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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. 

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. 

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.