Oscillating foils in synchronized pitch/heave motions can be used to harvest hydrokinetic energy. By understanding the wake structure and its correlation with the foil kinematics, predictive models for how foils can operate in array configurations can be developed. To establish a relationship between foil kinematics and wake characteristics, a wide range of kinematics is explored in a two-foil tandem configuration with interfoil spacing from four to nine chord lengths separation and multiple interfoil phases. Using data from experiments and simulations, an in-depth wake analysis is performed and the mean velocity and the turbulent kinetic energy are quantified in the wake. With this energy quantification, the trailing foil efficiency is modified to account for the mean flow in addition to the energy transported by the coherent leading edge vortices (LEVs) shed from the leading foil. With the mean wake velocity, a predictive wake model is able to distinguish three regimes through analyzing trailing foil efficiency profiles and the strength of the primary LEV shed from the leading foil. Dividing the wake into regimes is an insightful way to narrow the range of foil kinematics and configurations and improve the energy harvesting in a two-tandem foil array.
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 m…
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 …
A machine learning model is developed to establish wake patterns behind oscillating foils whose kinematics are within the energy harvesting regime. The role of wake structure is particularly important for array deployments of oscillating foils, since the unsteady wake highly influences performance of downstream foils. This work explores 46 oscillating foil kinematics, with the goal of parameterizing the wake based on the input kinematic variables and grouping vortex wakes through image analysis of vorticity fields. A combination of a convolutional neural network (CNN) with long short-term memo…
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…
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…
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…
We study experimentally the vortex streets produced by a flapping foil in a hydrodynamic tunnel, using 2D Particle Image Velocimetry (PIV). An analysis in terms of a flapping frequency-amplitude phase space allows to identify: 1) the transition from the well-known Bénard-von Kármán (BvK) wake to the reverse BvK vortex street that characterizes propulsive wakes, and 2) 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 significanc…
The fluid dynamics video illustrates the interaction of two disks falling in tandem at Reynolds number close to 100. Two fluorescent dyes were used to visualize the wake of each body. We can observe that the trailing body accelerates thanks to the entrainment provided by the wake of the leading body and eventually catches up the leadind body. Then, thick disks (diameter/thickness = 3) lose their initial wakes, separate laterally and fall side by side. On the contrary, the wakes of thinner disks (d/t = 10) merge in a single wake and the bodies continue their fall together adopting a stable Y-co…
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…
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…
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…
Machine learning techniques have received attention in fluid dynamics in terms of predicting, clustering and classifying complex flow physics. One application has been the classification or clustering of various wake structures that emanate from bluff bodies such as cylinders or flapping foils, creating a rich diversity of vortex formations specific to flow conditions, geometry, and/or kinematics of the body. When utilizing oscillating foils to harvest energy from tidal or river flows, it is critical to understand the intricate and nonlinear relationship between flapping kinematics and the dow…
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…
The two dimensional incompressible viscous flow past a flapping foil immersed in a uniform stream is studied numerically. Numerical simulations were performed using a Lattice-Boltzmann model for moderate Reynolds numbers. The computation of the hydrodynamic force on the foil is related to the the wake structure. In particular, when the foil's centre of mass is fixed in space, numerical results suggest a relation between drag coefficient behaviour and the flapping frequency which determines the transition from the von Kármán (vKm) to the inverted von Kármán wake. Beyond the inverted vKm transit…
Yaw control has proven to be promising in alleviating the wake effects that plague the efficiency of wind farms. In this work, the actuator line modeling (ALM) method is adopted to simulate the flows over two tandem turbines distanced by $3 - 7$ rotor diameters, with the yaw angle of the upstream rotor varying from $γ_1=0^{\circ}$ to $50^{\circ}$. The aim is to provide a comprehensive aerodynamic characterization of a simple wind farm under yaw misalignment. With increasing yaw angle, the power generated by the downstream rotor increases, compensating the power loss in the upstream rotor, and …
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…
An unsupervised machine learning strategy is developed to automatically cluster the vortex wakes of bio-inspired propulsors into groups of similar propulsive thrust and efficiency metrics. A pitching and heaving foil is simulated via computational fluid dynamics with $121$ unique kinematics by varying the frequency, heaving amplitude, and pitching amplitude. A Reynolds averaged Navier-Stokes (RANS) model is employed to simulate the flow over the oscillating foils at $Re=10^6$, computing the propulsive efficiency, thrust coefficient and the unsteady vorticity wake signature. Using a pairwise Pe…
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 show how phasing between tandem bioinspired fins flapping at high-stroke amplitudes modulates rear fin thrust production and wake characteristics. Load cell thrust measurements show that the rear fin generates 25% more thrust than the front fin when it lags the latter by a quarter cycle, and performs 8% worse when it leads the front fin by the same amount. The flow interactions between the fins responsible for these observations are analyzed using two-dimensional particle image velocimetry measurements and three-dimensional computational fluid dynamics simulations. Distributions of velocity…
The move to high performance applications greatly increases the demand to produce large instantaneous fluid forces for high-speed maneuvering and improved power efficiency for sustained propulsion. Animals achieve remarkable feats of maneuvering and efficiency by changing their body shape to generate unsteady fluid forces. Inspired by this, we have studied a range of immersed bodies which drastically change their shape to produce fluid forces. These include relatively simple shape- changes, such as quickly changing the angle of attack of a foil to induce emergency stops and the use of tandem f…
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 strength and trajectory of a leading edge vortex (LEV) formed by a pitching-heaving hydrofoil (chord $c$) is studied. The LEV is identified using the $Q$-criterion method, which is calculated from the 2D velocity field obtained from PIV measurements. The relative angle of attack at mid-stroke, ${α_{T/4}} $, proves to be an effective method of combining heave amplitude ($h_0/c$), pitch amplitude ($θ_0$), and reduced frequency ($f^*$) into a single variable that predicts the maximum value of $Q$ over a wide range of operating conditions. Once the LEV separates from the foil, it travels downs…
Fish schools are ubiquitous in marine life. Although flow interactions are thought to be beneficial for schooling, their exact effects on the speed, energetics, and stability of the group remain elusive. Recent experiments suggest that flow interactions stabilize in-tandem formations of heaving foils. Here, we propose a minimal approach based on the vortex sheet model that captures salient features of the flow interactions among flapping swimmers, and we study the free swimming of a pair of in-line swimmers driven with identical heaving or pitching motions. We find that, independent of the fla…
The buoyancy-driven dynamics of a pair of gas bubbles released in line is investigated numerically, focusing on highly inertial conditions under which isolated bubbles follow non-straight paths. In an early stage, the second bubble always drifts out of the wake of the leading one. Then, depending on the ratios of the buoyancy, viscous and capillary forces which define the Galilei ($Ga$) and Bond ($Bo$) numbers of the system, five distinct regimes specific to such conditions are identified, in which the two bubbles may rise independently or continue to interact and possibly collide in the end. …
