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Deflected wake interaction of tandem flapping foils
Abstract
Symmetric flapping foils are known to produce deflected jets at high frequency–amplitude combinations even at a zero mean angle of attack. This reduces the frequency range of useful propulsive configurations without side force. In this study, we numerically analyse the interaction of these deflected jets for tandem flapping foils undergoing coupled heave-to-pitch motion in a two-dimensional domain. The impact of the flapping Strouhal number, foil spacing and phasing on wake interaction is investigated. Our primary finding is that the back foil is capable of cancelling the wake deflection and mean side force of the front foil, even when located up to five chord lengths downstream. This is achieved by attracting the incoming dipoles and disturbing their cohesion within the limits of the back foil’s range of flapping motion. We also show that the impact on cycle-averaged thrust varies from high augmentation to drag generation depending on the wake patterns downstream of the back foil. These findings provide new insights towards the design of biomimetic tandem propulsors, as they expand their working envelope and ability to rapidly increase or decrease the forward speed by manipulating the size of the shed vortices.
... Previous research has mainly focused on the variation of the horizontal position of the hindwing [14,16,24], and the variation of its vertical position has seldom been considered. Arrangements considering variation of both the horizontal and vertical position of the hindwing could reveal new interaction mechanisms, potentially leading to improvements in the aerodynamic characteristics of tandem-wing arrangements. ...
... The NACA 0012 airfoil was employed in this study because the NACA-series airfoils have been commonly used in previous works [20,23,24]. The wing motion consists of plunge and pitch, and the functions of motion are defined as ...
... The values of Re, St, and J were calculated to be 34 410, 0.4, and 2.5, respectively. The value of Re is higher than that in most previous research [14][15][16][17]24] which has mainly focused on the aerodynamic characteristics of tandem wings in a Re range of 10 3 to 10 4 . This Re range is suitable for analyzing the flight of real dragonflies, but it is inappropriate for use in the design of tandem flapping-wing MAVs. ...
Tandem flapping-wing micro aerial vehicles, which are inspired by dragonflies, are unique in that they have two pairs of wings, and this could increase their maneuverability during flight. In this study, a series of tandem flapping-wing arrangements were designed in polar coordinates, and the polar distance and polar angles of the hindwing were used as design variables. Such a consideration of variations in both the horizontal and vertical positions of the hindwing in the design of tandem-wing arrangements has the potential to elucidate new interaction mechanisms, leading to improvements in the aerodynamic characteristics of tandem flapping-wings. Two-dimensional numerical analyses of these arrangements were conducted. The results of these analyses showed that, compared with a single flapping wing, tandem wings can increase the lift coefficient by 78.1% with an appropriate arrangement, but decrease the lift coefficient by 51.6% with an inappropriate arrangement. The vorticity distributions for typical wing arrangements were examined to establish the effect of the design variables on the aerodynamic characteristics of the tandem wings in forward flight. Two types of wing–wake interaction mechanisms were revealed based on this analysis. Both of these interactions can significantly reduce the negative force during the upstroke, resulting in an increase in the time-averaged lift.
... Muscutt et al. (2014) from the University of Southampton presented the results of a comprehensive series of 2D numerical simulations of tandem foils in heave and pitch. While the results have demonstrated the potential to improve thrust production and efficiency (Lagolopoulos et al., 2020), the extent of the phase-spacing-frequency parameter space effectively explored is very limited. Some studies have focussed on the effects of phase alone (Rival et al., 2011;Lian et al., 2014), or the effect of phase and frequency (Broering et al., 2012), or spacing and frequency (Kinsey and Dumas, 2012). ...
... A further increase in the oscillation amplitude triggers a symmetry breaking in the reverse BvK wake where a strong dipolar structure that propagates obliquely to one side of the symmetry line of the wake is formed in each flapping cycle, while a much weaker single vortex is shed on the other side (Godoy-Diana et al., 2008). The vast majority of foil propulsion applications aim to use the propulsion regime while the regime of asymmetric deflected wake has been only very recently studied for the tandem configuration (Lagolopoulos et al., 2020). ...
The present work investigates theoretical and numerical methods to model oscillating hydrofoils, in single and tandem arrangement. The first part of this work presents a semi-analytical 2D model for a hydrofoil propulsor travelling at constant speed, in infinite domain, undergoing heaving and pitching oscillations, based on the Theodorsen unsteady theory. Following the previous work, the model is developed to estimate the thrust and propulsive efficiency attempting to incorporate the main physical contributions. The second part investigates the same foil arrangements using a high-fidelity CFD approach. In particular, a robust deforming grid method is used, enabling the simulation of cases with large body motions. Results of the semi-analytical model are compared with available published numerical and experimental data, with good agreement. The numerical model results are analysed using verification and validation procedures, allowing accurate physical interpretation of the flow and forces. Additionally, the tandem foil configuration, if properly optimized, is found to increase the single foil thrust by almost threefold. The overall results suggest that the semi-analytical model may be quite suitable in design studies, and the CFD model showed capable of providing accurate results for the most complex cases and of contributing to a comprehensive understanding of the flow dynamics.
... In this work, smoothing and re-meshing schemes are used simultaneously to tackle the moving mesh. In the fluent setup, a laminar model is selected (as the flow is assumed to have a Re of 1173, as per the study of Lagopulouse et al. 23 ), and the material properties are set to water, and an inlet velocity of 0.1778 m/s (Ref. 23) is given at the inflow boundary condition. ...
... In the fluent setup, a laminar model is selected (as the flow is assumed to have a Re of 1173, as per the study of Lagopulouse et al. 23 ), and the material properties are set to water, and an inlet velocity of 0.1778 m/s (Ref. 23) is given at the inflow boundary condition. The outlet pressure is set to 0 Pa to ensure there is no back flow or disturbances at the outflow condition, and the water from the fluid domain is passed into the atmosphere smoothly. ...
It has always been a challenge to implement the natural flyer and swimmer kinematics into human-made aero/hydro vehicles for the enhancement of their performance. The propulsive performance of underwater vehicles can be enhanced by following the fishtailed kinematics. In the present study, a two-dimensional simulation has been performed on a tandem flapping foil by altering the simple flapping trajectory motion to a fishtailed trajectory by varying the Strouhal number ( St) in the range of 0.1–0.5. The effect of the inter-foil spacing and phasing between the foils on wake interaction is also investigated. The results show that fishtailed trajectory motion and inter-foil spacing of 2 c m –3 c m (where c m is the mean chord length) between the foils would enhance the propulsive efficiency of the downstream foil by up to 41%. The unfavorable spacing between the foils results in adverse wake interaction, which reduces the propulsive efficiency compared to solo flapping foil.
... The peaks in the thrust, power and efficiency coincide with the coherent mode wakes while the branched mode wakes are associated with the troughs. Recently, Lagopoulos, Weymouth & Ganapathisubramani (2020) focused more on the wake deflection and production of side force by simultaneously heaving and pitching foils in an in-line configuration. They identified three distinct vortex patterns in the wake and showed that wake deflection introduced by the upstream foil could be eliminated due to the presence of the downstream body. ...
... Two-dimensional versus three-dimensional simulations are an important numerical complexity that can have implications on wake dynamics at high Re flow conditions. To this effect, we carried out 3-D sensitivity studies to confirm that the underlying physics of coherent structures in the flow, including wake deflection, wake merging and vortex interactions, follow a 2-D or Q2D mechanism (Godoy-Diana et al. 2008, 2009Dewey et al. 2014;Shoele & Zhu 2015;Lagopoulos et al. 2020). Deng et al. (2016) notes that the 2-D to 3-D transition in the wake of pure pitching foils occurs at considerably high x/c St, which excludes the parameter space employed here. ...
The unsteady hydrodynamics of two pitching foils arranged in side-by-side (parallel)
configuration is examined for a range of Strouhal number, phase difference, oscillation
amplitude, and separation distance. Three distinct vortex patterns are identified in
wake maps, which include separated wake, merged wake, and transitional-merged wake.
Furthermore, a novel model is introduced based on fundamental flow variables including
velocity, location, and circulation of dipole structures to quantitatively distinguish vortex
patterns in the wake. The physical mechanism of wake merging process is also elucidated. When an oscillating foil experiences the jet deflection phenomenon, secondary structures separated from the primary street traverse in the other direction by making an angle with its parent vortex street. For in-phase pitching parallel foils, secondary structures from the vortex street of the lower foil interact with the primary vortex street of the upper foil under certain kinematic conditions. This interaction triggers the wake merging process by influencing circulation of coherent structures in the upper part of the wake. It is unveiled that merging of the wakes leads to enhancements in propulsive efficiency by increasing thrust generation without a significant alteration in power requirements. These are attributed to the formation of a high-momentum jet by the merged vortex street, which possesses significantly larger circulation due to the amalgamation of the vortices, and major alterations in the evolution of leading edge vortices. Thus, flow physics thoroughly explored here are crucial in providing novel insights for future development of flow control techniques for efficient designs of bio-inspired underwater propulsors.
... This beneficial vortex interaction is not D. Zhang et al. [194,195] (Fig. 21c) and interaction between the dorsal and caudal fins in swimming fish [121,196] (Fig. 21d). The board forms of vortex interaction lead to numerous studies on various subjects, from tandem filaments [197] to free-flying birds [198], through different methods, including theoretical analysis [199,200], experiments [201,202] and numerical simulations [41,203]. ...
... 2, the propulsors (wings or fins) of flapping-based flying and swimming can be modelled as foils undergoing flapping motion. Thus, simplified models consisting of multiple foils [191,201,203], plates [204,205] or filaments [206][207][208] are widely applied to study vortex interactions in biomimetic propulsion. These approaches extract key component from the complexity of biological flying and swimming without loss of generality and enable precise control and measurement of numerous variables to gain insight into the fundamental mechanisms of vortex interaction. ...
The swimming of aquatic animals and flying of insects and birds have fascinated physicists and biologists for more than a century. In this regard, great efforts have been made to develop new features and promote their applications in underwater and air propulsion. However, many challenges remain in understanding these forms of physical processes. Five key physical models are summarized to show how researchers use numerical and experimental methods to understand physiology, movement ecology and evolution from the viewpoint of fluid mechanics. They are morphological model, flexibility model, kinematics model, tethered/free model and force measurement model. Then, the latest progresses on the vortex dynamics of some simplified models and even high-fidelity models are presented, including the forming, growth, interaction, role and influence factors of the vortical structures. Some other aspects in swimming and flying, including stability, manoeuvrability and acoustics, are also briefly reviewed. Finally, the major challenges and several open issues in this field are highlighted.
... The peaks in the thrust, power and efficiency coincide with the coherent mode wakes while the branched mode wakes are associated with the troughs. Recently, Lagopoulos et al. (2020) focused more on the wake deflection and production of side force by simultaneously heaving and pitching foils in an in-line configuration. They identified three distinct vortex patterns in the wake and showed that wake deflection introduced by the upstream foil could be eliminated due to the presence of the downstream body. ...
... Two-dimensional versus three-dimensional simulations are an important numerical complexity that can have implications on wake dynamics at high Re flow conditions. To this effect, we carried out three-dimensional sensitivity studies to confirm that underlying physics of coherent structures in the flow, including wake deflection, wake merging, and vortex interactions, follow a two-dimensional or Q2D mechanism (Godoy-Diana et al. 2008, 2009Dewey et al. 2014;Shoele & Zhu 2015;Lagopoulos et al. 2020). Deng et al. (2016) notes that 2D-to-3D transition in the wake of pure in-phase pitching foils occur at considerably high St, which excludes the parameter space employed here. ...
The unsteady hydrodynamics of two in-phase pitching foils arranged in side-by-side (parallel) configurations is examined for a range of Strouhal number and separation distance. Three distinct vortex patterns are identified in the Strohual number−separation distance phase maps, which include separated wake, merged wake, and transitional-merged wake. Furthermore, a novel model is introduced based on fundamental flow variables including velocity, location, and circulation of dipole structures to quantitatively distinguish vortex patterns in the wake. The physical mechanism of wake merging process is also elucidated. When an oscillating foil experiences the jet deflection phenomenon, secondary structures shed from the primary street traverse in the other direction by making an angle with its parent vortex street. For parallel foils, secondary structures from the vortex street of the lower foil interact with the primary vortex street of the upper foil under certain kinematic conditions. This interaction triggers the wake merging process by influencing circulation of coherent structures in the upper part of the wake. It is unveiled that merging of the wakes leads to enhancements in propulsive efficiency by increasing thrust generation without a significant alteration in power requirements. These are attributed to the formation of a high-momentum jet by the merged vortex street, which possesses significantly larger circulation due to the amalgamation of the vortices, and major alterations in the evolution of leading edge vortices. Thus, flow physics that are thoroughly explored here are crucial in providing novel insights for future development of flow control techniques for efficient designs of bio-inspired underwater propulsors.
... Specifically, the break-up of the LEV shed from the front foil means that the back foil does not experience a coherent wake across its span, which limits the benefits derived from wake recapture. Therefore, although a ∼30 % increase in thrust can be noteworthy (Figure 10a for AR = 2), it is still far away from the optimal cases reported here or found in the literature (Akhtar, Mittal, Lauder, & Drucker, 2007;Boschitsch, Dewey, & Smits, 2014;Joshi & Mysa, 2021;Lagopoulos, Weymouth, & Ganapathisubramani, 2020;Muscutt et al., 2017aMuscutt et al., , 2017bXu et al., 2017). It should also be noted that a similar performance deterioration of inline flapping due to 3-D associated effects has been witnessed within insect-like concepts, where lower Re C and S C have been used (Arranz et al., 2020). ...
In this work, we describe the impact of aspect ratio ( $AR$ ) on the performance of optimally phased, identical flapping flippers in a tandem configuration. Three-dimensional simulations are performed for seven sets of single and tandem finite foils at a moderate Reynolds number, with thrust producing, heave-to-pitch coupled kinematics. Increasing slenderness (or $AR$ ) is found to improve thrust coefficients and thrust augmentation but the benefits level off towards higher values of $AR$ . However, the propulsive efficiency shows no significant change with increasing $AR$ , while the hind foil outperforms the single by a small margin. Further analysis of the spanwise development and propagation of vortical structures allows us to gain some insights into the mechanisms of these wake interactions and provide valuable information for the design of novel biomimetic propulsion systems.
... Furthermore, with the re-absorption of the CFF on the separated flow, the wake structure and airflow on the surface of the propulsive wing are complex, which affects the performance of the entire aircraft. However, few detailed numerical studies have been performed on the wake characteristics of the propulsive wing, which are closely related to the structure, 21,22 aerodynamic interference, [23][24][25] and noise characteristics 26 of the propulsive wing aircraft. ...
The propulsive wing is a new concept wing of automatic propulsion with high lift coefficients and has great application value in plant protection and forest fire control. The propulsive wing wake is a reverse Bénard–von Kármán (RBvK) vortex street, which is considered a thrust-generating wake. The wake structure will change greatly at high angles of attack and lead to changes in the aerodynamic performance of the propulsive wing. To explore the optimal working range and the wake characteristics of the propulsive wing, the wake transition and aerodynamic efficiency of the propulsive wing in cruise are numerically studied. The results indicate that there are three types of structures for the propulsive wing wake. When α ≤ 20°, the wake transits from the RBvK vortex street to the critical state with the increase in cruise speed, and the Strouhal number approaches 1.9. The critical wake region decreases gradually with the increase in the angle of attack. The maximum propulsive efficiency is 0.17 at a cruise speed of 15 m/s. When α > 20°, the wake transits directly from the RBvK vortex street to the Bénard–von Kármán (BvK) vortex street and the Strouhal number approaches 0.34. The maximum propulsive efficiency appears at a cruise speed of 10 m/s, which is close to the BvK vortex street boundary. Before entering the stall state, the lift efficiency of the propulsive wing increases with the increase in cruise speed and angle of attack, up to 3–5.
... Specific to wake interaction of an aircraft wing with a tailplane, this can be categorized as a parallel interaction, or a tandem aerofoil interaction. Research at small scale has been reported on tandem aerofoil interactions as a potential biomimetic propulsor [5]. At full-scale, wake interaction can cause significant problems in aircraft design. ...
This paper presents in-flight measurements of the interaction of the wing wake of a stalled Slingsby T67 Firefly light aircraft with the aircraft tailplane. Tailplane data was recorded by a GoPro360 camera and analyzed using spatial correlation methods. The tailplane movement and corresponding spectra indicate that the aerodynamic wake shedding frequency closely matches the resonant frequency of the tailplane, resulting in a significant excitation of the structure during heavy stall. Large magnitude, lower frequency tailplane movement was also identified by analysis of the pitch attitude from the image data, with results consistent in post-stall behavior reported by previous modelling and measurements.
... Direct measurements for the aerodynamic characteristics of two-wing configurations were acquired by Jones et al. [118] for a range of values of stagger and gap. Lagopoulos et al. [19] provided the first explanation for the significant impact of the downstream field to the front foil through change of foil spacing as well as Strouhal number and phasing of tandem flapping foils. In fact, various parameters should be paid more attention. ...
The effects of pivot locations (xp/c) and spacing (ds=λc) between the biplane airfoils was studied using the numerical method. SST k-ω turbulence model and U-RANS equations were solved when adopting overset grids. The findings revealed the aerodynamic characteristics of tilting biplane airfoil existed phase lag under five fixed pivot points from LE to TE but if the wall effect in the gap was so strong, the hysteresis of CL,lower significantly collapse. Besides, CM curves drop as pivot moves upward comparing to coincident relative and increasing λ could improve total lift coefficients. These results could be explained from the view of vorticity evolution where LEV, SV and TEV showed diverse structures to induce dynamic stall. Additionally, with rearward movement of the pivot point, the emergence of identical flow structures was delayed, and thus aerodynamic characteristics had the high similarity under different xp/c and λ. Therefore, a concept of effective angle of attack of biplane airfoils was first proposed and its function introduced a new factor λ in order to study the backward shift of pivot point in the centerline.
... There exists a known correlation between the side (lateral) force production and asymmetric wakes 30,31 for pitching and heaving foils. This may also be relevant to the case of tandem foils undergoing abrupt changes in their pitching synchronization, as also suggested by Gungor and Hemmati. ...
Alterations to the unsteady wake dynamics imposed by abrupt changes in the phase angle between two pitching side-by-side foils are computationally examined at the Reynolds number of 1000 and 4000 and Strouhal number of 0.25–0.5. Four hybrid modes are considered in this study inspired by the swimming habits of red nose tetra fish and burst-and-coast swimming phenomenon. At the higher Strouhal number of 0.50, abrupt changes in the phase angle result in the formation and growth of a secondary vortex street between the two primary streets, which enable and maintain a split-wake configuration. Furthermore, phase switching alters pressure levels on the top and bottom surfaces of both foils to similar levels, which attribute to lowering the side-force. The growth rate of the secondary vortex street remains consistent for all four hybrid modes. At lower Strouhal numbers (0.25–0.4), however, the abrupt change in the phase angle converts the wake to a single vortex street. Thus, this indicates that the wake reactions for such cases in synchronization substantially change at lower Strouhal number. Although a different behavior of total side force production is observed at a lower Reynolds number for Strouhal number of 0.50, the wake dynamics implies that phase alterations act as a similar flow control mechanism to stabilize the wake. Finally, it is identified that the suspension of oscillations significantly limits the implications of initiation of oscillations on wake dynamics and performance following abrupt changes in the phase angle.
... The force production on the hindfoils could be augmented if the rotational directions of the captured vortices and the leading edge vortices (LEVs) were the same. Besides, Lagopoulos et al. [23] implemented 2D numerical simulations on deflected wakes in a tandem-foil configuration, where the hindfoil not only cancelled the wake deflection and the mean side force of the forefoil but also noticeably enhanced the thrust production at a proper phase angle. Additionally, the performances of flexible tandem wings were experimentally studied by Zheng et al. [24] using time-resolved particle image velocimetry (PIV). ...
The performance augmentation mechanism of a tandem-foil system undergoing time-asymmetric flapping with unequal up- and downstroke durations (velocities) is investigated at three different phase angles, 0°, 90°, and 180°. Specifically, an asymmetry ratio, ranging from 0 to 0.4, is introduced to quantify the degree of the stroke time-asymmetry and to serve as the primary kinematic parameter of interest that affects the foil performances. Numerical simulations are implemented to predict the force production and to investigate the associated mechanism at different asymmetry ratios and phase angles. Validations are performed using digital particle image velocimetry in water tunnel experiments with two identical 3D printed wings. The results suggest that the foil performances at proper phase angles can be enhanced by stroke time-asymmetry. The force production during in-phase flapping obtains 15% increments while that during counterstroke flapping achieves remarkable enhancements by 2.5 times, as the asymmetry ratio increases from 0 to 0.4. The study also demonstrates that such enhancements are achieved through the changes in foil flapping velocities and foil-vortex interactions between the unequal up and downstrokes. These findings not only provide insights toward the characteristics of tandem foils which are operated in non-sinusoidal flapping strokes but also offer a reference to the design of efficient wing kinematics for high-performance biomimetic propulsors.
... At the same time, the newly developed theory is not without limitations. In particular, the flat structure of vortex wakes implied by the theory precludes discussion of more exotic phenomena, such as vortex sheet roll-up or wake deflection [12,49,31,37], which may play a role in altering hydrodynamic forces under certain circumstances. It might be possible to extend the theory to higher order to capture such effects, and such an extension is a worthwhile endeavor for future investigations. ...
Early research in aerodynamics and biological propulsion was dramatically advanced by the analytical solutions of Theodorsen, von K\'{a}rm\'{a}n, Wu and others. While these classical solutions apply only to isolated swimmers, the flow interactions between multiple swimmers are relevant to many practical applications, including the schooling and flocking of animal collectives. In this work, we derive a class of solutions that describe the hydrodynamic interactions between an arbitrary number of swimmers in a two-dimensional inviscid fluid. Our approach is rooted in multiply-connected complex analysis and exploits several recent results. Specifically, the transcendental (Schottky-Klein) prime function serves as the basic building block to construct the appropriate conformal maps and leading-edge-suction functions, which allows us to solve the modified Schwarz problem that arises. As such, our solutions generalize classical thin aerofoil theory, specifically Wu's waving-plate analysis, to the case of multiple swimmers. For the case of a pair of interacting swimmers, we develop an efficient numerical implementation that allows rapid computations of the forces on each swimmer. We investigate flow-mediated equilibria and find excellent agreement between our new solutions and previously reported experimental results. Our solutions recover and unify disparate results in the literature, thereby opening the door for future studies into the interactions between multiple swimmers.
... There exists a known correlation between the side (lateral) force production and asymmetric wakes (Khalid et al., 2015;Lagopoulos et al., 2020), for pitching and heaving foils. This may also be relevant to the case of tandem foils undergoing abrupt changes in their pitching synchronization, as also suggested by Gungor and Hemmati (n.d.). ...
This study was inspired from the swimming habits of red nose tetra fish that prefer side-by-side configurations and exhibit changes to their synchronization mid-swimming. Using numerical simulations, alterations to the unsteady wake dynamics imposed by abrupt changes in the phase angle between two pitching side-by-side foils were examined at Reynolds number of 4, 000 and Strouhal number of 0.50. Four hybrid modes were considered in this study with two modes representing an abrupt phase change by π during the 20 th cycle. The other two modes represented a simplified case of burst-and-coast swimming, in which there was a brief (2 oscillation periods) suspension of oscillations before imposing a change in phase angle. In all cases, the foils initially performed out-of-phase pitching, and then they started their in-phase motion by either performing the upstroke or down-stroke first. This kinematic change resulted in the formation and growth of a secondary vortex street in between two primary streets, which enabled and maintained a split wake configuration. Furthermore, the phase switching altered the pressure levels on the top and bottom surfaces of both foils to almost similar levels, which attributed to a reduction in the side-force. The growth rate of the secondary vortex street remained consistent for all four hybrid modes.
Fishes school to swim more efficiently while not much of fish schooling is understood from the perspective of fluid–structure interactions. To understand the benefits of fish schooling, we investigate thrust, efficiency, and wake structure of a two-hydrofoil system where the upstream hydrofoil is forced pitching (active) and the downstream hydrofoil is free pitching (passive). The streamwise and lateral separations between the two hydrofoils are 0.109c and 1.0D, respectively, where c is the chord length and D is the diameter of the leading edge. The active hydrofoil pitches with normalized amplitudes A∗=0.55 – 0.80 and normalized frequencies StD=0.23–0.33. It is found that the upstream active hydrofoil undergoes up to 38% thrust enhancement in the presence of the downstream passive hydrofoil while the downstream passive hydrofoil achieves the same thrust as the upstream active hydrofoil under certain conditions. The maximum combined thrust and efficiency achieved for the two-hydrofoil system are 95% and 180% higher than those for a single isolated hydrofoil. These are some reasons for fish swimming in school. Three distinct flow structures (vortex impingement flow, vortex trapping flow, and vortex splitting flow) are identified in the A∗– StD domain, where the vortex trapping flow provides the greatest thrust and efficiency enhancement.
In nature, insects with their forewings and hindwings undergoing small-gap flapping motion experiences strong aerodynamic interaction. Conventional studies mainly focus on the propulsion performance of tandem flapping wings, while the interaction between a flapping wing and a fixed wing in the tandem configuration at low Reynolds numbers ( Re) is unclear. In this paper, we numerically studied the aerodynamic performance and vortex structure of this tandem flapping-fixed airfoil configuration. The effects of horizontal distance ( L X ), vertical distance ( L Y ), and geometric angle of attack ( α) of the fixed wing on the thrust and lift performance are investigated. The results show that L X dominates the propulsion performance, while L Y and α control the lift performance. The thrust enhancement of the flapping airfoil is effective only within a small range of L X , and the thrust is mainly determined by the changing rate of the impulse of the vortices directly connected to the airfoils. The lift reaches its peak when L Y approaches the plunging amplitude. Compared with a fixed airfoil, the flapping-fixed configuration shows a larger lift-to-drag ratio, indicating a lift enhancement led by the interaction with the upstream flapping airfoil. Moreover, increasing L Y and α simultaneously can lead to additional advantages in lift generation. Further analysis shows that changes of L Y and α both manifest in a variation of the effective angle of attack of the fixed airfoil, thereby manipulating its lift generation. This paper provides aerodynamic database and guidance for the design of Micro Air Vehicles (MAVs) using tandem flapping-fixed wings.
The effect of hydrodynamic interactions on the collective locomotion of fish schools is still poorly understood. In this paper, the flow-mediated organization of two tandem flapping foils, which are free in both the longitudinal and lateral directions, is numerically studied. It is found that the tandem formation is unstable for two foils when they can self-propel in both the longitudinal and lateral directions. Three types of resultant regular formations are observed, i.e. semi-tandem formation, staggered formation and transitional formation. Which type of regular formation occurs depends on the flapping parameters and the initial longitudinal distance between the two foils. Moreover, there is a threshold value of the cycle-averaged longitudinal distance below which both velocity enhancement and efficiency augmentation can be achieved by two foils in regular formations. The results obtained here may shed some light on understanding the emergence of regular formations of fish schools.
Biplane airfoils at high angles of attack have interesting nonlinear characteristics, the purpose of this work is to evaluate the impacts of spacing ratio (λ=ds/c=0.25, 0.5, 1, 2 and 4, where ds is the vertical distance between biplane airfoils and c is chord length) and Reynolds number (0.87×105≤Re≤4.35×105) on buffeting and lock-in phenomenon at angle of attack α=40∘ throughout numerical investigation. Present simulation results show that biplane configuration usually can reduce buffeting frequency slightly comparing to the single airfoil, yet reasonable spacing λ=2 is helpful to suppress buffeting and continuous acceleration also promotes stability. Particular attention is paid to stagnation point region that moves away from leading edge of the upper airfoil with increasing λ. However, the lower airfoil corresponds to the fixed stagnation point region. Additionally, limit cycle oscillation (LCO) of biplane airfoils is determined by pitching angles (θ), and in consideration of spacing effect, limit cylces of the lower airfoil move downward but those of the upper airfoil move in the opposite direction. Moreover, the shape of limit cycle for the later first collapses then inflates. Unique 8-shaped hysteresis of the upper airfoil in λ=1 is caused by sporadically wake interference. On the whole, V-shaped lock-in region will expand and shift left to some extent based on λ in contrast to the single airfoil. In terms of area, lock-in region shrinks then expands with rising λ, and the proportion of the left part increases as λ increases.
The present study investigates the mechanisms of wake-induced flow dynamics in tandem National Advisory Committee for Aeronautics 0015 flapping foils at low Reynolds number of Re = 1100. A moving mesh arbitrary Lagrangian–Eulerian framework is utilized to realize the prescribed flapping motion of the foils while solving the flow via incompressible Navier–Stokes equations. The effect of the gap between the two foils on the thrust generation is studied for gaps of 1–10 times the chord of the downstream foil. The mean thrust as well as the propulsive efficiency vary periodically with the gap indicating alternate regions of higher and lower thrust generation, emphasizing the profound effect of upstream foil's wake interaction with the downstream foil. Five crucial wake–foil interactions leading to either favorable or unfavorable conditions for thrust generation are identified and different modes depending on the interactions are proposed for the tandem flapping foils. It is observed that the effect of the wake of the upstream foil on the downstream foil decreases with increasing gap. The study also focuses on the effect of the chord sizes of the upstream and the downstream foils on the propulsive forces, where the chord of the upstream foil is selected as 0.25–1 times the downstream foil's chord length. The effect of the chord size on the thrust is noticed to diminish as the chord size of the upstream foil decreases. Furthermore, the effect of the phase difference between the kinematics of the upstream and the downstream foils on flow dynamics is also explored along with its relationship with the chord sizes. For a fixed chord size, the effect of the phase difference on the propulsive performance is observed to be similar to that by varying the gap between the foils due to similar type of vortex interactions. The mechanisms of vortex interactions are linked to provide a comprehensive and generic understanding of the flow dynamics of tandem foils.
With the environmental deterioration and people's increasing attention to its protection, it is urgent to save energy and reduce emissions from ships. Reducing ships' drag and using a biomimetic propulsion device as the alternative power to drive them is an effective solution. In this paper, a ship propulsion unit composed of movable flapping foils is proposed. The flapping foils make a reciprocating treading motion in water to generate power to propel and heave ships. By heaving ships out of the water, the drag of the hull is eliminated, which considerably reduces energy consumption. By controlling the attack angle of flapping foils in groups, a good motion control performance can be obtained. Compared with hydrofoil ships, the propulsion unit can heave the ship out of the water at a low speed, and it utilizes both the lift and the drag from foils. It can actuate the ship with 6 degrees of freedom.
Biplane configuration is a critical configuration for aircrafts all the time, but the dynamics and flow mechanism remain elusive, with no systematic description forthcoming. This paper reported a numerical investigation of spacing effect (λ=d/c=0.4∼5, c is the chord length and c=6inch) and the mean and fluctuating aerodynamics for biplane airfoils at angles of attack ranging from 30∘ to 90∘. Additionally, particular attention was devoted to vorticity fields and Strouhal number (St). The primary finding was that C¯L and C¯D of the lower airfoil were greater than those of the upper airfoil whatever λ was located to. And the turning points for C¯L and C¯D of the upper airfoil showed an evident regularity with increasing λ.But the maximum deviation first plungs then jumps with increasing λ. What inspired us was the fluctuating aerodynamics in λ=1.5 converged quickly which may contribute to enhancing stability. Interestingly, overall lift-to-drag ratio trends in all cases were strikingly similar to a single airfoil. Three vortices regimes were identified from the generation mechanism of traling-edge vortices (TEVs), named integrated vortices, transition with deformed vortices and coshedding vortices, respectively. And the vortices regime was also related to the angle of attack. Besides, in the integrated and coshedding vortices regimes, two Strouhal numbers of the lower airfoil and the upper airfoil were equivalent, but St can’t be estimated which one is larger in the transition regime.
The hydrodynamic interactions between two pitching foils arranged in a side-by-side configuration are investigated numerically for a broad parameter space. This includes a range of Reynolds numbers between 1000 and 12 000, Strouhal numbers between 0.25 and 0.5, separation distances between 0.5c and 2c, and phase differences between 0° and 180°. The propulsive performance of side-by-side foils are compared to an isolated foil over a range of Reynolds number and Strouhal number, which show a consistent impact on their performance. The system experiences thrust enhancements with increasing Reynolds number although the coefficient of power does not change significantly. The Strouhal number at which a drag producing foil transitions to a thrust generating foil increases for the by side-by-side configuration compared to a solitary oscillating foil. At higher Reynolds number, the difference on the transitioning Strouhal number is smaller. A new scaling model is developed for propulsive performance of side-by-side pitching foils for a range of Strouhal number, Reynolds number, separation distance, and phase difference. Moreover, the new scaling model well encompasses the performance characteristics of an isolated foil, representing the case of a very large (infinite) separation distance between the foils.
In this study we investigate numerically the vortex wake formation behind the profile performing simple harmonic motion known in the literature as plunging. This research was inspired by the flapping motion which is appropriate for birds, insects and fishes. We assume the two dimensional model of flow. Depending on the parameters such as plunging amplitude, frequency and the Reynolds number, we demonstrate many different types of vortex street behind the profile. It is well known that the type of vortex wake determines the hydrodynamic forces acting on the profile. Dependences of the plunging amplitude, the Strouhal number and various topology vortices are established by constructing the phase transition diagram. The areas in the diagram related to the drag, thrust, and lift force generation are captured. We notice also the areas where the vorticity field is disordered. The disordered vorticity field does not allow maintenance of the periodic forces on the profile. An increase in the Reynolds number leads to the transition of the vortex wake behind the profile. The transition is caused by the phenomenon of boundary layer eruption. Further increase of the Reynolds number causes the vortex street related to the generation of the lift force to vanish.
Force and particle image velocimetry measurements were conducted on a NACA 0012 aerofoil undergoing small-amplitude high-frequency plunging oscillation at low Reynolds numbers and angles of attack in the range 0–. For angles of attack less than or equal to the stall angle, at high Strouhal numbers, significant bifurcations are observed in the time-averaged lift coefficient resulting in two lift-coefficient branches. The upper branch is associated with an upwards deflected jet, and the lower branch is associated with a downwards deflected jet. These branches are stable and highly repeatable, and are achieved by increasing or decreasing the frequency in the experiments. Increasing frequency refers to starting from stationary and increasing the frequency very slowly (while waiting for the flow to reach an asymptotic state after each change in frequency); decreasing frequency refers to impulsively starting at the maximum frequency and decreasing the frequency very slowly. For the latter case, angle of attack, starting position and initial acceleration rate are also parameters in determining which branch is selected. The bifurcation behaviour is closely related to the properties of the trailing-edge vortices. The bifurcation was therefore not observed for very small plunge amplitudes or frequencies due to insufficient trailing-edge vortex strength, nor at larger angles of attack due to greater asymmetry in the strength of the trailing-edge vortices, which creates a preference for a downward deflected jet. Vortex strength and asymmetry parameters are derived from the circulation measurements. It is shown that the most appropriate strength parameter in determining the onset of deflected jets is the circulation normalized by the plunge velocity.
Foils oscillating transversely to an oncoming uniform flow produce, under certain conditions, thrust. It is shown through experimental data from flapping foils and data from fish observation that thrust develops through the formation of a reverse von Kármán street whose preferred Strouhal number is between 0.25 and 0.35, and that optimal foil efficiency is achieved within this Strouhal range.
It is the objective of this paper to review recent developments in the understanding and prediction of flapping-wing aerodynamics. To this end, several flapping-wing configurations are considered. First, the problem of single flapping wings is treated with special emphasis on the dependence of thrust, lift, and propulsive efficiency on flapping mode, amplitude, frequency, and wing shape. Second, the problem of hovering flight is studied for single flapping wings. Third, the aerodynamic phenomena and benefits produced by the flapping-wing interactions on tandem wings or biplane configurations are discussed. Such interactions occur on dragonflies or on a recently developed micro air vehicle. The currently available two- and three-dimensional inviscid and viscous flapping-wing flow solutions are presented. It is shown that the results are strongly dependent on flapping frequency, amplitude, and Reynolds number. These findings are substantiated by comparison with the available experimental data.
The vortex streets produced by a flapping foil of span to chord aspect ratio of 4:1 are studied in a hydrodynamic tunnel experiment. In particular, the mechanisms giving rise to the symmetry breaking of the reverse Bénard–von Kármán (BvK) vortex street that characterizes fishlike swimming and forward flapping flight are examined. Two-dimensional particle image velocimetry (PIV) measurements in the midplane perpendicular to the span axis of the foil are used to characterize the different flow regimes. The deflection angle of the mean jet flow with respect to the horizontal observed in the average velocity field is used as a measure of the asymmetry of the vortex street. Time series of the vorticity field are used to calculate the advection velocity of the vortices with respect to the free stream, defined as the phase velocity Uphase, as well as the circulation Γ of each vortex and the spacing ξ between consecutive vortices in the near wake. The observation that the symmetry-breaking results from the formation of a dipolar structure from each couple of counter-rotating vortices shed on each flapping period serves as the starting point to build a model for the symmetry-breaking threshold. A symmetry-breaking criterion based on the relation between the phase velocity of the vortex street and an idealized self-advection velocity of two consecutive counter-rotating vortices in the near wake is established. The predicted threshold for symmetry breaking accounts well for the deflected wake regimes observed in the present experiments and may be useful to explain other experimental and numerical observations of similar deflected propulsive vortex streets reported in the literature.
The wake of a flexible foil undergoing pitching oscillations in a low-speed
hydrodynamic tunnel is used to examine the effect of chord-wise foil
flexibility in the dynamical features of flapping-based propulsion. We compare
the regime transitions in the wake with respect to the case of a rigid foil and
show that foil flexibility inhibits the symmetry breaking of the reverse
B\'enard-von K\'arm\'an wake reported in the literature. A momentum balance
calculation shows the average thrust to be up to three times greater for the
flexible foil than for the rigid foil. We explain both of these observations by
analyzing the vortex dynamics in the very near wake.
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.
Here we show, by qualitative free- and tethered-flight flow visualization, that dragonflies fly by using unsteady aerodynamic mechanisms to generate high-lift, leading-edge vortices. In normal free flight, dragonflies use counterstroking kinematics, with a leading-edge vortex (LEV) on the forewing downstroke, attached flow on the forewing upstroke, and attached flow on the hindwing throughout. Accelerating dragonflies switch to in-phase wing-beats with highly separated downstroke flows, with a single LEV attached across both the fore- and hindwings. We use smoke visualizations to distinguish between the three simplest local analytical solutions of the Navier-Stokes equations yielding flow separation resulting in a LEV. The LEV is an open U-shaped separation, continuous across the thorax, running parallel to the wing leading edge and inflecting at the tips to form wingtip vortices. Air spirals in to a free-slip critical point over the centreline as the LEV grows. Spanwise flow is not a dominant feature of the flow field--spanwise flows sometimes run from wingtip to centreline, or vice versa--depending on the degree of sideslip. LEV formation always coincides with rapid increases in angle of attack, and the smoke visualizations clearly show the formation of LEVs whenever a rapid increase in angle of attack occurs. There is no discrete starting vortex. Instead, a shear layer forms behind the trailing edge whenever the wing is at a non-zero angle of attack, and rolls up, under Kelvin-Helmholtz instability, into a series of transverse vortices with circulation of opposite sign to the circulation around the wing and LEV. The flow fields produced by dragonflies differ qualitatively from those published for mechanical models of dragonflies, fruitflies and hawkmoths, which preclude natural wing interactions. However, controlled parametric experiments show that, provided the Strouhal number is appropriate and the natural interaction between left and right wings can occur, even a simple plunging plate can reproduce the detailed features of the flow seen in dragonflies. In our models, and in dragonflies, it appears that stability of the LEV is achieved by a general mechanism whereby flapping kinematics are configured so that a LEV would be expected to form naturally over the wing and remain attached for the duration of the stroke. However, the actual formation and shedding of the LEV is controlled by wing angle of attack, which dragonflies can vary through both extremes, from zero up to a range that leads to immediate flow separation at any time during a wing stroke.
We study experimentally the vortex streets produced by a flapping foil in a hydrodynamic tunnel, using two-dimensional particle image velocimetry. An analysis in terms of a flapping frequency-amplitude phase space allows the identification of (i) the transition from the well-known Bénard-von Kármán (BvK) wake to the reverse BvK vortex street that characterizes propulsive wakes, and (ii) the symmetry breaking of this reverse BvK pattern giving rise to an asymmetric wake. We also show that the transition from a BvK wake to a reverse BvK wake precedes the actual drag-thrust transition and we discuss the significance of the present results in the analysis of flapping systems in nature.
Dragonflies are dramatic, successful aerial predators, notable for their flight agility and endurance. Further, they are highly capable of low-speed, hovering and even backwards flight. While insects have repeatedly modified or reduced one pair of wings, or mechanically coupled their fore and hind wings, dragonflies and damselflies have maintained their distinctive, independently controllable, four-winged form for over 300Myr. Despite efforts at understanding the implications of flapping flight with two pairs of wings, previous studies have generally painted a rather disappointing picture: interaction between fore and hind wings reduces the lift compared with two pairs of wings operating in isolation. Here, we demonstrate with a mechanical model dragonfly that, despite presenting no advantage in terms of lift, flying with two pairs of wings can be highly effective at improving aerodynamic efficiency. This is achieved by recovering energy from the wake wasted as swirl in a manner analogous to coaxial contra-rotating helicopter rotors. With the appropriate fore-hind wing phasing, aerodynamic power requirements can be reduced up to 22 per cent compared with a single pair of wings, indicating one advantage of four-winged flying that may apply to both dragonflies and, in the future, biomimetic micro air vehicles.
Propulsive flapping foils are widely studied in the development of swimming and fly- ing animal-like autonomous systems. Numerical studies in this topic are mainly two- dimensional (2D) studies as they are quicker and cheaper, but, this inhibits the three- dimensional (3D) evolution of the shed vortices from leading- and trailing-edges. In this work, we examine the similarities and differences between 2D and 3D simulations through a case study in order to evaluate the efficacy and limitations of using 2D simulations to describe a 3D system. We simulate an infinite-span NACA0016 foil both in 2D and 3D at a Reynolds number of 5300 and an angle-of-attack of 10◦. The foil is subject to prescribed heaving and pitching kinematics with varying trailing-edge deflection amplitude A. Our primary finding is that the flow and forces are effectively 2D at intermediate amplitude- based Strouhal numbers (StA = 2Af/U where U is the freestream velocity and f is the flapping frequency); StA ≈ 0.3 for heaving, StA ≈ 0.3–0.6 for pitching and StA ≈ 0.15–0.45 for coupled motion, while 3D effects dominate outside of these ranges. These 2D regions begin when the fluid energy induced by the flapping motion overcomes the 3D vortex shedding found on a stationary foil, and the flow reverts back to 3D when the strength of the shed vortices overwhelms the stabilizing influence of viscous dissipation. These results indicate that 3D-to-2D transitions or vice-versa are a balance between the strength and stability of leading-/trailing-edge vortices and the flapping energy. 2D simulations can still be used for flapping flight/swimming studies provided the flapping amplitude/frequency is within a given range.
The effects of flexibility on the wake structures of a foil under a heaving motion in a viscous uniform flow are numerically studied using an immersed boundary method. An inspection of the phase diagram of the wake structures in a map of the chord-length-based dimensionless heaving amplitude (AL) and Strouhal number (StL) shows that the wake transition boundaries of the rigid foil are well predicted by constant amplitude-based Strouhal number (StA) lines, similar to previous studies. However, the wake transition boundaries of the flexible foil are predictable by constant StA lines only for high StL cases. A large deformation angle of a flexible foil by the amplitude difference and phase difference between the leading and trailing edge cross-stream displacements reduces the effective leading edge velocity, with an accompanying decrease in the leading edge circulation. However, the trailing edge circulation for a flexible foil is increased due to increased trailing edge amplitude. The sum of the leading and trailing edge circulations plays an important role in determining the wake pattern behind a rigid and flexible foil, and wake transitions are observed beyond critical circulations. The decrease in the thrust coefficient for large values of StL and AL is closely associated with the generation of a complex wake pattern behind a foil, and the complex wake is a direct consequence of sufficiently large leading edge circulation. A critical effective phase velocity in a vortex dipole model is proposed to predict the maximum thrust coefficient without a complex wake pattern.
Reversed von Kármán streets are responsible for a velocity surplus in the wake of flapping foils, indicating the onset of thrust generation. However, the wake pattern cannot be predicted based solely on the flapping peak-to-peak amplitude and frequency because the transition also depends sensitively on other details of the kinematics. In this work we replace with the cycle-averaged swept trajectory of the foil chordline. Two-dimensional simulations are performed for pure heave, pure pitch and a variety of heave-to-pitch coupling. In a phase space of dimensionless we show that the drag-to-thrust wake transition of all tested modes occurs for a modified Strouhal . Physically, the product expresses the induced velocity of the foil and indicates that propulsive jets occur when this velocity exceeds . The new metric offers a unique insight into the thrust-producing strategies of biological swimmers and flyers alike, as it directly connects the wake development to the chosen kinematics, enabling a self-similar characterisation of flapping foil propulsion.
The extinct ocean-going plesiosaurs were unique within vertebrates because they used two flipper pairs identical in morphology for propulsion. Although fossils of these Mesozoic marine reptiles have been known for more than two centuries, the function and dynamics of their tandem-flipper propulsion system has always been unclear and controversial. We address this question quantitatively for the first time in this study, reporting a series of precisely controlled water tank experiments that use reconstructed plesiosaur flippers scaled from well-preserved fossils. Our aim was to determine which limb movements would have resulted in the most efficient and effective propulsion. We show that plesiosaur hind flippers generated up to 60% more thrust and 40% higher efficiency when operating in harmony with their forward counterparts, when compared with operating alone, and the spacing and relative motion between the flippers was critical in governing these increases. The results of our analyses show that this phenomenon was probably present across the whole range of plesiosaur flipper motion and resolves the centuries-old debate about the propulsion style of these marine reptiles, as well as indicating why they retained two pairs of flippers for more than 100 million years. © 2017 The Author(s) Published by the Royal Society. All rights reserved.
The propulsive performance of a pair of tandem flapping foils is sensitively dependent on the spacing and phasing between them. Large increases in thrust and efficiency of the hind foil are possible, but the mechanisms governing these enhancements remain largely unresolved. Two-dimensional numerical simulations of tandem and single foils oscillating in heave and pitch at a Reynolds number of 7000 are performed over a broad and dense parameter space, allowing the effects of inter-foil spacing ( $S$ ) and phasing ( $\unicode[STIX]{x1D711}$ ) to be investigated over a range of non-dimensional frequencies (or Strouhal number, $St$ ). Results indicate that the hind foil can produce from no thrust to twice the thrust of a single foil depending on its spacing and phasing with respect to the fore foil, which is consistent with previous studies that were carried out over a limited parameter space. Examination of instantaneous flow fields indicates that high thrust occurs when the hind foil weaves between the vortices that have been shed by the fore foil, and low thrust occurs when the hind foil intercepts these vortices. Contours of high thrust and minimal thrust appear as inclined bands in the $S-\unicode[STIX]{x1D711}$ parameter space and this behaviour is apparent over the entire range of Strouhal numbers considered $(0.2\leqslant St\leqslant 0.5)$ . A novel quasi-steady model that utilises kinematics of a virtual hind foil together with data obtained from simulations of a single flapping foil shows that performance augmentation is primarily determined through modification of the instantaneous angle of attack of the hind foil by the vortex street established by the fore foil. This simple model provides estimates of thrust and efficiency for the hind foil, which is consistent with data obtained through full simulations. The limitations of the virtual hind foil method and its physical significance is also discussed.
This paper introduces a virtual boundary method for compressible viscous fluid flow that is capable of accurately representing moving bodies in flow and aeroacoustic simulations. The method is the compressible extension of the boundary data immersion method (BDIM, Maertens & Weymouth (2015)). The BDIM equations for the compressible Navier-Stokes equations are derived and the accuracy of the method for the hydrodynamic representation of solid bodies is demonstrated with challenging test cases, including a fully turbulent boundary layer flow and a supersonic instability wave. In addition we show that the compressible BDIM is able to accurately represent noise radiation from moving bodies and flow induced noise generation without any penalty in allowable time step.
A perching bird is able to rapidly decelerate while maintaining lift and control, but the underlying aerodynamic mechanism is poorly understood. In this work we perform a study on a simultaneously decelerating and pitching aerofoil section to increase our understanding of the unsteady aerodynamics of perching. We first explore the problem analytically, developing expressions for the added-mass and circulatory forces arising from boundary-layer separation on a flat-plate aerofoil. Next, we study the model problem through a detailed series of experiments at Re = 22 000 and two-dimensional simulations at Re = 2000. Simulated vorticity fields agree with particle image velocimetry measurements, showing the same wake features and vorticity magnitudes. Peak lift and drag forces during rapid perching are measured to be more than 10 times the quasi-steady values. The majority of these forces can be attributed to added-mass energy transfer between the fluid and aerofoil, and to energy lost to the fluid by flow separation at the leading and trailing edges. Thus, despite the large angles of attack and decreasing flow velocity, this simple pitch-up manoeuvre provides a means through which a perching bird can maintain high lift and drag simultaneously while slowing to a controlled stop.
An accurate Cartesian-grid treatment for intermediate Reynolds number fluid-solid interaction problems is described. We first identify the inability of existing immersed boundary methods to handle intermediate Reynolds number flows to be the discontinuity of the velocity gradient at the interface. We address this issue by generalizing the Boundary Data Immersion Method (BDIM, Weymouth and Yue (2011)), in which the field equations of each domain are combined analytically, through the addition of a higher order term to the integral formulation. The new method retains the desirable simplicity of direct forcing methods and smoothes the velocity field at the fluid-solid interface while removing its bias. Based on a second-order convolution, it achieves second-order convergence in the L 2 norm, regardless of the Reynolds number. This results in accurate flow predictions and pressure fields without spurious fluctuations, even at high Reynolds number. A treatment for sharp corners is also derived that significantly improves the flow predictions near the trailing edge of thin airfoils. The second-order BDIM is applied to unsteady problems relevant to ocean energy extraction as well as animal and vehicle locomotion for Reynolds numbers up to 10 5 .
A two-dimensional numerical study is performed to investigate the relation between the direction of a deflected wake and the vortex pairing mechanisms. The deflection angle can be correlated with two effective phase velocities defined to represent the trends of symmetry breaking and symmetry holding, respectively. The deflection angle increases with the strength of the vortex pairs, which is associated with the heaving amplitude, frequency, and the free stream Reynolds number. Furthermore, not only the influence of Strouhal number but also those of the two heaving motion components – amplitude and frequency – are studied individually under different Reynolds numbers. The study shows that the deflection angle consistently increases with the difference between the symmetry-breaking phase velocity and symmetry-holding phase velocity.
In a tandem wing configuration, the hindwing often operates in the wake of the forewing and, hence, its performance is affected by the vortices shed by the forewing. Changes in the phase angle between the flapping motions of the fore and the hind wings, as well as the spacing between them, can affect the resulting vortex/wing and vortex/vortex interactions. This study uses 2D numerical simulations to investigate how these changes affect the leading dege vortexes (LEV) generated by the hindwing and the resulting effect on the lift and thrust coefficients as well as the efficiencies. The tandem wing configuration was simulated using an incompressible Navier-Stokes solver at a chord-based Reynolds number of 5 000. A harmonic single frequency sinusoidal oscillation consisting of a combined pitch and plunge motion was used for the flapping wing kinematics at a Strouhal number of 0.3. Four different spacings ranging from 0.1 chords to 1 chord were tested at three different phase angles, 0°, 90° and 180°. It was found that changes in the spacing and phase angle affected the timing of the interaction between the vortex shed from the forewing and the hindwing. Such an interaction affects the LEV formation on the hindwing and results in changes in aerodynamic force production and efficiencies of the hindwing. It is also observed that changing the phase angle has a similar effect as changing the spacing. The results further show that at different spacings the peak force generation occurs at different phase angles, as do the peak efficiencies.
It is the objective of this paper to review recent developments in the understanding and prediction of flapping-wing aerodynamics. To this end, several flapping-wing configurations are considered. First, the problem of single flapping wings is treated with special emphasis on the question of which flapping modes, amplitudes, frequencies, and wing shapes produce optimum cruise flight efficiencies. Second, the problem of hovering flight is studied for single flapping wings. Third, aerodynamic phenomena produced by flapping wing interactions are discussed, such as tandem wing configurations, as used by dragonflies, or biplane configurations, as used on the authors' micro air vehicle. Potential flow and viscous flow solutions are presented and the role of vortex shedding, especially from wing leading edges, is discussed. Comparisons with available experimental results are provided.
A systematic series of wind-tunnel tests was conducted on an ornithopter configuration consisting of two sets of symmetrically flapping wings, located one behind the other in tandem. It was discovered that the tandem arrangement can give thrust and efficiency increases over a single set of flapping wings for certain relative phase angles and longitudinal spacing between the wing sets. In particular, close spacing on the order of 1 chord length is generally best, and phase angles of approximately 0 +/- 50 deg give the highest thrusts and propulsive efficiencies. Asymmetrical flapping was also studied, which consists of the two sets of wings rocking relative to one another 180 deg out of phase. It was found that the performance of such an arrangement is poor, relative to the best performing symmetrical tandem flapping.
Flying insects can generally be divided into two groups: ‘primitive’ orders with forewings and hindwings that move independently (for example, Odonata, Orthoptera, Isoptera) and more ‘advanced’ orders with wings that are functionally one pair, with the fore- and hindwings in contact so as to function as one wing (for example, Hymenoptera, Lepidoptera, Homoptera), or with only one pair of wings that functions primarily as a lifting surface (for example, Diptera, Strepsiptera).
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.
The vortical flow patterns in the wake of a NACA 0012 airfoil pitching
at small amplitudes are studied in a low speed water channel. It is
shown that a great deal of control can be exercised on the structure of
the wake by the control of the frequency, amplitude and also the shape
of the oscillation waveform. An important observation in this study has
been the existence of an axial flow along the cores of the wake
vortices. Estimates of the magnitude of the axial flow suggest a linear
dependence on the oscillation frequency and amplitude.
We present an experimental investigation of the flow structure and vorticity field in the wake of a NACA-0012 airfoil pitching sinusoidally at small amplitude and high reduced frequencies. Molecular tagging velocimetry is used to quantify the characteristics of the vortex array (circulation, peak vorticity, core size, spatial arrangement) and its downstream evolution over the first chord length as a function of reduced frequency. The measured mean and fluctuating velocity fields are used to estimate the mean force on the airfoil and explore the connection between flow structure and thrust generation.
Results show that strong concentrated vortices form very rapidly within the first wavelength of oscillation and exhibit interesting dynamics that depend on oscillation frequency. With increasing reduced frequency the transverse alignment of the vortex array changes from an orientation corresponding to velocity deficit (wake profile) to one with velocity excess (reverse Kármán street with jet profile). It is found, however, that the switch in the vortex array orientation does not coincide with the condition for crossover from drag to thrust. The mean force is estimated from a more complete control volume analysis, which takes into account the streamwise velocity fluctuations and the pressure term. Results clearly show that neglecting these terms can lead to a large overestimation of the mean force in strongly fluctuating velocity fields that are characteristic of airfoils executing highly unsteady motions. Our measurements show a decrease in the peak vorticity, as the vortices convect downstream, by an amount that is more than can be attributed to viscous diffusion. It is found that the presence of small levels of axial velocity gradients within the vortex cores, levels that can be difficult to measure experimentally, can lead to a measurable decrease in the peak vorticity even at the centre of the flow facility in a flow that is expected to be primarily two-dimensional.
Two-dimensional turbulence is investigated experimentally in thin liquid films. This study shows the spontaneous formation of couples of opposite-sign vortices in von Karman wakes. The structure of these couples, their behavior and their role in turbulent flows is then studied using both a numerical simulation and laboratory results.
General aerodynamic theory-perfect fluids
- T Von Kármán
Von Karman, T. 1935 General aerodynamic theory-perfect fluids. Aerodynamic theory 2, 346-349.
Die gesetzedes luftwiderstandes
- R Knoller
Knoller, R. 1909 Die gesetzedes luftwiderstandes. Flug-und Motortechnik (Wien) 3 (21), 1-7.