Forces on oscillating foils for propulsion and maneuvering

Experiments were performed on an oscillating foil to assess its performance in producing large forces for propulsion and effective maneuvering. First, experiments on a harmonically heaving and pitching foil were performed to determine its propulsive efficiency under conditions of significant thrust production, as function of the principal parameters: the heave amplitude, Strouhal number, angle of attack, and phase angle between heave and pitch. Planform area thrust coefficients of 2.4 were recorded for 35° maximum angle of attack and efficiencies of up to 71.5% were recorded for 15° maximum angle of attack. A plateau of good efficiency, in the range of 50–60%, is noted. A phase angle of 90–100° between pitch and heave is found to produce the best thrust performance. Also, the introduction of higher harmonics in the heave motion, so as to ensure a sinusoidal variation in the angle of attack produced much higher thrust coefficient at high Strouhal numbers. Second, experiments on a harmonically oscillating foil with a superposed pitch bias, as well as experiments on impulsively moving foils in still water, were conducted to assess the capability of the foil to produce large lateral forces for maneuvering. Mean side force coefficients of up to 5.5, and instantaneous lift coefficients of up to 15 were recorded, demonstrating an outstanding capability for maneuvering force production.     

Control of backward-facing step flow using a flapping foil

The effect of oscillating a small foil in plunge on the reattachment of a separated shear layer in a two-dimensional backward-facing step flow has been studied using flow visualization and single component laser Doppler velocimetry (LDV) measurements. It has been shown that a jet instead of a wake is generated by the flapping action of the foil. Results indicate that this action induces strong mixing and entrainment when the foil is located within the recirculation flow region, thereby reducing the reattachment length by as much as 70%. Furthermore, it has been shown that the flapping foil is most effective in reducing the size of the separation zone when placed close to the wall and to the step. It is least effective when placed outside the separated shear layer or downstream of the reattachment zone. Received: 26 August 1999 / Accepted: 29 May 2001     

Vortical structures on a flapping wing

A wing in the form of a rectangular flat plate is subjected to periodic flapping motion. Space–time imaging provides quantitative representations of the flow structure along the wing. Regions of spanwise flow exist along the wing surface; and depending on the location along the span, the flow is either toward or away from the tip of the wing. Onset and development of large-scale, streamwise-oriented vortical structures occur at locations inboard of the tip of the wing, and they can attain values of circulation of the order of one-half the circulation of the tip vortex. Time-shifted images indicate that these streamwise vortical structures persist over a major share of the wing chord. Space–time volume constructions define the form and duration of these structures, relative to the tip vortex.     

Design and development considerations for biologically inspired flapping-wing micro air vehicles

In this paper, the decade of numerical and experimental investigations leading to the development of the authors’ unique flapping-wing micro air vehicle is summarized. Early investigations included the study of boundary layer energization by means of a small flapping foil embedded in a flat-plate boundary layer, the reduction of the recirculatory flow region behind a backward-facing step by means of a small flapping foil, and the reduction or suppression of flow separation behind blunt or cusped airfoil trailing edges by flapping a small foil located in the wake flow region. These studies were followed by systematic investigations of the aerodynamic characteristics of single flapping airfoils and airfoil combinations. These unsteady flows were described using flow visualization, laser-Doppler velocimetry in addition to panel and Navier–Stokes computations. It is then shown how this flapping-wing database was used to conceive, design and develop a micro air vehicle which has a fixed wing for lift and two flapping wings for thrust generation. While animal flight is characterized by a coupled force generation, the present design appears to separate lift and thrust. However, in fact, the performance of one surface is closely coupled to the other surfaces.     

Investigation of flow mechanism of a robotic fish swimming by using flow visualization synchronized with hydrodynamic force measurement

When swimming in water by flapping its tail, a fish can overcome the drag from uniform flow and propel its body. The involved flow mechanism concerns 3-D and unsteady effects. This paper presents the investigation of the flow mechanism on the basis of a 3-D robotic fish model which has the typical geometry of body and tail with periodic flapping 2-freedom kinematical motion testing in the case of St = 0.78, Re = 6,600 and phase delay mode (φ = −75°), in which may have a greater or maximum propulsion (without consideration of the optimal efficiency). Using a special technique of dye visualization which can clearly show vortex sheet and vortices in detail and using the inner 3-component force balance and cable supporting system with the phase-lock technique, the 3-D flow structure visualized in the wake of fish and the hydrodynamic force measurement were synchronized and obtained. Under the mentioned flapping parameters, we found the key flow structure and its evolution, a pair of complex 3-D chain-shape vortex (S–H vortex-rings, S₁–H₁ and S₂–H₂, and their legs L₁ and L₂) flow structures, which attach the leading edge and the trailing edge, then shed, move downstream and outwards and distribute two anti-symmetric staggering arrays along with the wake of the fish model in different phase stages during the flapping period. It is different with in the case of St = 0.25–0.35. Its typical flow structure and evolution are described and the results prove that they are different from the viewpoints based on the investigation of 2-D cases. For precision of the dynamic force measurement, in this paper it was provided with the method and techniques by subtracting the inertial forces and the forces induced by buoyancy and gravity effect in water, etc. from original data measured. The evolution of the synchronized measuring forces directly matching with the flow structure was also described in this paper.     

Investigation of the vortex induced unsteadiness of a separation bubble via time-resolved and scanning PIV measurements

A transitional separation bubble on the suction side of an SD7003 airfoil is considered. The transition process that forces the separated shear layer to reattach seems to be governed by Kelvin–Helmholtz instabilities. Large scale vortices are formed due to this mechanism at the downstream end of the bubble. These vortices possess a three-dimensional structure and detach from the recirculation region, while other vortices are formed within the bubble. This separation of the vortex is a highly unsteady process, which leads to a bubble flapping. The structure of these vortices and the flapping of the separation bubble due to these vortices are temporally and spatially analyzed at angles of attack from 4° to 8° and chord-length based Reynolds numbers Re _c = 20,000–60,000 using time-resolved PIV measurements in a 2D and a 3D set-up, i.e., stereo-scanning PIV measurements are done in the latter case. These measurements complete former studies at a Reynolds number of Re _c = 20,000. The results of the time-resolved PIV measurements in a single light-sheet show the influence of the angle of attack and the Reynolds number. The characteristic parameters of the separation bubble are analyzed focusing on the unsteadiness of the separation bubble, e.g., the varying size of the main recirculation region, which characterizes the bubble flapping, and the corresponding Strouhal number are investigated. Furthermore, the impact of the freestream turbulence is investigated by juxtaposing the current and former results. The stereo-scanning PIV measurements at Reynolds numbers up to 60,000 elucidate the three-dimensional character of the vortical structures, which evolve at the downstream end of the separation bubble. It is shown that the same typical structures are formed, e.g., the c-shape vortex and the screwdriver vortex at each Reynolds number and angle of attack investigated and the occurrence of these patterns in relation to Λ-structures is discussed. To evidence the impact of the freestream turbulence, these results are compared with findings of former measurements.     

Investigation of the development of unsteady flow separation from a model swept wing

The results of an experimental wind-tunnel investigation of the flow patterns on the swept wing of a model aircraft realized for pitching oscillations with an amplitude A _α = 5° with respect to setup angles of attack α₀ = 10 and 16° are presented.     

Aerodynamic forces and flow fields of a two-dimensional hovering wing

This paper reports the results of an experimental investigation on a two-dimensional (2-D) wing undergoing symmetric simple harmonic flapping motion. The purpose of this investigation is to study how flapping frequency (or Reynolds number) and angular amplitude affect aerodynamic force generation and the associated flow field during flapping for Reynolds number (Re) ranging from 663 to 2652, and angular amplitudes (α _A) of 30°, 45° and 60°. Our results support the findings of earlier studies that fluid inertia and leading edge vortices play dominant roles in the generation of aerodynamic forces. More importantly, time-resolved force coefficients during flapping are found to be more sensitive to changes in α _A than in Re. In fact, a subtle change in α _A may lead to considerable changes in the lift and drag coefficients, and there appears to be an optimal mean lift coefficient around α _A = 45°, at least for the range of flow parameters considered here. This optimal condition coincides with the development a reverse Karman Vortex street in the wake, which has a higher jet stream than a vortex dipole at α _A = 30° and a neutral wake structure at α _A = 60°. Although Re has less effect on temporal force coefficients and the associated wake structures, increasing Re tends to equalize mean lift coefficients (and also mean drag coefficients) during downstroke and upstroke, thus suggesting an increasing symmetry in the mean force generation between these strokes. Although the current study deals with a 2-D hovering motion only, the unique force characteristics observed here, particularly their strong dependence on α _A, may also occur in a three-dimensional hovering motion, and flying insects may well have taken advantage of these characteristics to help them to stay aloft and maneuver. An erratum to this article can be found at     

High fidelity numerical simulation of airfoil thickness and kinematics effects on flapping airfoil propulsion

High-fidelity numerical simulations with the spectral difference (SD) method are carried out to investigate the unsteady flow over a series of oscillating NACA 4-digit airfoils. Airfoil thickness and kinematics effects on the flapping airfoil propulsion are highlighted. It is confirmed that the aerodynamic performance of airfoils with different thickness can be very different under the same kinematics. Distinct evolutionary patterns of vortical structures are analyzed to unveil the underlying flow physics behind the diverse flow phenomena associated with different airfoil thickness and kinematics and reveal the synthetic effects of airfoil thickness and kinematics on the propulsive performance. Thickness effects at various reduced frequencies and Strouhal numbers for the same chord length based Reynolds number (=1200) are then discussed in detail. It is found that at relatively small Strouhal number (=0.3), for all types of airfoils with the combined pitching and plunging motion (pitch angle 20°, the pitch axis located at one third of chord length from the leading edge, pitch leading plunge by 75°), low reduced frequency (=1) is conducive for both the thrust production and propulsive efficiency. Moreover, relatively thin airfoils (e.g. NACA0006) can generate larger thrust and maintain higher propulsive efficiency than thick airfoils (e.g. NACA0030). However, with the same kinematics but at relatively large Strouhal number (=0.45), it is found that airfoils with different thickness exhibit diverse trend on thrust production and propulsive efficiency, especially at large reduced frequency (=3.5). Results on effects of airfoil thickness based Reynolds numbers indicate that relative thin airfoils show superior propulsion performance in the tested Reynolds number range. The evolution of leading edge vortices and the interaction between the leading and trailing edge vortices play key roles in flapping airfoil propulsive performance.     

Hydrodynamics of a biologically inspired tandem flapping foil configuration

Numerical simulations have been used to analyze the effect that vortices, shed from one flapping foil, have on the thrust of another flapping foil placed directly downstream. The simulations attempt to model the dorsal–tail fin interaction observed in a swimming bluegill sunfish. The simulations have been carried out using a Cartesian grid method that allows us to simulate flows with complex moving boundaries on stationary Cartesian grids. The simulations indicate that vortex shedding from the upstream (dorsal) fin is indeed capable of increasing the thrust of the downstream (tail) fin significantly. Vortex structures shed by the upstream dorsal fin increase the effective angle-of-attack of the flow seen by the tail fin and initiate the formation of a strong leading edge stall vortex on the downstream fin. This stall vortex convects down the surface of the tail and the low pressure associated with this vortex increases the thrust on the downstream tail fin. However, this thrust augmentation is found to be quite sensitive to the phase relationship between the two flapping fins. The numerical simulations allows us to examine in detail, the underlying physical mechanism for this thrust augmentation.      

Flow field characteristics study of a flapping airfoil using computational fluid dynamics

The flow field of a flapping airfoil in Low Reynolds Number (LRN) flow regime is associated with complex nonlinear vortex shedding and viscous phenomena. The respective fluid dynamics of such a flow is investigated here through Computational Fluid Dynamics (CFD) based on the Finite Volume Method (FVM). The governing equations are the unsteady, incompressible two-dimensional Navier-Stokes (N-S) equations. The airfoil is a thin ellipsoidal geometry performing a modified figure-of-eight-like flapping pattern. The flow field and vortical patterns around the airfoil are examined in detail, and the effects of several unsteady flow and system parameters on the flow characteristics are explored. The investigated parameters are the amplitude of pitching oscillations, phase angle between pitching and plunging motions, mean angle of attack, Reynolds number (Re), Strouhal number (St) based on the translational amplitudes of oscillations, and the pitching axis location (x/c). It is shown that these parameters change the instantaneous force coefficients quantitatively and qualitatively. It is also observed that the strength, interaction, and convection of the vortical structures surrounding the airfoil are significantly affected by the variations of these parameters.     

Unsteady separated and reattaching turbulent flow over a two-dimensional square rib

The spatio-temporal characteristics of the separated and reattaching turbulent flow over a two-dimensional square rib were studied experimentally. Synchronized measurements of wall-pressure fluctuations and velocity fluctuations were made using a microphone array and a split-fiber film, respectively. Profiles of time-averaged streamwise velocity and wall-pressure fluctuations showed that the shear layer separated from the leading edge of the rib sweeps past the rib and directly reattaches on the bottom wall (x/H=9.75) downstream of the rib. A thin region of reverse flow was formed above the rib. The shedding large-scale vortical structures (fH/U₀=0.03) and the flapping separation bubble (fH/U₀=0.0075) could be discerned in the wall-pressure spectra. A multi-resolution analysis based on the maximum overlap discrete wavelet transform (MODWT) was performed to extract the intermittent events associated with the shedding large-scale vortical structures and the flapping separation bubble. The convective dynamics of the large-scale vortical structures were analyzed in terms of the autocorrelation of the continuous wavelet-transformed wall pressure, cross-correlation of the wall-pressure fluctuations, and the cross-correlation between the wall pressure at the time-averaged reattachment point and the streamwise velocity field. The convection speeds of the large-scale vortical structures before and after the reattachment point were U_c=0.35U₀ and 0.45U₀, respectively. The flapping motion of the separation bubble was analyzed in terms of the conditionally averaged reverse-flow intermittency near the wall region. The instantaneous reattachment point in response to the flapping motion was obtained; these findings established that the reattachment zone was a 1.2H-long region centered at x/H=9.75. The reverse-flow intermittency in one period of the flapping motion demonstrated that the thin reverse flow above the rib is influenced by the flapping motion of the separation bubble behind the rib.     

Propulsive performance of a flapping plate near a free surface

The propulsive performance, i.e., the time-averaged thrust coefficient or the propulsive efficiency, of a flapping flat plate advancing near an otherwise quiescent free surface (liquid–gas interface) with Re of 1000, Fr of 0.2 and 0.8, and various submergence depths is numerically investigated by employing an adaptive Cartesian cut-cell/level-set method. The flapping kinematics parameters excluding the pitch-leading-heave phase angle were fixed as those commonly seen in literature. Results show that for submergence depth larger than the heave amplitude, the propulsive performance peaks at a smaller pitch-leading-heave phase angle with a shallower submergence for Fr of 0.2 but at the same phase angle for Fr of 0.8. Proximity to the free surface enhances the peak propulsive performance for Fr of 0.2 but the influence is minor for Fr of 0.8. The propulsive performance with Fr of 0.2 increases with decreasing chord-normalized submergence depth for the pitch-leading-heave phase angle smaller than 100°. The trend is reversed for the pitch-leading-heave phase angle larger than 100°. However, the propulsive performance with Fr of 0.8 hardly depends on the chord-normalized submergence depth. For submergence depth equal to the heave amplitude, the temporal variation in the thrust coefficient exhibits characteristics inherently different from those with other submergence depths for Fr of 0.2. Also, the time-averaged thrust coefficient exhibits a unique variation with the pitch-leading-heave phase angle. However, the various characteristics of the propulsive performance are similar to those with other submergence depths for Fr of 0.8. For submergence depth smaller than the heave amplitude and Fr of 0.2, the propulsive performance gains much from exposure of the upper surface of the plate to the gas phase. The efficiency enhancement is linked to the weakening of the leading edge vortices. A second harmonic with significant amplitude is found in the upstream wave for Fr of 0.2 with a typical pitch-leading-heave phase angle.     

Unsteady free surface wave-induced separation: Vortical structures and instabilities

Vortical structures and instability mechanisms of the unsteady free surface wave-induced separation around a surface-piercing NACA0024 foil at a Froude number of 0.37 and a Reynolds number of 1.52×10⁶ are studied using an unsteady Reynolds-averaged Navier–Stokes (URANS) code with a blended k?ε/k?ω turbulence model and a free surface tracking method. At the free surface, the separated flow reattaches to the foil surface resulting in a wall-bounded separation bubble. The mean and instantaneous flow topologies in the separation region are similar to the owl-face pattern. The initial shear-layer instability, the Karman-like instability, and the flapping instability are identified, and their scaling and physical mechanisms are studied. Validation with experimental fluid dynamics (EFD) and comparison with complementary detached-eddy simulation (DES) indicate that URANS resolves part of the organized oscillations due to the large-scale unsteady vortical structures and instabilities, thereby capturing the gross features of the unsteady separation. The URANS solutions show an initial amplitude defect of 30% for the free surface oscillations where the shear layer separates, and the defect progressively increases downstream as URANS rapidly dissipates the rolled up vortices.     

Scaling of flow separation on a pitching low aspect ratio plate

We use two different dye injection approaches, in two different water tunnels, to visualize the formation and subsequent evolution of leading-edge vortices and related separated structures, for a pitching low aspect ratio plate. The motion is a smoothed linear pitch ramp from 0° to 40° incidence, brief hold, and return to 0°, executed at reduced pitch rates ranging from 0.1 to 0.35 and about various pivot locations. All cases evince a leading edge vortex with pronounced axial flow, which leads to formation of large-scale, three-dimensional flow structures, culminating in a large vortical structure centered at the wing symmetry plane. Pitch is also compared to plunge, where the plunge-induced angle of attack is taken as the geometric pitch incidence angle, ignoring pitch-rate effects. At successively increasing values of convective time C/U, the three-dimensional patterns of the flow structure are remarkably similar for the pitching and plunging motions. The similarity of these patterns persists, though they are shifted in time, for variation of either the location of the pitching axis or the dimensionless pitch rate.     

An inviscid model for vortex shedding from a deforming body

An inviscid vortex sheet model is developed in order to study the unsteady separated flow past a two-dimensional deforming body which moves with a prescribed motion in an otherwise quiescent fluid. Following Jones (J Fluid Mech 496, 405–441, 2003) the flow is assumed to comprise of a bound vortex sheet attached to the body and two separate vortex sheets originating at the edges. The complex conjugate velocity potential is expressed explicitly in terms of the bound vortex sheet strength and the edge circulations through a boundary integral representation. It is shown that Kelvin’s circulation theorem, along with the conditions of continuity of the normal velocity across the body and the boundedness of the velocity field, yields a coupled system of equations for the unknown bound vortex sheet strength and the edge circulations. A general numerical treatment is developed for the singular principal value integrals arising in the solution procedure. The model is validated against the results of Jones (J Fluid Mech 496, 405–441, 2003) for computations involving a rigid flat plate and is subsequently applied to the flapping foil experiments of Heathcote et al. (AIAA J, 42, 2196–2204, 2004) in order to predict the thrust coefficient. The utility of the model in simulating aquatic locomotion is also demonstrated, with vortex shedding suppressed at the leading edge of the swimming body.      

Heaving and pitching oscillating foil propulsion in ground effect

A detailed series of experiments is performed to investigate the ‘ground effect’ experienced by propulsive flapping foils operating near a solid boundary. A high aspect ratio foil is towed at constant speed and oscillated in pitch and heave at varying distances from a rigid wall. It is shown that this distance has a significant impact on the lift and thrust forces generated by the foil, both in the time averaged mean forces and the phase averaged periodic forces. For some thrust producing kinematics, the instantaneous force profile may change significantly without altering the time averaged mean force; thus, mean force measurements alone are not sufficient to indicate the proximity, or the effect, of the solid boundary. Results are presented across a wide range of thrust generating kinematics, showing that the strength of the ground effect can be modulated, for any achievable level of thrust, through appropriate selection of kinematics. This finding in particular has significance for underwater vehicles propelled by oscillating foil thrusters, as it follows that the sensitivity of the thrusters to ground effect can be controlled independently of the desired thrust. While propulsive efficiency is increased slightly near the wall for some kinematics, in general this does not occur for kinematics where a strong ground cushion (repulsion) effect is observed. Finally, the results suggest that span-wise flow around the tip of the foil is important in determining whether the foil is repelled from or pulled into the wall.     

Experimental study on surface wave and film breakdown of falling liquid film flow

In order to evaluate characteristics of the liquid film flow and their influences on heat and mass transfer, measurements of the instantaneous film thickness using a capacitance method and observation of film breakdown are performed. Experimental results are reported in the paper. Experiments are carried out at Re = 250–10000, T _in = 20–50°C and three axial positions of vertically falling liquid films for film thickness measurements. Instantaneous surface waveshapes are given by the interpretation of the test data using the cubic spline method. The correlation of the mean film thickness versus the film Reynolds number is also given by fitting the test data. It is revealed that the surface wave has nonlinear behavior. Observation of film breakdown is performed at Re = 1.40 × 10³–1.75 × 10⁴ and T _in = 85–95°C. From experimental results, the correlation of the film breakdown criterion can be obtained as follows: Bd = 1.567 × 10⁻⁶ Re ^1.183     

A soap film shock tube to study two-dimensional compressible flows

 A new experimental approach to the study of the two-dimensional compressible flow phenomena is presented. In this technique, a variety of compressible flows were generated by bursting plane vertical soap films. An aureole and a “shock wave” preceding the rim of the expanding hole were clearly observed using traditional high-speed flash photography and a fast line-scan charge coupled device (CCD) camera. The moving shock wave images obtained from the line-scan CCD camera were similar to the x–t diagrams in gas dynamics. The moving shock waves cause thickness jumps and induce supersonic flows. Photographs of the supersonic flows over a cylinder and a wedge are presented. The results suggest clearly the feasibility of the “soap film shock tube”. Received: 11 May 2000/Accepted: 2 November 2000     

Supersonic flow past a cylindrical body with transverse jets at large angles of attack

Supersonic flow past a cylindrical body with a system of transverse jets ejected from its surface at angles of attack α=60–120^o is characterized by a complicated gasdynamic flow pattern [1]. The body surface is affected by both the oncoming flow and the ejected jets which shield a portion of the surface from the external flow. This results in considerable transverse and longitudinal pressure gradients appearing on the body surface. The experimental pressure distributions over a cylindrical model with four transverse jets at a Mach number M=4 and α=60°, 90°, and 120° make it possible to study the specific features of the flowfield and derive correlations for the "jet obstacle" dimensions. Moscow. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 1, pp. 179–183, January–February, 1998.