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 memory (LSTM) units is developed to classify the wakes into three groups. To fully verify the physical wake differences among foil kinematics, a convolutional autoencoder combined with k-means++ clustering is utilized and four different wake patterns are found. With the classification model, these patterns are associated with a range of foil kinematics. Future work can use these correlations to predict the performance of foils placed in the wake and build optimal foil arrangements for tidal energy harvesting.
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 a…
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…
Investigation of Submergence Depth and Wave-Induced Effects on the Performance of a Fully Passive Energy Harvesting Flapping Foil Operating Beneath the Free Surface
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…
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…
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…
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 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-…
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 …
The development of energy harvesting systems based on fluid/structure interactions is part of the global search for innovative tools to produce renewable energy. In this paper, the possibility to harvest energy from a flow using vortex-induced vibrations (VIV) of a tensioned flexible cable is analyzed. The fluid loading on the vibrating solid and resulting dynamics are computed using an appropriate wake-oscillator model, allowing one to perform a systematic parametric study of the efficiency. The generic case of an elastically-mounted rigid cylinder is first investigated, before considering an…
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 vortex street that characterizes fish-like swimming and forward flapping flight are examined. Two-dimensional particle image velocimetry measurements in the mid-plane 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 velocit…
In this work a fully passive energy harvesting foil is studied computationally. An in-house 2nd order finite volume CFD solver, MaPFlow, is strongly coupled with a rigid body dynamics solver to investigate the foil operation under uniform and sheared inflow conditions with/without free surface. The mesh follows the airfoil motion using a radial basis function (RBF) mesh deformation approach. Initially, MaPFlow predictions are compared to experimental and numerical results available in the literature, where reasonable agreement is found. Next, one-phase simulations are considered for linearly s…
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…
Co-locating horizontal- and vertical-axis wind turbines has been recently proposed as a possible approach to enhance the land-area power density of wind farms. In this work, we aim to study the benefits associated with such a co-location using large-eddy simulation (LES) and analytical wake models. In this regard, small-scale vertical-axis wind turbines (VAWTs) in triangular clusters are deployed within a finite-size wind farm consisting of horizontal-axis wind turbines (HAWTs). Wake flow within the wind farm and the effect of VAWTs on the overall wind-farm efficiency are investigated and quan…
Vortex-induced vibrations (VIV) of flexible cables are an example of flow-induced vibrations that can act as energy harvesting systems by converting energy associated with the spontaneous cable motion into electricity. This work investigates the optimal positioning of the harvesting devices along the cable, using numerical simulations with a wake oscillator model to describe the unsteady flow forcing. Using classical gradient-based optimization, the optimal harvesting strategy is determined for the generic configuration of a flexible cable fixed at both ends, including the effect of flow force…
Many technologies based on fluid-structure interaction mechanisms are being developed to harvest energy from geophysical flows. The velocity of such flows is low, and so is their energy density. Large systems are therefore required to extract a significant amount of energy. The question of the efficiency of energy harvesting using vortex-induced vibrations (VIV) of cables is addressed in this paper, through two reference configurations: (i) a long tensioned cable with periodically-distributed harvesters and (ii) a hanging cable with a single harvester at its upper extremity. After validation a…
The emergence and understanding of new design paradigms that exploit flow induced mechanical instabilities for propulsion or energy harvesting demands robust and accurate flow structure interaction numerical models. In this context, we develop a novel two dimensional algorithm that combines a Vortex Particle-Mesh (VPM) method and a Multi-Body System (MBS) solver for the simulation of passive and actuated structures in fluids. The hydrodynamic forces and torques are recovered through an innovative approach which crucially complements and extends the projection and penalization approach of Coque…
Marine hydrokinetic (MHK) power generation systems enable harvesting energy from waterways without the need for water impoundment. A major research challenge for numerical simulations of field-scale MHK farms stems from the large disparity in scales between the size of waterway and the energy harvesting device. We propose a large-eddy simulation (LES) framework to perform high-fidelity, multi-resolution simulations of MHK arrays in a real-life marine environment using a novel unstructured Cartesian flow solver coupled with a sharp-interface immersed boundary method. The potential of the method…
Betz's law, purportedly, says an ideal wind harvester cannot extract more than 16/27 ($\sim$59\%) of the wind energy. As the law's derivation relies on momentum and energy conservation with incompressible flow and not the physical mechanism coupling the wind-field to the extraction of work it is ubiquitously regarded as a "universal" upper bound on efficiency, as inclusion of mechanics, aerodynamics and thermodynamics are presumed to worsen this upper bound. Here we show that when unneeded assumptions in the Betz's law derivation are relaxed a higher bound of 2/3 ($\sim$67\%) can be achieved. …
