A Physics- and Data-Driven Study on the Ground Effect on the Propulsive Performance of Tandem Flapping Wings

In this paper, we present a physics- and data-driven study on the ground effect on the propulsive performance of tandem flapping wings. With numerical simulations, the impact of the ground effect on the aerodynamic force, energy consumption, and efficiency is analyzed, revealing a unique coupling effect between the ground effect and the wing–wing interference. It is found that, for smaller phase differences between the front and rear wings, the thrust is higher, and the boosting effect due to the ground on the rear wing (maximum of 12.33%) is lower than that on a single wing (maximum of 43.83%) For a larger phase difference, a lower thrust is observed, and it is also found that the boosting effect on the rear wing is above that on a single wing. Further, based on the bidirectional gate recurrent units (BiGRUs) time-series neural network, a surrogate model is further developed to predict the unsteady aerodynamic characteristics of tandem flapping wings under the ground effect. The surrogate model exhibits high predictive precision for aerodynamic forces, energy consumption, and efficiency. On the test set, the relative errors of the time-averaged values range from −4% to 2%, while the root mean squared error of the transient values is less than 0.1. Meanwhile, it should be pointed out that the established surrogate model also demonstrates strong generalization capability. The findings contribute to a comprehensive understanding of the ground effect mechanism and provide valuable insights for the aerodynamic design of tandem flapping-wing air vehicles operating near the ground.