Modeling inline oscillating foils using periodic conformal mapping

Inline oscillating foils can obtain hydrodynamic benefits by adequately maintaining their spacing and interacting with the oncoming wakes. Since the complexity increases with the group size, this work explores the hydrodynamic performance of in-phase oscillating foils with inline configuration using periodic conformal mapping. An array of infinite foils in the physical domain is mapped from a circle in the complex circular domain with a branch cut designed for the periodic boundary condition. The flow field is described by complex potential functions that satisfy the corresponding boundary conditions. The wake generated by each foil is represented as point vortices shed from the trailing edge of the foil. The thrust coefficient, power coefficient, and propulsive efficiency of the foils with various sway amplitudes, maximum angles of attack, Strouhal numbers, and along-stream separation distances are compared in simulations. Based on the results, the velocity agreement between the foil motion and the oncoming vortex-induced flow affects the thrust production and power consumption of the foils. The foils obtain efficiency enhancement when the separation distance between each foil is close to an integer multiple of wavelength. The results can help explore the flow interactions between inline oscillating foils and may be beneficial to forming schooling control strategies.