Scaling laws for the thrust production and power consumption of a purely pitching hydrofoil in ground effect are presented. For the first time, ground effect scaling laws based on physical insights capture the propulsive performance over a wide range of biologically-relevant Strouhal numbers, dimensionless amplitudes, and dimensionless ground distances. This is achieved by advancing previous scaling laws (Moored & Quinn 2018) with physics-driven modifications to the added mass and circulatory forces to account for ground distance variations. The key physics introduced are the increase in the added mass of a foil near the ground and the reduction in the influence of a wake vortex system due to the influence of its image system. The scaling laws are found to be in good agreement with new inviscid simulations and viscous experiments, and can be used to accelerate the design of bio-inspired hydrofoils that oscillate near a ground plane or two out-of-phase foils in a side-by-side arrangement.
Scaling laws for the propulsive performance of rigid foils undergoing oscillatory heaving and pitching motions are presented. Water tunnel experiments on a nominally two-dimensional flow validate the scaling laws, with the scaled data for thrust, power, and efficiency all showing excellent collapse. The analysis indicates that the behaviour of the foils depends on both Strouhal number and reduced frequency, but for motions where the viscous drag is small the thrust closely follows a linear dependence on reduced frequency. The scaling laws are also shown to be consistent with biological data on…
Scaling laws for the thrust production and energetics of self-propelled or fixed-velocity three-dimensional rigid propulsors undergoing pitching motions are presented. The scaling relations extend the two-dimensional scaling laws presented in Moored & Quinn (2018) by accounting for the added mass of a finite-span propulsor, the downwash/upwash effects from the trailing vortex system of a propulsor, and the elliptical topology of shedding trailing-edge vortices. The novel three-dimensional scaling laws are validated with self-propelled inviscid simulations and fixed-velocity experiments over a …
In this paper, we numerically investigate the propulsive performance of three-dimensional pitching flexible plates with varying flexibility and trailing edge shapes. To eliminate the effect of other geometric parameters, only the trailing edge angle is varied from 45° (concave), 90° (rectangular) to 135° (convex) while maintaining the constant area of the flexible plate. We examine the impact of the frequency ratio f* defined as the ratio of the natural frequency of the flexible plate to the actuated pitching frequency. Through our numerical simulations, we find that the global maximum mean th…
We experimentally studied the effect of flexibility on the flow produced by sinusoidally pitching foil in quiescent fluid. The rigid foil produces a weak, divergent and meandering jet. On the contrary, the foil with a flexible flap produces an orderly, narrow, coherent jet. It has been observed that such orderly jet is produced when the flap has appropriate flexibility. The jet produced in quiescent fluid by the flexible foil is accompanied by a corresponding thrust. In that sense, this is simple and different type of hovering.
We consider the propulsive performance of an unsteady heaving and pitching foil, experimentally studying an extensive parameter space of motion amplitudes, frequencies, and phase offsets between the heave and pitch motions. The phase offset $ϕ$ between the heaving and pitching motions proves to be a critical parameter in determining the dynamics of the foil and its propulsive performance. To maximize thrust, the heave and pitch motions need to be nearly in phase ($ϕ=330^\circ$), but to maximize efficiency, the pitch motion needs to lag the heave motion ($ϕ=270^\circ$), corresponding to slicing…
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 effect of flexibility on the hydrodynamic loads and on the flow structures generated on a rectangular foil when oscillating in pitch has been studied. Hydrodynamic loads were measured with a 6-axes balance, and the flow structures were investigated by using a Digital Particle Image Velocimetry (DPIV). It is known from nature's fin based propulsion mechanisms, that appendage stiffness plays an important role in their propulsive efficiency. We have studied four different stiffnesses, ranging from completely rigid to highly flexible. Optimal efficiency has been observed for an intermediate ca…
A flexible foil undergoing pitching oscillations is studied experimentally in a wind tunnel with different imposed free stream velocities. The chord-based Reynolds number is in the range 1600--4000, such that the dynamics of the system is governed by inertial forces and the wake behind the foil exhibits the reverse Bénard-von Kármán vortex street characteristic of flapping-based propulsion. Particle Image Velocimetry (PIV) measurements are performed to examine the flow around the foil, whilst the deformation of the foil is also tracked. The first natural frequency of vibration of the foil is w…
A transient two-dimensional acoustic boundary element solver is coupled to a potential flow boundary element solver via Powell's acoustic analogy to determine the acoustic emission of isolated hydrofoils performing biologically-inspired motions. The flow-acoustic boundary element framework is validated against experimental and asymptotic solutions for the noise produced by canonical vortex-body interactions. The numerical framework then characterizes the noise production of an oscillating foil, which is a simple representation of a fish caudal fin. A rigid NACA 0012 hydrofoil is subjected to c…
The hydrodynamic influence of surface texture on static surfaces ranges from large drag penalties (roughness) to potential performance benefits (shark-like skin). Although, it is of wide-ranging research interest, the impact of roughness on flapping systems has received limited attention. In this work, we explore the effect of roughness on unsteady performance of a harmonically pitching foil through experiments using foils with different surface roughness, at a fixed Strouhal number and within the Reynolds number (Re) range of 15k-30k. The foils' surface roughness is altered by changing the di…
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 thisstudy with two modes representing an abrupt phase change by pi during the 20th cycle. The other two modes represented a simplified case of burst-and-coast swimmi…
This article reports on a full replication study in computational fluid dynamics, using an immersed boundary method to obtain the flow around a pitching and rolling elliptical wing. As in the original study, the computational experiments investigate the wake topology and aerodynamic forces, looking at the effect of: Reynolds number (100--400), Strouhal number (0.4--1.2), aspect ratio, and rolling/pitching phase difference. We also include a grid-independence study (from 5 to 72 million grid cells). The trends in aerodynamic performance and the characteristics of the wake topology were replicat…
Inviscid computations are presented of a self-propelled virtual body connected to a combined heaving and pitching foil that uses continuous and intermittent motions. It is determined that intermittent swimming can improve efficiency when the dimensionless heave ratio is $h^* < 0.7$ while it degrades efficiency for $h^* \geq 0.7$. This is a consequence of the physical origins of the force production for pitch-dominated ($h^* < 0.5$) and heave-dominated ($h^* > 0.5$) motions. Based on insight derived from classic unsteady thin airfoil theory, it is discovered that pitch-dominated motions are dri…
Biological locomotion, observed in the flexible wings of birds and insects, bodies and fins of aquatic mammals and fishes, consists of their ability to morph the wings/fins. The morphing capability holds significance in the abilities of fishes to swim upstream without spending too much energy and that of birds to glide for extended periods of time. Simplifying the wing or fins to a foil, morphing refers to the ability of the foil to change its camber smoothly, without sharp bends on the foil surface. This allows precise control over flow separation and vortex shedding. Compared to conventional…
In this study, we present two and three-dimensional numerical investigation to understand the combined effects of the non-dimensional heave amplitude varying from 0 to 1 and the pitch amplitude ranging from 0 to 30 on the propulsive performance for a single and tandem foil system at Reynolds number 1100 and reduced frequency 0.2. We initially present a systematic analysis on the thrust generation due to the kinematic parameters for a single foil. The significance of effective angle of attack and the projected area of the foil has been emphasized in explaining the dynamics of lift and drag forc…
Experiments are reported on the performance of a pitching and heaving two-dimensional foil in a water channel in either continuous or intermittent motion. We find that the thrust and power are independent of the mean freestream velocity for two-fold changes in the mean velocity (four-fold in the dynamic pressure), and for oscillations in the velocity up to 38\% of the mean, where the oscillations are intended to mimic those of freely swimming motions where the thrust varies during the flapping cycle. We demonstrate that the correct velocity scale is not the flow velocity but the mean velocity …
We investigate the role of linear mechanisms in the emergence of nonlinear horizontal self-propelled states of a heaving foil in a quiescent fluid. Two states are analyzed: a periodic state of unidirectional motion and a quasi-periodic state of slow back & forth motion around a mean horizontal position. The states emergence is explained through a fluid-solid Floquet stability analysis of the non-propulsive symmetric base solution. Unlike a purely-hydrodynamic analysis, our analysis accurately determine the locomotion states onset. An unstable synchronous mode is found when the unidirectional p…
The propulsive dynamics of a flexible undulating foil in a self-propelled swimming configuration near a wall is studied experimentally. Measurements of the swimming speed and the propulsive force are presented, together with image acquisition of the kinematics of the foil and particle image velocimetry (PIV) in its wake. The presence of the wall enhances the cruising velocity in some cases up to 25% and the thrust by a 45%, for swept angles of 160 and 240 degrees. The physical mechanisms underlying this effect are discussed by studying the vorticity dynamics in the wake of the foil. Proper Ort…
Bio-inspired oscillatory foil propulsion has the ability to traverse various propulsive modes by dynamically changing the foil's heave and pitch kinematics. This research characterizes the propulsion properties and wake dynamics of a symmetric oscillating foil, specifically targeting the high Reynolds number operation of small to medium surface vessels whose propulsive specifications have a broad range of loads and speeds. An unsteady Reynolds-averaged Navier-Stokes (URANS) solver with a k-$ω$ SST turbulence model is used to sweep through pitch amplitude and frequency at two heave amplitudes o…
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 Bénard-von Kármán 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…
Large-amplitude oscillations of foils have been observed to yield greater propulsive efficiency than small-amplitude oscillations. Using scaling relations and experiments on foils with peak-to-peak trailing edge amplitudes of up to two chord lengths, we explain why this is so. In the process, we reveal the importance of drag, specifically how it can significantly reduce the efficiency, and how this effect depends on amplitude. The scaling relations and experimental data also reveal a fundamental tradeoff between high thrust and high efficiency, where the drag also plays a crucial role.
We present new unconstrained simulations and constrained experiments of a pair of pitching hydrofoils in a leader-follower in-line arrangement. Free-swimming simulations of foils with $matched$ pitching amplitudes show self-organization into stable formations at a constant gap distance without any control. Leading-edge separation on the follower foil plays a crucial role in creating these formations by acting as an additional dynamic drag source on the follower, which depends on the gap spacing and phase synchronization. Over a wide range of phase synchronization, amplitude, and Lighthill numb…
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 $A$ and frequency $f$ because the transition also depends sensitively on other details of the kinematics. In this work we replace $A$ with the cycle-averaged swept trajectory $\mathcal{T}$ of the foil chord-line. Two dimensional simulations are performed for pure heave, pure pitch and a variety of heave-to-pitch coupling. In a phase space of dimensionless $\m…
The energy extraction and vortex dynamics from the sinusoidal heaving and pitching motion of an elliptical hydrofoil is explored through large-eddy simulations (LES) at a Reynolds number of $50,000$. The LES is able to capture the time-dependent vortex shedding and dynamic stall properties of the foil as it undergoes high relative angles of attack. Results of the computations are validated against experimental flume data in terms of power extraction and leading edge vortex (LEV) position and trajectory. The kinematics for optimal efficiency are found in the range of heave amplitude $h_o/c=0.5-…
