AERODYNAMIC FORCE AND FLOW STRUCTURES OF TWO AIRFOILS IN FLAPPING MOTIONS

Aerodynamic force and flow structures of two airfoils in a tandem configuration in flapping motions axe studied, by solving the Navier-Stokes equations in moving overset grids. Three typical phase differences between the fore- and aft-airfoil flapping cycles are considered. It is shown that: (1) in the case of no interaction (single airfoil), the time average of the vertical force coefficient over the downstroke is 2.74, which is about 3 times as large as the maximum steady-state lift coefficient of a dragonfly wing; the time average of the horizontal force coefficient is 1.97, which is also large. The reasons for the large force coefficients are the acceleration at the beginning of a stroke, the delayed stall and the 'pitching-up' motion near the end of the stroke. (2) In the cases of two-airfoils, the time-variations of the force and moment coefficients on each airfoil are broadly similar to that of the single airfoil in that the vertical force is mainly produced in downstroke and the horizontal force in upstroke, but very large differences exist due to the interaction. (3) For in-phase stroking, the major differences caused by the interaction are that the vertical force on FA in downstroke is increased and the horizontal force on FA in upstroke decreased. As a result, the magnitude of the resultant force is almost unchanged but it inclines less forward. (4) For counter stroking, the major differences are that the vertical force on AA in downstroke and the horizontal force on FA in upstroke are decreased. As a result, the magnitude of the resultant force is decreased by about 20 percent but its direction is almost unchanged. (5) For 90 degrees -phase-difference stroking, the major differences axe that the vertical force on AA in downstroke and the horizontal force on FA in upstroke axe decreased greatly and the horizontal force on AA in upstroke increased. As a result, the magnitude of the resultant force is decreased by about 28% and it inclines more forward. (6) Among the three cases of phase angles, inphase flapping produces the largest vertical force (also the largest resultant force); the 90 degrees -phase-difference flapping results in the largest horizontal force, but the smallest resultant force.

Experimental and numerical study on the flapping motion of submerged turbulent plane jet

A submerged,vertical turbulent plane water jet impinging onto a free surface will be self-excited into a flapping oscillation when the jet velocity,leaving the jet orifice,exceeds a critical value.The flapping phenomenon was verified simultaneously in this paper by laser Doppler velocimeter measurement and numerical analyses with volume of fluid approach coupled with a large eddy simulation turbulent model.The general agreement of mean velocities between numerical predictions and experimental results in self-similar region is good for two cases:Reynolds numbers 2090 and 2970,which correspond to the stable impinging jet and flapping jet.Results show that the flapping jet is a new flow pattern for submerged turbulent plane jets with characteristic flapping frequency,and that the decay of the mean velocity along the jet centerline is considerably faster than that of the stable impinging state.

Flow Characteristics of Flapping Motion of a Plane Water Jet Impinging onto Free Surface

A submerged turbulent plane jet in shallow water impinging vertically onto the free surface will produce a large-scale flapping motion when the jet exit velocity is larger than a critical one.The flapping phenomenon is verified in this paper through a large eddy simulation where the free surface is modeled by volume of fluid approach.The quantitative results for flapping jet are found to be in good agreement with available experimental data in terms of mean velocity,flapping-induced velocity and turbulence intensity.Results show that the flapping motion is a new flow pattern with characteristic flapping frequency for submerged turbulent plane jets,the mean centerline velocity decay is considerably faster than that of the stable impinging jet without flapping motion,and the flapping-induced velocities are as important as the turbulent fluctuations.

A STUDY ON THE MECHANISM OF HIGH-LIFT GENERATION BY AN AIRFOIL IN UNSTEADY MOTION AT LOW REYNOLDS NUMBER

The aerodynamic force and flow structure of NACA 0012 airfoil performing an unsteady motion at low Reynolds number (Re = 100) are calculated by solving Navier-Stokes equations. The motion consists of three parts: the first translation, rotation and the second translation in the direction opposite to the first. The rotation and the second translation in this motion are expected to represent the rotation and translation of the wing-section of a hovering insect. The flow structure is used in combination with the theory of vorticity dynamics to explain the generation of unsteady aerodynamic force in the motion. During the rotation, due to the creation of strong vortices in short time, large aerodynamic force is produced and the force is almost normal to the airfoil chord. During the second translation, large lift coefficient can be maintained for certain time period and (C) over bar (L), the lift coefficient averaged over four chord lengths of travel, is larger than 2 (the corresponding steady-state lift coefficient is only 0.9). The large lift coefficient is due to two effects. The first is the delayed shedding of the stall vortex. The second is that the vortices created during the airfoil rotation and in the near wake left by previous translation form a short 'vortex street' in front of the airfoil and the 'vortex street' induces a 'wind'; against this 'wind' the airfoil translates, increasing its relative speed. The above results provide insights to the understanding of the mechanism of high-lift generation by a hovering insect.

Self-propulsion of flapping bodies in viscous fluids: Recent advances and perspectives

Flapping-powered propulsion is used by many animals to locomote through air or water. Here we review recent experimental and numerical studies on self-propelled mechanical systems powered by a flapping motion. These studies improve our understanding of the mutual interaction between actively flapping bodies and surrounding fluids. The results obtained in these works provide not only new insights into biolocomotion but also useful information for the biomimetic design of artificial flyers and swimmers.

Effect of Spanwise Flexibility on Propulsion Performance of a Flapping Hydrofoil at Low Reynolds Number

Spanwise flexibility is a key factor influencing propulsion performance of pectoral foils. Performances of bionic fish with oscillating pectoral foils can be enhanced by properly selecting the spanwise flexibility. The influence law of spanwise flexibility on thrust generation and propulsion efficiency of a rectangular hydro-foil is discussed. Series foils constructed by the two-component silicon rubber are developed. NACA0015 shape of chordwise cross-section is employed. The foils are strengthened by fin rays of different rigidity to realize variant spanwise rigidity and almost the same chordwise flexibility. Experiments on a towing platform developed are carried out at low Reynolds numbers of 10 000, 15 000, and 20 000 and Strouhal numbers from 0.1 to 1. The following experimental results are achieved: (1) The average forward thrust increases with the St number increased; (2) Certain degree of spanwise flexibility is beneficial to the forward thrust generation, but the thrust gap is not large for the fins of different spanwise rigidity; (3) The fin of the maximal spanwise flexibility owns the highest propulsion efficiency; (4) Effect of the Reynolds number on the propulsion efficiency is significant. The experimental results can be utilized as a reference in deciding the spanwise flexibility of bionic pectoral fins in designing of robotic fish prototype propelled by flapping-wing.

Numerical analysis on transitions and symmetry-breaking in the wake of a flapping foil

Flying and marine animals often use flapping wings or tails to generate thrust. In this paper, we will use the simplest flapping model with a sinusoidal pitching mo- tion over a range of frequency and amplitude to investigate the mechanism of thrust generation. Previous work focuses on the Karman vortex street and the reversed Karman vor- tex street but the transition between two states remains un- known. The present numerical simulation provides a com- plete scenario of flow patterns from the Karman vortex street to reversed Karman vortex street via aligned vortices and the ultimate state is the deflected Karman vortex street, as the parameters of flapping motions change. The results are in agreement with the previous experiment. We make further discussion on the relationship of the observed states with drag and thrust coefficients and explore the mechanism of enhanced thrust generation using flapping motions.

Time-history performance optimization of flapping wing motion using a deep learning based prediction model

Flapping Wing Micro Aerial Vehicles(FWMAVs)have caused great concern in various fields because of their high efficiency and maneuverability.Flapping wing motion is a very important factor that affects the performance of the aircraft,and previous works have always focused on the time-averaged performance optimization.However,the time-history performance is equally important in the design of motion mechanism and flight control system.In this paper,a time-history performance optimization framework based on deep learning and multi-island genetic algorithm is presented,which is designed in order to obtain the optimal two-dimensional flapping wing motion.Firstly,the training dataset for deep learning neural network is constructed based on a validated computational fluid dynamics method.The aerodynamic surrogate model for flapping wing is obtained after the convergence of training.The surrogate model is tested and proved to be able to accurately and quickly predict the time-history curves of lift,thrust and moment.Secondly,the optimization framework is used to optimize the flapping wing motion in two specific cases,in which the optimized propulsive efficiencies have been improved by over 40%compared with the baselines.Thirdly,a dimensionless parameter C_(variation)is proposed to describe the variation of the time-history characteristics,and it is found that C_(variation)of lift varies significantly even under close time-averaged performances.Considering the importance of time-history performance in practical applications,the optimization that integrates the propulsion efficiency as well as C_(variation)is carried out.The final optimal flapping wing motion balances good time-averaged and time-history performance.

CALCULATION OF HELICOPTER ROTOR FLAPPING ANGLESAND COMPARISON WITH MEASURED DATA

Helicopter rotor flapping angles from hover to low speed forward flight are calculated and compared with the measured data in this paper. The analytical method is based on a second order lifting line/full span free wake model as well as a fully coupled rotor trim model. It is shown that, in order to accurately predict the lateral flapping angle at low advance ratio, it is necessary to use free wake analysis to account for the highly non uniform inflow induced by the distorted wake geometry at rotor disc plane.

Flapping Characteristics of 2D Submerged Turbulent Jets in Narrow Channels

Flapping characteristics of the self-excited flapping motion of submerged vertical turbulent jet in narrow channels are studied theoretically and experimentally.It is found that the water depth is a most important parameter to the critical jet exit velocity and the jet flapping frequency.The results indicate that the critical jet exit velocity increases with water depth and the jet flapping frequency is inversely proportional to the water depth.Meanwhile,experimental result also shows that the surface disturbance wave changes the frequency of flapping motion,i.e.the flapping frequency locks-in the disturbing frequency when the disturbing frequency is near and less than the natural flapping frequency.

The Functional Role of the Hollow Region of the Butterfly Pyrameis atalanta (L.) Scale

Questions concerning the functional role of the hollow region of the butterfly Pyrameis atalanta （L.） scale are experimentally investigated. Attention was initially directed to this problem by observation of the complex microstrucmre of the butterfly scale as well as other studies indicating higher lift on butterfly wings covered with scale. The aerodynamic forces were measured for two oscillating scale models. Results indicated that the air cavity of an oscillating model of the Pyrameis atalanta （L.） scale increased the lift by a factor of 1.15 and reduced the damping coefficients by a factor of 1.38. The modification of the aerodynamic effects on the model of butterfly scale was due to an increase of the virtual air mass, which influenced the body. The hollow region of the scale increased the virtual air mass by a factor of 1.2. The virtual mass of the butterfly scale with the hollow region was represented as the sum of air mass of two imaginary geometrical figures： a circular cylinder around the scale and a right-angled parallelepiped within the hollow region. The interaction mechanism of the butterfly Pyrameis atalanta （L.） scale with a flow was described. This novel interaction mechanism explained most geometrical features of the airpermeable butterfly scale （inverted V-profile of the ridges, nozzle of the tip edge, hollow region, and openings of the upper lamina） and their arrangement.

Aerodynamic analysis of insect-like flapping wings in fan-sweep and parallel motions with the slit effect

In this study,the aerodynamic performance of flapping wings using a parallel motion was investigated and compared with the insect-like‘‘fan-sweep’’motion,and the effect of adding a slit to the wings was analyzed.First,numerical simulations were performed to analyze the wing aerodynamics of two flapping motions with equivalent stroke amplitudes over a range of pitching angles based on computational fluid dynamics(CFD).The simulation results indicated that flapping wings with a rapid and short parallel motion achieved better lift and efficiency than those of the fan-sweep motion while maintaining the same aerodynamic characteristics regarding stall delay and leading-edge vortices.For a parallel motion with a pitching angle of 25◦and 100 mm stroke amplitude,the wings generated an average lift of 8.4 gf with a lift-to-drag ratio of 1.06,respectively,which were 1.8%and 26%greater than those of the fan-sweep motion with a corresponding 96◦stroke amplitude.This situation was reversed when the pitching angle and stroke amplitude were increased to 45◦and 144◦for the fan-sweep motion,which was equivalent to the parallel motion with a 150 mm stroke amplitude.The slit effect in the parallel motion was also evaluated,and the CFD results indicated that a slit width of 1 mm(1/50 wing chord)increased the lift of the wing by approximately 27%in the case of the 150 mm stroke amplitude.Further,the slit width slightly influenced the lift and aerodynamic efficiency.

A review of bird-like flapping wing with high aspect ratio

Bird-like flapping-wing vehicles with a high aspect ratio have the potential to fulfill missions given to micro air vehicles,such as high-altitude reconnaissance,surveillance,rescue,and bird group guidance,due to their good loading and long endurance capacities.Biologists and aeronautical researchers have explored the mystery of avian flight and made efforts to reproduce flapping flight in bioinspired aircraft for decades.However,the cognitive depth from theory to practice is still very limited.The mechanism of generating sufficient lift and thrust during avian flight is still not fully understood.Moving wings with unique biological structures such as feathers make modeling,simulation,experimentation,and analysis much more difficult.This paper reviews the research progress on bird-like flapping wings from flight mechanisms to modeling.Commonly used numerical computing methods are briefly compared.The aeroelastic problems are also highlighted.The results of the investigation show that a leading-edge vortex can be found during avian flight.Its induction and maintenance may have a close relationship with wing configuration,kinematics and deformation.The present models of flapping wings are mainly two-dimensional airfoils or three-dimensional single root-jointed geometric plates,which still exhibit large differences from real bird wings.Aeroelasticity is encouraged to consider the nonignorable effect on aerodynamic performance due to large-scale nonlinear deformation.Introducing appropriate flexibility can improve the peak values and efficiencies of lift and thrust,but the detailed conclusions always have strong background dependence.

Cluster observations of large-scale southward movement and dawnward-duskward flapping of Earth's magnetotail current sheet

In August 2001,Cluster satellites observed that the mid-tail current sheet(CS) moved southward continuously for almost seven hours.Meanwhile,Cluster crossed back and forth the CS repeatedly.This means that the large-scale southward movement of the CS was accompanied by a small-scale CS flapping during this period.Using the minimum-variation-analysis(MVA) method and the multi-spacecraft data,we calculated the normal vector,current density and the magnetic curvature of the CS,the results showed that the CS alternated between flattened CS and tilted CS for several times.Strong dawn-dusk oscillations were found for the tilted CS,which caused the repeated crossings of the center of CS by the satellites.This feature is obviously different from the previous observations of the vertical flapping of the CS induced by the kink instability.Two types of flapping were observed:One of them is accompanied with bursty bulk flows(BBFs) and the other is not.This suggests that in this event there was no direct relationship between the CS flapping and BBFs.

NUMERICAL ANALYSIS OF THE UNSTEADY FORCE IN INSECT FORWARD FLIGHT

The objective of this study is to get into physical insights to the unsteady force and the relevant mechanisms in forward flight of insects. Unsteady force in the forward flight was studied, based on a virtual model problem of a foil with oscillating translation and rotation in a uniform flow, by solving the two-dimensional incompressible Navier-Stokes equations with a finite element method. The effects of typical parameters, including the advance ratio, the inclined angle of stroke plane, the stroke amplitude, and the amplitude of pitching angle of attack, on the forces and the flow structures were analyzed.