounding flight. For this purpose, a realistic mathematical model is developed to describe the flight dynamics of a bird with regard to a motion which comprises flapping and bound phases involving acceleration and deceleration as well as, simultaneously, pull-up and push-down maneuvers. Furthermore, a mathematical optimization method is used for determining that bounding flight mode which yields the minimum energy expenditure per range. Thus, it can be shown to what extent bounding flight is aerodynamically superior to continuous flapping flight, yielding a reduction in the energy expenditure in the speed range practically above the maximum range speed. Moreover, the role of the body lift for the efficiency of bounding flight is identified and quantified. Introducing an appropriate non-dimensionalization of the relations describing the bird’s flight dynamics, results of generally valid nature are derived for the addressed items.     

Perturbation analysis of 6DoF flight dynamics and passive dynamic stability of hovering fruit fly Drosophila melanogaster

Insects exhibit exquisite control of their flapping flight, capable of performing precise stability and steering maneuverability. Here we develop an integrated computational model to investigate flight dynamics of insect hovering based on coupling the equations of 6 degree of freedom (6DoF) motion with the Navier-Stokes (NS) equations. Unsteady aerodynamics is resolved by using a biology-inspired dynamic flight simulator that integrates models of realistic wing-body morphology and kinematics, and a NS solver. We further develop a dynamic model to solve the rigid body equations of 6DoF motion by using a 4th-order Runge-Kutta method. In this model, instantaneous forces and moments based on the NS-solutions are represented in terms of Fourier series. With this model, we perform a systematic simulation-based analysis on the passive dynamic stability of a hovering fruit fly, Drosophila melanogaster, with a specific focus on responses of state variables to six one-directional perturbation conditions during latency period. Our results reveal that the flight dynamics of fruit fly hovering does not have a straightforward dynamic stability in a conventional sense that perturbations damp out in a manner of monotonous convergence. However, it is found to exist a transient interval containing an initial converging response observed for all the six perturbation variables and a terminal instability that at least one state variable subsequently tends to diverge after several wing beat cycles. Furthermore, our results illustrate that a fruit fly does have sufficient time to apply some active mediation to sustain a steady hovering before losing body attitudes.     

Lateral Flight Stability of Two Hovering Model Insects

The longitudinal disturbance motion of different insects at hovering flight has the same modal structure. Here, we consider the case of lateral motion. The lateral dynamic flight stability of two model insects, hoverfly and honeybee, at hovering flight is studied. The method of computational fluid dynamics is applied to compute the stability derivatives. The techniques of eigenvalue and eigenvector analysis are used to solve the equations of motion. Results show that the lateral disturbance motion of the hoverfly has three natural modes of motion： an unstable divergence mode, a stable oscillatory mode and a stable subsidence mode, and the flight is unstable; while the honeybee has a different modal structure （a stable slow subsidence mode, a stable fast subsidence mode, and a nearly neutrally stable oscillatory mode） and the flight is nearly neutrally stable. The change in modal structure between the two insects is due to their roll-moment/side-velocity derivative having different sign, and the sign difference is because that the hoverfly has a relatively small, but the honeybee has a relatively large, distance between the wing roots and the center of mass. Thus, unlike the case of longitudinal motion, for lateral motion, some insects have different modal structures and stability properties from others.     

Propulsion of a fin whale (Balaenoptera physalus): why the fin whale is a fast swimmer

Measurements of an immature fin whale (Balaenoptera physalus), which died as a result of entrapment in fishing gear near Frenchmans Cove, Newfoundland (47 degrees 9' N, 55 degrees 25' W), were made to obtain estimates of volume and surface area of the animal. Detailed measurements of the flukes, both planform and sections, were also obtained. A strip theory was developed to calculate the hydrodynamic performance of the whale's flukes as an oscillating propeller. This method is based on linear, two-dimensional, small-amplitude, unsteady hydrofoil theory with correction factors used to account for the effects of finite span and finite amplitude motion. These correction factors were developed from theoretical results of large-amplitude heaving motion and unsteady lifting-surface theory. A model that makes an estimate of the effects of viscous flow on propeller performance was superimposed on the potential-flow results. This model estimates the drag of the hydrofoil sections by assuming that the drag is similar to that of a hydrofoil section in steady flow. The performance characteristics of the flukes of the fin whale were estimated by using this method. The effects of the different correction factors, and of the frictional drag of the fluke sections, are emphasized. Frictional effects in particular were found to reduce the hydrodynamic efficiency of the flukes significantly. The results are discussed and compared with the known characteristics of fin-whale swimming.