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Effect of aspect ratio on the propulsive performance of tandem flapping foils
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Abstract and Figures
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 aspect ratio - AR) is found to improve thrust coefficients and thrust augmentation but the benefits level off towards higher values of AR. On the other hand, 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 on the mechanisms of these wake interactions and provide valuable information for the design of novel biomimetic propulsion systems.
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Pakistan Understanding the connection between physiology and kinematics of natural swimmers is of great importance to design efficient bio-inspired underwater vehicles. This study looks at high-fidelity three-dimensional numerical simulations for flows over an undulating American eel with prescribed anguilliform kinematics. Particularly, our work focuses on why natural anguilliform swimmers employ wavelengths shorter than their bodylengths while performing wavy kinematics. For this purpose, we vary the undulatory wavelength for a range of values generally observed in different aquatic animals at Strouhal numbers 0.30 and 0.40. We observe that our anguilliform swimmer is able to demonstrate more suitable hydrodynamic performance for wavelengths of 0.65 and 0.80. For longer wavelengths , the swimmer experiences large frictional drag, which deteriorates its performance. The wake topology was dominated by hairpin-like structures, which are closely linked with the underlying physics of anguilliform swimming found in nature.
The propulsive performance of a flexible foil with prescribed pitching and heaving motions about any pivot point location and passive chordwise flexural deflection is analysed within the framework of the linear potential flow theory and the Euler–Bernoulli beam equation using a quartic approximation for the deflection. The amplitude of the flexural component of the deflection and its phase, the thrust force, input power and propulsive efficiency are computed analytically in terms of the stiffness and mass ratio of the plate, frequency, pivot point location and remaining kinematic parameters. It is found that the maximum flexural deflection amplitude, thrust and input power are related to the first fluid–structure natural frequency of the system, corresponding to the deflection approximation considered. The same relation is observed for the propulsive efficiency when an offset drag is included in the analytical expressions. These results, which are valid for small amplitude and sufficiently large stiffness of the foil, are compared favourably with previous related results when the foil pivots about the leading edge. The configurations generating maximum thrust and efficiency enhancement by flexibility are analysed in relation to those of an otherwise identical rigid foil.
We address the fluid-structure interaction of flexible fin models oscillated in a water flow. Here, we investigate in particular the dependence of hydrodynamic force distributions on fin geometry and flapping frequency. For this purpose, we employ state-of-the-art techniques in pressure evaluation to describe fluid force maps with high temporal and spatial resolution on the deforming surfaces of the hydrofoils. Particle tracking velocimetry (PTV) is used to measure the 3D fluid velocity field, and the hydrodynamic stress tensor is subsequently calculated based on the Navier-Stokes equation. The shape and kinematics of the fin-like foils are linked to their ability to generate propulsive thrust effciently, as well as the accumulation of external contact forces and the resulting internal tension throughout a flapping cycle.
The importance of the leading-edge sweep angle of propulsive surfaces used by unsteady swimming and flying animals has been an issue of debate for many years, spurring studies in biology, engineering, and robotics with mixed conclusions. In this work, we provide results from three-dimensional simulations on single-planform finite foils undergoing tail-like (pitch-heave) and flipper-like (twist-roll) kinematics for a range of sweep angles covering a substantial portion of animals while carefully controlling all other parameters. Our primary finding is the negligible 0.043 maximum correlation between the sweep angle and the propulsive force and power for both tail-like and flipper-like motions. This indicates that fish tails and mammal flukes with similar range and size can have a large range of potential sweep angles without significant negative propulsive impact. Although there is a slight benefit to avoiding large sweep angles, this is easily compensated by adjusting the fin’s motion parameters such as flapping frequency, amplitude and maximum angle of attack to gain higher thrust and efficiency.
Animals and bio-inspired robots can swim/fly faster near solid surfaces, with little to no loss in efficiency. How these benefits change with propulsor aspect ratio is unknown. Here we show that lowering the aspect ratio weakens unsteady ground effect, thrust enhancements become less noticeable, stable equilibrium altitudes shift lower and become weaker, and wake asymmetries become less pronounced. Water-channel experiments and potential flow simulations reveal that these effects are consistent with known unsteady aerodynamic scalings. We also discovered a second equilibrium altitude even closer to the wall (<0.35 chord lengths). This second equilibrium is unstable, particularly for high-aspect-ratio foils. Active control may therefore be required for high-aspect-ratio swimmers hoping to get the full benefit of near-ground swimming. The fact that aspect ratio alters near-ground propulsion suggests that it may be a key design parameter for animals and robots that swim/fly near a seafloor or surface of a lake.
Flapping flight and swimming are increasingly studied due to both their intrinsic scientific richness and their applicability to novel robotic systems. Strip theory is often applied to flapping wings, but such modeling is only rigorously applicable in the limit of infinite aspect ratio (AR) where the geometry and kinematics are effectively uniform. This work compares the flow features and forces of strip theory and three-dimensional flapping foils, maintaining similitude in the rolling and twisting kinematics while varying the foil AR. We find the key influence of finite AR and spanwise varying kinematics is the generation of a time-periodic spanwise flow which stabilizes the vortex structures and enhances the dynamics at the foil root. An aspect-ratio correction for flapping foils is developed analogous to Prandtl finite wing theory, enabling future use of strip theory in analysis and design of finite aspect ratio flapping foils.
Based on a high-order implicit discontinuous Galerkin method, numerical simulations of a two-dimensional oscillating foil are performed to explore the origin of basic aspects of the flow such as the generation of interesting flow structures in the wake and the associated aerodynamic forces. Dimensional arguments suggest that the flow is characterized by non dimensional aerodynamic coefficients depending on the kinematics of the oscillation, such its frequency and amplitude, and on the dynamics of the flow, such as the Reynolds number. Most of the studies have concentrated their attention on the role played by the kinematic of the oscillation with less or no attention to the effect of the Reynolds number. Here, we show that this effect cannot be neglected in the study of the phenomena at the basis of the generation of lift and thrust. We found that the Reynolds number plays a fundamental role for the development of thrust by defining critical values Rec for the switch from drag to thrust conditions. It is also shown that for Re>Rec, the Reynolds number defines additional subcritical values which are at the basis of flow instabilities leading to smooth and sharp transitions of the structure of the wake and of the related aerodynamic forces. For the analysis of the behaviour of the flow, the space of phases composed by the instantaneous lift and thrust (cL,cT) is introduced. It is shown how the orbits in the (cL,cT)-space allow us for a clear understanding of the physical evolution of the flow system and of the cyclical phenomena composing it.
The role of aspect ratio on the dynamic stall process of an unswept finite wing is investigated using high-fidelity large-eddy simulations. Three aspect ratios ($AR = 4$, 8, and 16) are explored for a finite wing with a NACA 0012 profile and rounded wing-tips. Following previous work, the finite wing at chord-Reynolds number $Re_c = 2 \times 10^5$ and freestream Mach number $M_\infty = 0.1$ pitches sinusoidally from an initial incidence of 4$^\circ$ to a maximum angle of attack of 22$^\circ$ with reduced frequency $k = \pi f c /U_\infty$ = $\pi$/16 over one pitching cycle. Examination of the 3D unsteady flow-fields show distinctly different evolutions of the dynamic stall flow structure at the higher $AR$ in contrast to the lower, baseline $AR$. Rather than evolving into a $Lambda$-vortex following the bursting of the laminar separation bubble observed at $AR = 4$, the higher $AR$ show multiple arch-like cells forming across the DSV core from instabilities generated by the DSV's interaction with the wing. These structures eventually break down as they interact with a more span-wise coherent trailing edge vortex in contrast to forming into an arch-vortex that ejects into the wake as a ring-like structure seen at the lower $AR$. Examination of the unsteady loads show an increase in maximum lift and minimum pitching moment, earlier onset of stall, and the emergence of a secondary minimum peak in the pitching moment indicative of an increasingly coherent trailing edge vortex with increasing $AR$.
In this paper, we numerically investigate the effects of time-varying bending stiffness on the propulsion performance of a flapping foil using a fully coupled fluid-structure interaction model. The flow field is simulated using a Navier–Stokes solver while the structural dynamics is resolved by a nonlinear beam model. The force generation, the passive deformation, and the flow field of the flexible foil are significantly affected by the time dependency of flexibility. Here, both the actuation at the leading edge and the stiffness of the foil vary sinusoidally, and the phase ϕ between them plays an important role in determining the performance of the foil. At ϕ = 0°, the maximum time-averaged thrust coefficient can be increased by ∼52% whereas the highest propulsion efficiency remains almost the same as that of the foil with a constant flexibility. This is of significance when the size of the wing is often constrained. In addition, the foil with time-varying stiffness generates considerable lift force, which is attributed to the non-symmetrical deformations and deflected vortex-shedding patterns. Finally, the force generation due to added mass is discussed using a simplified model.