Deep-Learning-Based Reduced-Order Model for Power Generation Capacity of Flapping Foils

Inspired by nature, oscillating foils offer viable options as alternate energy resources to harness energy from wind and water. Here, we propose a proper orthogonal decomposition (POD)-based reduced-order model (ROM) of power generation by flapping airfoils in conjunction with deep neural networks. Numerical simulations are performed for incompressible flow past a flapping NACA-0012 airfoil at a Reynolds number of 1100 using the Arbitrary Lagrangian-Eulerian approach. The snapshots of the pressure field around the flapping foil are then utilized to construct the pressure POD modes of each case, which serve as the reduced basis to span the solution space. The novelty of the current research relates to the identification, development, and employment of long-short-term neural network (LSTM) models to predict temporal coefficients of the pressure modes. These coefficients, in turn, are used to reconstruct hydrodynamic forces and moment, leading to computations of power. The proposed model takes the known temporal coefficients as inputs and predicts the future temporal coefficients followed by previously estimated temporal coefficients, very similar to traditional ROM. Through the new trained model, we can predict the temporal coefficients for a long time duration that can be far beyond the training time intervals more accurately. It may not be attained by traditional ROMs that lead to erroneous results. Consequently, the flow physics including the forces and moment exerted by fluids can be reconstructed accurately using POD modes as the basis set.