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This research investigates the wake–foil interactions between two oscillating foils in a tandem configuration undergoing energy harvesting kinematics. Oscillating foils have been shown to extract hydrokinetic energy from free-stream flows through a combination of periodic heave and pitch motions, at relatively higher amplitudes and lower reduced frequency than thrust generating foils. When placed in tandem, the wake–foil interactions can govern the energy harvesting efficiency of the system due to a reduced relative flow velocity in combination with a structured and coherent wake of vortices shed from the high amplitude flapping of upstream foils. This work utilizes simulations of two tandem foils to parameterize and model the energy harvesting performance as a function of array configuration and foil kinematics. Once the wake of the leading foil has been fully parameterized, the placement, phase angle and kinematic stroke of the second foil is utilized to estimate the time-dependent power curve. The algorithm predicts the power of the second foil through the mean and unsteady wake characteristics, including the direct impingement of a vortex with the trailing foil. 

Abstract The spanwise undulated cylinder geometry inspired by seal whiskers has been shown to alter shedding frequency and reduce fluid forces significantly compared to smooth cylindrical geometry. Prior research has parameterized the whisker-inspired geometry and demonstrated the relevance of geometric variations on force reduction properties. Among the geometric parameters, undulation wavelength was identified as a significant contributor to forcing changes. To analyze the effect of undulation wavelength, a thorough investigation isolating changes in wavelength is performed to expand upon previous research that parameterized whisker-inspired geometry and the relevance of geometric variations on the force reduction properties. A set of five whisker-inspired models of varying wavelength are computationally simulated at a Reynolds number of 250 and compared with an equivalent aspect ratio smooth elliptical cylinder. Above a critical non-dimensional value, the undulation wavelength reduces the amplitude and frequency of vortex shedding accompanied by a reduction in oscillating lift force. Frequency shedding is tied to the creation of wavelength-dependent vortex structures which vary across the whisker span. These vortices produce distinct shedding modes in which the frequency and phase of downstream structures interact to decrease the oscillating lift forces on the whisker model with particular effectiveness around the wavelength values typically found in nature. The culmination of these location-based modes produces a complex and spanwise-dependent lift frequency spectra at those wavelengths exhibiting maximum force reduction. Understanding the mechanisms of unsteady force reduction and the relationship between undulation wavelength and frequency spectra is critical for the application of this geometry to vibration tuning and passive flow control for vortex-induced vibration (VIV) reduction. 

Pinniped vibrissae possess a unique and complex three-dimensional topography, which has beneficial fluid flow characteristics such as substantial reductions in drag, lift, and vortex induced vibration. To understand and leverage these effects, the downstream vortex dynamics must be studied. Dye visualization is a traditional qualitative method of capturing these downstream effects, specifically in comparative biological investigations where complex equipment can be prohibitive. High-fidelity numerical simulations or experimental particle image velocimetry are commonplace for quantitative high-resolution flow measurements, but are computationally expensive, require costly equipment, and can have limited measurement windows. This study establishes a method for extracting quantitative data from standard dye visualization experiments on seal whisker geometries by leveraging novel but intuitive computer vision techniques, which maintain simplicity and an advantageous large experimental viewing window while automating the extraction of vortex frequency, position, and advection. Results are compared to direct numerical simulation (DNS) data for comparable geometries. Power spectra and Strouhal numbers show consistent behavior between methods for a Reynolds number of 500, with minima at the canonical geometry wavelength of 3.43 and a peak frequency of 0.2 for a Reynolds number of 250. The vortex tracking reveals a clear increase in velocity from roll-up to 3.5 whisker diameters downstream, with a strong overlap with the DNS data but shows steady results beyond the limited DNS window. This investigation provides insight into a valuable bio-inspired engineering model while advancing an analytical methodology that can readily be applied to a broad range of comparative biological studies. 

A machine learning model is developed to establish wake patterns behind oscillating foils for energy harvesting. The role of the wake structure is particularly important for array deployments of oscillating foils since the unsteady wake highly influences the 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 with long short-term memory units is developed to classify the wakes into three classes. To fully verify the physical wake differences among foil kinematics, a convolutional autoencoder combined with [Formula: see text]-means++ clustering is used to reveal four wake patterns via an unsupervised method. Future work can use these patterns to predict the performance of foils placed in the wake and build optimal foil arrangements for tidal energy harvesting. 

This work investigates the response of forces from fluid flow around seal whisker inspired cylinder geometry at swept back angles. The unique, undulated surface of seal whiskers has been shown to reduce drag and oscillating lift in comparison to smooth cylinders of equivalent dimensions. As seals swim through the water, their whisker orientation with respect to the freestream is constantly changing due to body position, but also the ability to manipulate the position of their whiskers while sensing. Though the effects of orientation and geometry parameters such as varied angle of attack, changes to undulation wavelength, amplitude, and aspect ratio have been investigated in previous literature, there is little research dedicated to characterizing the response of undulated cylinder geometry at sweep angles. In this paper, direct numerical simulation of incompressible flow over a highly resolved whisker surface is used to simulate flow structures and forces over whisker-inspired cylinders at a range of sweep angles from 0 to 60 degrees. It is observed that the decrease in forces in comparison to circular cylinders is still present at all swept angles tested. Root-mean-squared lift coefficient displays a 51.9 to 93.8% reduction, whereas drag displays a 12.9 to 39.1% reduction. When compared to forces on a streamlined elliptical cylinder, sweep angles of 0 to 30 degrees result in a force reduction advantage for the undulated cylinder geometry. Beyond this range at sweep angles of 45 and 60, drag and lift coefficients closely mirror those of the streamlined ellipse and undulated geometry offers no improvement. 

Oscillating foil turbines can be utilized to extract hydrokinetic energy from tidal or river flows. When foils are placed in arrays, the reduced velocity between foils and the unsteady disturbances associated with the leading foil motion both affect the performance of downstream foils. To compare the performance between foils, a wide range of kinematics is numerically explored in a two-foil tandem configuration with matching strokes, but varying the inter-foil phase angle and spacing. The effects of the wake on the trailing foil performance are quantified by evaluating the difference between the normalized power extracted by each foil. The difference in normalized power extraction is a function of the wake phase parameter, Φ, and ranges from -65% to +6%, depending on the kinematic regime. It is also determined that the difference in normalized power is dominated by the pressure contribution from the heave stroke, whereas the viscous components are negligible. In general, these differences illustrate the unsteady effects within the wake of the first foil, and the various interaction modes of the downstream foil. These trends can be used to estimate power in other array configurations and provide a more robust model for wake-foil interactions for energy harvesting. 

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 blu˙ 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 downstream vortex wake structure for optimal siting and operation of arrays. This paper develops a classification model to obtain groups of kinematics that contain similar wake patterns within the energy harvesting regime. Data is obtained through simulations of 27 unique oscillating foil kinematics for a total of 13,650 samples of the wake vorticity field. Within these samples three groups are visually labeled based on the relative angle of attack. A machine learning approach combining a convolutional neural network (CNN) with long short-term memory (LSTM) units is utilized to automatically classify the wakes into the three groups. The average accuracy on five test data subsets is 80% when the three visually labeled groups are used for classification. After analyzing the test subset with lowest accuracy, an update on the group division boundaries is proposed. With this update, the algorithm achieves an average accuracy of 90%, demonstrating that the three groups are able to discern distinct wake structures within a range of energy harvesting kinematics.