Deep learning-based prediction of Reynolds-averaged Navier-Stokes solutions for vertical-axis turbines

Abstract

The optimization of turbine array layouts for maximized power generation is an important and challenging problem in the fields of wind and hydrokinetic energy. Since multi-turbine simulations with resolved rotor geometries are beyond the capacity of modern computers, turbine arrays are generally modelled by replacing each rotor with a permeable, zero-thickness momentum sink, known as an actuator. Although actuator models are computationally inexpensive, they do not easily replicate the wake structures observed in experiments and foil-resolved simulations. With the aim of developing an alternative approach for modelling turbine interactions, the following study explores the potential of a deep learning-based turbine modelling technique. In the proposed method, a Convolutional Neural Network (CNN) is trained to predict the solutions of a foil resolved, two-dimensional (2-D) Reynolds-Averaged Navier-Stokes (RANS) model, for a vertical-axis hydrokinetic turbine operating in free-stream velocities between 1 and 3 m/s. Based on the boundary conditions of free-stream velocity and rotor position, the flow gradients of x-velocity, y-velocity, pressure, and turbulent viscosity are predicted, in addition to the angular velocity of the rotor. Training and testing data are generated from the solutions of five RANS simulations, with free stream velocities of 1, 1.5, 2, 2.5 and 3 m/s. Three trained CNN models are produced to evaluate the effects of (1) the dimensions of the training data, and (2) the number of simulations that are used as training cases. Smaller data sizes were found to improve prediction accuracy overall, while diminishing the computational cost associated with the generation of data from RANS solutions. Dramatic improvements in prediction accuracy were achieved by increasing the number of training cases from two to three. For the best achieved CNN model, the variables of x-velocity, y-velocity, pressure, turbulent viscosity, and angular velocity were predicted with mean relative errors of 5.97%, 8.98%, 12.68%, 7.37%, and 0.88%, respectively.