Different routes to optimal flapping in unsteady conditions

Fish can significantly improve their swimming performance if their kinematics and paths are adequately adapted to the incoming flow. When the optimum path is unknown, the first step is to accurately predict the performance that could be obtained for several route candidates. Next, we can select the trajectory that increases the thrust or efficiency. In this study, we develop a sparse database of cases where a flapping foil executes transition motions inside an unsteady incoming flow. The delay component with respect to the upstream wake governs the course of the foil. Next, we use a Koopman operator-based approach to obtain several predictive models to estimate the performance of the foil for a given candidate path. We found that the predictive error is reduced to less than 20% for all test cases only after incorporating a wake model that calculates the relative location between the foil and the incoming upstream vortices. The wake model-based predictive tool will be used to develop a new transition approach to position the foil on the optimum route to maximise its performance.